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BEGIN:VEVENT
SUMMARY:Andras Vasy (Stanford University)
DTSTART:20200521T160000Z
DTEND:20200521T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/1
DESCRIPTION:Title:
The inverse problem for the X-ray transform\nby Andras Vasy (Stanford
University) as part of International Zoom Inverse Problems Seminar\, UC Ir
vine\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Inverse/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shari Moskow (Drexel University)
DTSTART:20200528T160000Z
DTEND:20200528T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/2
DESCRIPTION:Title:
Reduced order models for spectral domain inversion: embedding into the con
tinuous problem and generation of internal data\nby Shari Moskow (Drex
el University) as part of International Zoom Inverse Problems Seminar\, UC
Irvine\n\n\nAbstract\nWe generate data-driven reduced order models (ROMs)
for inversion of the\none and two dimensional Schrodinger equation in th
e spectral domain given boundary data\nat a few frequencies. The ROM is th
e Galerkin projection of the Schrodinger operator onto\nthe space spanned
by solutions at these sample frequencies. The ROM matrix is in general\nf
ull\, and not good for extracting the potential. However\, using an orthog
onal change of\nbasis via Lanczos iteration\, we can transform the ROM to
a block triadiagonal form from\nwhich it is easier to extract q. In one di
mension\, the tridiagonal matrix corresponds to\na three-point staggered f
inite difference system for the Schrodinger operator discretized\non a so
-called spectrally matched grid which is almost independent of the medium.
In\nhigher dimensions\, the orthogonalized basis functions play the role
of the grid steps. The\northogonalized basis functions are localized and a
lso depend only very weakly on the\nmedium\, and thus by embedding into th
e continuous problem\, the reduced order model\nyields highly accurate int
ernal solutions. That is to say\, we can obtain\, just from boundary\ndata
\, very good approximations of the solution of the Schrodinger equation i
n the whole\ndomain for a spectral interval that includes the sample frequ
encies. We present inversion\nexperiments based on the internal solutions
in one and two dimensions.\n\n*joint with L. BORCEA\, V. DRUSKIN\, A. MAMO
NOV\, M. ZASLAVSKY\n
LOCATION:https://researchseminars.org/talk/Inverse/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Plamen Stefanov (Purdue University)
DTSTART:20200604T160000Z
DTEND:20200604T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/3
DESCRIPTION:Title:
Noise in linear inverse problems\nby Plamen Stefanov (Purdue Universit
y) as part of International Zoom Inverse Problems Seminar\, UC Irvine\n\n\
nAbstract\nWe study how noise in the data affects the noise in the reconst
ruction\, for linear inverse problems\, more precisely when the operator w
e have to invert is a Fourier Integral Operator. We apply the results to t
he Radon transform in the plane in parallel and in fan-bean coordinates. I
n this talk\, we concentrate on additive noise\, assuming that it is white
but the methods apply to non-white noise as well. We propose the microlo
cal defect measure as a measure of the spectral power of the noise in the
phase space. We show that one can compute the spectral power of the noise
in the reconstruction\, including its standard deviation\, as a function o
f the known statistical characteristics of the input noise. For the Radon
transform in parallel geometry\, we show that the induced noise is positio
n independent\, isotropic\, and “blue”. In fan-bean coordinates\, the
noise varies with position and it is not isotropic anymore but still “bl
ue”. This dependence is weak however and the standard deviation which we
compute\, still gives a good characterization of the strength of the indu
ced noise.\n \nThis is a joint project\, still in progress\, with Samy Tin
del\, Purdue.\n
LOCATION:https://researchseminars.org/talk/Inverse/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabriel Paternain (University of Cambridge)
DTSTART:20200611T160000Z
DTEND:20200611T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/4
DESCRIPTION:Title:
The non-Abelian X-ray transform\nby Gabriel Paternain (University of C
ambridge) as part of International Zoom Inverse Problems Seminar\, UC Irvi
ne\n\n\nAbstract\nI will discuss the problem of how to reconstruct a matri
x-valued potential from the knowledge of its scattering data along geodesi
cs on a compact non-trapping Riemannian manifold with boundary.\n\n\nThe p
roblem arises in new experiments designed to measure magnetic fields insid
e materials by shooting them with neutron beams from different directions\
, like in a CT scan.\n\n\nTowards the end of the lecture I will focus on t
he recent solutionof the injectivity question on simple surfaces for any m
atrix Lie group.\n
LOCATION:https://researchseminars.org/talk/Inverse/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Habib Ammari (ETH Zürich)
DTSTART:20200702T160000Z
DTEND:20200702T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/5
DESCRIPTION:Title:
Wave Interaction with Subwavelength Resonators\nby Habib Ammari (ETH Z
ürich) as part of International Zoom Inverse Problems Seminar\, UC Irvine
\n\n\nAbstract\nIn this lecture\, the speaker reviews recent results on su
bwavelength resonances. His main focus is on developing a mathematical and
computational framework for their analysis. By characterizing and exploit
ing subwavelength resonances in a variety of situations\, he proposes a ma
thematical explanation for super-focusing of waves\, double-negative metam
aterials\, Dirac singularities in honeycomb subwavelength structures\, and
topologically protected defect modes at the subwavelength scale. He also
describes a new resonance approach for modelling the cochlea which predict
s the existence of a travelling wave in the acoustic pressure in the cochl
ea fluid and offers a basis for the tonotopic map.\n
LOCATION:https://researchseminars.org/talk/Inverse/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hiroshi Isozaki (University of Tsukuba)
DTSTART:20200723T160000Z
DTEND:20200723T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/6
DESCRIPTION:Title:
Inverse scattering on non-compact manifolds with general metric\nby Hi
roshi Isozaki (University of Tsukuba) as part of International Zoom Invers
e Problems Seminar\, UC Irvine\n\n\nAbstract\nWe consider a class of non-c
ompact Riemannian manifolds\, as large as possible\, whose Laplacian has a
continuous spectrum\, and show that the associated scattering matrix dete
rmines the manifold\, its topology and Riemannian metric. Knowledge of one
end is sufficient to determine the whole manifold. If the end is a cusp\,
by introducing a generalized S-matrix\, one can derive the same conclusio
n. We can also allow conic singularities for our manifolds so that they in
clude Riemannian orbifolds. As for the volume growth of each end\, it can
be polynomially or exponentially increasing or decreasing. So\, it is a na
tural largest class of manifolds on which we can develop the spectral and
scattering theory. This is a joint work with Matti Lassas (and Yaroslav Ku
rylev).\n
LOCATION:https://researchseminars.org/talk/Inverse/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Colin Guillarmou (Université Paris-Sud)
DTSTART:20200625T160000Z
DTEND:20200625T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/7
DESCRIPTION:Title:
Asymptotically Euclidean metrics without conjugate points on R^n are flat<
/a>\nby Colin Guillarmou (Université Paris-Sud) as part of International
Zoom Inverse Problems Seminar\, UC Irvine\n\n\nAbstract\nWe show that Riem
annian metrics on R^n that are asymptotic to the Euclidean metrics to orde
r O(1/|x|^3) and that have no conjugate points must be isometric to the fl
at metric. This is joint work with M. Mazzucchelli and L. Tzou.\n
LOCATION:https://researchseminars.org/talk/Inverse/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergio Vessella (University of Florence)
DTSTART:20200730T160000Z
DTEND:20200730T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/8
DESCRIPTION:by Sergio Vessella (University of Florence) as part of Interna
tional Zoom Inverse Problems Seminar\, UC Irvine\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Inverse/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Schotland (University of Michigan)
DTSTART:20200813T160000Z
DTEND:20200813T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/9
DESCRIPTION:by John Schotland (University of Michigan) as part of Internat
ional Zoom Inverse Problems Seminar\, UC Irvine\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Inverse/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Josselin Garnier (Ecole Polytechnique)
DTSTART:20200618T160000Z
DTEND:20200618T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/10
DESCRIPTION:Title: Wave Propagation and Imaging in Random Media: From Gaussian to non-Gaussi
an statistics\nby Josselin Garnier (Ecole Polytechnique) as part of In
ternational Zoom Inverse Problems Seminar\, UC Irvine\n\n\nAbstract\nWe co
nsider wave propagation and imaging in random media with the aim to descri
be the wave statistics and to discuss correlation-based imaging. When scat
tering is strong enough the coherent (mean) wave vanishes and the second-o
rder moments of the wave field (more exactly\, the statistical Wigner tran
sform) satisfies a radiative transfer equation. Under such circumstances t
he wave correlations or Wigner transform should be used for correlation-ba
sed imaging. In this talk we discuss the statistical stability of the empi
rical Wigner transform. We discuss two regimes with different behaviors. I
n the random paraxial regime the fluctuations of the smoothed Wigner trans
form are small and correlation-based imaging is possible. In randomly pert
urbed open waveguides the fluctuations of the mode powers and wave intensi
ties grow exponentially and correlation-based imaging is challenging.\n
LOCATION:https://researchseminars.org/talk/Inverse/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maarten de Hoop (Rice University)
DTSTART:20200709T160000Z
DTEND:20200709T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/11
DESCRIPTION:Title: Globally injective deep neural networks\nby Maarten de Hoop (Rice Uni
versity) as part of International Zoom Inverse Problems Seminar\, UC Irvin
e\n\n\nAbstract\nWe present an analysis of injective\, ReLU\, deep neural
networks. We establish sharp conditions for injectivity of ReLU layers and
networks\, both fully connected and convolutional. We show through a laye
r-wise analysis that an expansivity factor of two is necessary for injecti
vity\; we also show sufficiency by constructing weight matrices which guar
antee injectivity. Further\, we show that global injectivity with iid Gaus
sian matrices\, a commonly used tractable model\, requires considerably la
rger expansivity. We then derive the inverse Lipschitz constant and study
the approximation-theoretic properties of injective neural networks. Using
arguments from differential topology we prove that\, under mild technical
conditions\, any Lipschitz map can be approximated by an injective neural
network. This justifies the use of injective neural networks in problems
which a priori do not require injectivity.\n\nJoint work with M. Puthawala
\, K. Kothari\, M. Lassas and I. Dokmani\\'{c}.\n
LOCATION:https://researchseminars.org/talk/Inverse/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Niky Kamran (McGill University)
DTSTART:20200716T160000Z
DTEND:20200716T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/12
DESCRIPTION:Title: Non-uniqueness results for the anisotropic Calder\\’on problem at fixed
energy.\nby Niky Kamran (McGill University) as part of International
Zoom Inverse Problems Seminar\, UC Irvine\n\n\nAbstract\nIn its geometric
formulation\, the anisotropic Calder\\’on problem consists in recovering
up to some natural gauge equivalences the metric of a Riemannian manifold
with boundary from the knowledge of the Dirichlet-to-Neumann map. I will
survey some recent non-uniqueness results obtained in collaboration with T
hierry Daud\\’e (Cergy-Pontoise) and Francois Nicoleau (Nantes) for the
anisotropic Calder\\’on problem at fixed energy\, in the case of disjoin
t or partial data. The underlying manifolds arising in these examples are
diffeomorphic to toric cylinders with two connected boundary components. I
n the case of disjoint data the metric is a suitably chosen warped product
metric which is everywhere smooth. For partial data\, the metric\, which
is adapted from Miller’s example of an elliptic operator which fails to
satisfy the unique continuation principle\, is smooth in the interior of t
he manifold\, but only H\\”older continuous on one connected component o
f the boundary.\n
LOCATION:https://researchseminars.org/talk/Inverse/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Liliana Borcea (University of Michigan)
DTSTART:20200820T160000Z
DTEND:20200820T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/13
DESCRIPTION:Title: Reduced order modeling for inverse problems\nby Liliana Borcea (Unive
rsity of Michigan) as part of International Zoom Inverse Problems Seminar\
, UC Irvine\n\n\nAbstract\nI will discuss two approaches for building redu
ced order models for solving inverse problems. One is for finding reflecto
rs in a medium using an array of sensors that probes the medium with pulse
s and measures the resulting waves. The other is for an inverse problem fo
r parabolic (heat) equations.\n
LOCATION:https://researchseminars.org/talk/Inverse/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:François Monard (UC Santa Cruz)
DTSTART:20200806T160000Z
DTEND:20200806T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/14
DESCRIPTION:Title: Abelian and Non-Abelian X-ray transforms. Sharp mapping properties and Ba
yesian inversion\nby François Monard (UC Santa Cruz) as part of Inter
national Zoom Inverse Problems Seminar\, UC Irvine\n\n\nAbstract\nAbelian
and Non-Abelian X-ray transforms are examples of integral-geometric transf
orms with applications to X-ray Computerized Tomography and the imaging of
magnetic fields inside of materials (Polarimetric Neutron Tomography).\n\
n(1). We will first discuss recent results on a sharp description of the m
apping properties of the X-ray transform (and its associated normal operat
or I*I) on the Euclidean disk\, associated with a special L2 topology on i
ts co-domain.\n\n(2). We will then focus on how to use this framework to s
how that attenuated X-ray transforms (with skew-hermitian attenuation matr
ix)\, more specifically their normal operators\, satisfy similar mapping p
roperties. \n\n(3). Finally\, I will discuss an important application of t
hese results to the Bayesian inversion of the problem of reconstructing an
attenuation matrix (or Higgs field) from its scattering data corrupted wi
th additive Gaussian noise. Specifically\, I will discuss a Bernstein-VonM
ises theorem on the ‘local asymptotic normality’ of the posterior dist
ribution as the number of measurement points tends to infinity\, useful fo
r uncertainty quantification purposes. Numerical illustrations will be giv
en. \n\n(2) and (3) are joint work with R. Nickl and G.P.Paternain (Cambri
dge).\n
LOCATION:https://researchseminars.org/talk/Inverse/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lauri Oksanen (University College London)
DTSTART:20200903T160000Z
DTEND:20200903T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/15
DESCRIPTION:Title: Lorentzian Calderón problem under curvature bounds\nby Lauri Oksanen
(University College London) as part of International Zoom Inverse Problem
s Seminar\, UC Irvine\n\n\nAbstract\nWe introduce a method of solving inve
rse boundary value problems for wave equations on Lorentzian manifolds\, a
nd show that zeroth order coefficients can be recovered under certain curv
ature bounds. The set of Lorentzian metrics satisfying the curvature bound
s has a non-empty interior in the sense of smooth\, compactly supported pe
rturbations of the metric\, whereas all previous results on this problem i
mpose conditions on the metric that force it to be real analytic with resp
ect to a suitably defined time variable. The analogous problem on Riemanni
an manifolds is called the Calderón problem\, and in this case the known
results require the metric to be independent of one of the variables. Our
approach is based on a new unique continuation result in the exterior of t
he double null cone emanating from a point. The approach shares features w
ith the classical Boundary Control method\, and can be viewed as a general
ization of this method to cases where no real analyticity is assumed. The
talk is based on joint work with Spyros Alexakis and Ali Feizmohammadi.\n
LOCATION:https://researchseminars.org/talk/Inverse/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pedro Caro (BCAM)
DTSTART:20200910T160000Z
DTEND:20200910T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/16
DESCRIPTION:Title: The Calderón problem with corrupted data\nby Pedro Caro (BCAM) as pa
rt of International Zoom Inverse Problems Seminar\, UC Irvine\n\n\nAbstrac
t\nThe inverse Calderón problem consists in determining the conductivity
inside a medium by electrical measurements on its surface. Ideally\, these
measurements determine the Dirichlet-to-Neumann map and\, therefore\, one
usually assumes the data to be given by such map. This situation correspo
nds to having access to infinite-precision measurements\, which is totally
unrealistic. In this talk\, I will consider the Calderón problem assumin
g data to contain measurement errors and provide formulas to reconstruct t
he conductivity and its normal derivative on the surface (joint work with
Andoni García). I will also present similar results for Maxwell’s equat
ions (joint work with Ru-Yu Lai\, Yi-Hsuan Lin\, Ting Zhou ). When modelli
ng errors in these two different frameworks\, one realizes the existence o
f certain freedom that yields different reconstruction formulas. To unders
tand the whole picture of what is going on\, we rewrite the problem in a d
ifferent setting\, which will bring us to analyse the observational limit
of wave packets with noisy measurements (joint work with Cristóbal J. Mer
oño).\n
LOCATION:https://researchseminars.org/talk/Inverse/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Kuchment (Texas A&M University)
DTSTART:20200917T160000Z
DTEND:20200917T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/17
DESCRIPTION:Title: Detecting presence of low-emission radiation sources\nby Peter Kuchme
nt (Texas A&M University) as part of International Zoom Inverse Problems S
eminar\, UC Irvine\n\n\nAbstract\nThe talk will describe the problem of de
tecting presence of a low emission nuclear source shielded by strong backg
round and/or cargo.\n
LOCATION:https://researchseminars.org/talk/Inverse/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Johannes Sjostrand (Université de Bourgogne)
DTSTART:20200924T160000Z
DTEND:20200924T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/18
DESCRIPTION:Title: On a d\, d-bar system with a large parameter\nby Johannes Sjostrand (
Université de Bourgogne) as part of International Zoom Inverse Problems S
eminar\, UC Irvine\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Inverse/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vesselin Petkov (University of Bordeaux)
DTSTART:20201008T160000Z
DTEND:20201008T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/19
DESCRIPTION:Title: Location and Weyl asymptotics for the eigenvalues of some non self-adjoin
t operators\nby Vesselin Petkov (University of Bordeaux) as part of In
ternational Zoom Inverse Problems Seminar\, UC Irvine\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Inverse/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rakesh (University of Delaware)
DTSTART:20201022T160000Z
DTEND:20201022T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/20
DESCRIPTION:Title: The fixed angle scattering problem\nby Rakesh (University of Delaware
) as part of International Zoom Inverse Problems Seminar\, UC Irvine\n\n\n
Abstract\nWe first discuss our (with Mikko Salo) uniqueness result for the
fixed angle scattering problem that the acoustic property (zeroth order c
oefficient) of a medium is uniquely determined by the far-field data\, mea
sured in all directions for all frequencies\, associated with two incoming
plane waves from opposite directions. Next we discuss our (with Venky Kri
shnan and Soumen Senapati) uniqueness result for a similar problem where t
he coefficient depends on space and time variables. \n\nBoth problems are
formally determined and the results are proved by showing Lipschitz stabil
ity for two inverse problems for hyperbolic PDEs with boundary data\, usin
g a variation of the Bukhgeim-Klibanov method.\n
LOCATION:https://researchseminars.org/talk/Inverse/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Allan Greenleaf (University of Rochester)
DTSTART:20201029T160000Z
DTEND:20201029T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/21
DESCRIPTION:Title: Microlocal analysis of Doppler synthetic aperture radar\nby Allan Gre
enleaf (University of Rochester) as part of International Zoom Inverse Pro
blems Seminar\, UC Irvine\n\n\nAbstract\nConventional monostatic synthetic
aperture radar (SAR) uses range data obtained from measurements of scatte
red radar waves to produce images of the Earth’s surface. The waveforms\
, which are transmitted from an air- or space-borne platformand measured b
y a co-located receiver\, are pulses with small temporal duration but wide
bandwidth.The short duration of the pulses can give rise to high spatial
resolution in the images\,and there is a considerable mathematical literat
ure concerning SAR.I will discuss an alternative approach\, called Doppler
SAR\, which uses a single frequency waveform. We use techniques of micr
olocal analysis to describe the artifacts that might arise in DSAR imaging
\,and characterize some artifact-free regions. This is joint work with Ral
uca Felea\, Romina Gaburro and Cliff Nolan.\n
LOCATION:https://researchseminars.org/talk/Inverse/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Perry (University of Kentucky)
DTSTART:20201203T170000Z
DTEND:20201203T180000Z
DTSTAMP:20260422T225802Z
UID:Inverse/22
DESCRIPTION:by Peter Perry (University of Kentucky) as part of Internation
al Zoom Inverse Problems Seminar\, UC Irvine\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Inverse/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chrysoula Tsogka (UC Merced)
DTSTART:20201001T160000Z
DTEND:20201001T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/23
DESCRIPTION:Title: The Noise Collector for sparse recovery in high dimensions\nby Chryso
ula Tsogka (UC Merced) as part of International Zoom Inverse Problems Semi
nar\, UC Irvine\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Inverse/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kui Ren (Columbia University)
DTSTART:20201105T170000Z
DTEND:20201105T180000Z
DTSTAMP:20260422T225802Z
UID:Inverse/24
DESCRIPTION:Title: Inverse problems in photoacoustic imaging of nonlinear physics\nby Ku
i Ren (Columbia University) as part of International Zoom Inverse Problems
Seminar\, UC Irvine\n\n\nAbstract\nThis talk will discuss inverse problem
s in the photoacoustic imaging of two-photon absorption of heterogeneous m
edia where we intend to reconstruct coefficients in systems of semilinear
diffusion and transport equations from single or multiple given data sets.
The main goal of the talk is (a) to give an overview of recent developmen
ts on the modeling\, computational and mathematical aspects of the problem
\, and (b) to point out some important questions that need to be addressed
.\n
LOCATION:https://researchseminars.org/talk/Inverse/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gregory Eskin (UCLA)
DTSTART:20201112T170000Z
DTEND:20201112T180000Z
DTSTAMP:20260422T225802Z
UID:Inverse/25
DESCRIPTION:by Gregory Eskin (UCLA) as part of International Zoom Inverse
Problems Seminar\, UC Irvine\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Inverse/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yavar Kian (Aix Marseille University)
DTSTART:20201015T160000Z
DTEND:20201015T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/26
DESCRIPTION:Title: Simultaneous determination of internal source and coefficients of a diffu
sion equation from a single boundary measurement\nby Yavar Kian (Aix
Marseille University) as part of International Zoom Inverse Problems Semin
ar\, UC Irvine\n\n\nAbstract\nIn this talk\, we will consider the inverse
problem of determining simultaneously several class of coefficients and a
n internal source (a source term or an initial condition) appearing in a
diffusion equation from a single boundary measurement. Our problem can be
formulated as the simultaneous determination of information about a diffu
sion process (velocity field\, density of the medium) and of the source of
diffusion. We consider this problems in the context of a classical diffus
ion process described by a convection-diffusion equation as well as an ano
malous diffusion phenomena described by a time fractional diffusion equat
ion. Some parts of this talk are based on a joint work with Zhiyuan Li\, Y
ikan Liu and Masahiro Yamamoto.\n
LOCATION:https://researchseminars.org/talk/Inverse/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ozan Öktem (KTH)
DTSTART:20201210T170000Z
DTEND:20201210T180000Z
DTSTAMP:20260422T225802Z
UID:Inverse/27
DESCRIPTION:by Ozan Öktem (KTH) as part of International Zoom Inverse Pro
blems Seminar\, UC Irvine\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Inverse/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hamid Hezari (UC Irvine)
DTSTART:20201119T170000Z
DTEND:20201119T180000Z
DTSTAMP:20260422T225802Z
UID:Inverse/28
DESCRIPTION:by Hamid Hezari (UC Irvine) as part of International Zoom Inve
rse Problems Seminar\, UC Irvine\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Inverse/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ali Feizmohammadi (University College London)
DTSTART:20210121T170000Z
DTEND:20210121T180000Z
DTSTAMP:20260422T225802Z
UID:Inverse/29
DESCRIPTION:Title: The Jacobi weighted ray transform\nby Ali Feizmohammadi (University C
ollege London) as part of International Zoom Inverse Problems Seminar\, UC
Irvine\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Inverse/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yiran Wang (Emory University)
DTSTART:20210211T170000Z
DTEND:20210211T180000Z
DTSTAMP:20260422T225802Z
UID:Inverse/30
DESCRIPTION:by Yiran Wang (Emory University) as part of International Zoom
Inverse Problems Seminar\, UC Irvine\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Inverse/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hamid Hezari (UC Irvine)
DTSTART:20210114T170000Z
DTEND:20210114T180000Z
DTSTAMP:20260422T225802Z
UID:Inverse/31
DESCRIPTION:Title: The inverse spectral problem for centrally symmetric real analytic domain
s\nby Hamid Hezari (UC Irvine) as part of International Zoom Inverse P
roblems Seminar\, UC Irvine\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Inverse/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lexing Ying (Stanford University)
DTSTART:20210128T170000Z
DTEND:20210128T180000Z
DTSTAMP:20260422T225802Z
UID:Inverse/32
DESCRIPTION:Title: Solving Inverse Problems with Deep Learning\nby Lexing Ying (Stanford
University) as part of International Zoom Inverse Problems Seminar\, UC I
rvine\n\n\nAbstract\nThis talk is about some recent progress on solving in
verse problems using deep learning. Compared to traditional machine learni
ng problems\, inverse problems are often limited by the size of the traini
ng data set. We show how to overcome this issue by incorporating mathemati
cal analysis and physics into the design of neural network architectures.
We first describe neural network representations of pseudodifferential ope
rators and Fourier integral operators. We then continue to discuss applica
tions including electric impedance tomography\, optical tomography\, inver
se acoustic/EM scattering\, seismic imaging\, and travel-time tomography.\
n
LOCATION:https://researchseminars.org/talk/Inverse/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandru Tamasan (University of Central Florida)
DTSTART:20210204T170000Z
DTEND:20210204T180000Z
DTSTAMP:20260422T225802Z
UID:Inverse/33
DESCRIPTION:Title: On a source reconstruction in an absorbing and scattering domain in the p
lane from measurements of fluxes at the boundary\nby Alexandru Tamasan
(University of Central Florida) as part of International Zoom Inverse Pro
blems Seminar\, UC Irvine\n\n\nAbstract\nThis talk concerns the source rec
onstruction problem in a transport problem through an absorbing and scatte
ring medium from measurements of boundary fluxes at the boundary. I will
focus on the full boundary data in the scattering case\, and the partial d
ata (measurements on an arc) in the non-scattering case\, and explain how
a combination of these two cases solves the reconstruction problem in the
partial data case. The method\, specific to two dimensional domains\, reli
es on Bukgheim’s theory of A-analytic maps and it is joint work with H.
Fujiwara (Kyoto U) and K. Sadiq (RICAM).\n
LOCATION:https://researchseminars.org/talk/Inverse/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carola-Bibiane Schönlieb (University of Cambridge)
DTSTART:20210218T170000Z
DTEND:20210218T180000Z
DTSTAMP:20260422T225802Z
UID:Inverse/34
DESCRIPTION:Title: Machine Learned Regularization for Solving Inverse Problems\nby Carol
a-Bibiane Schönlieb (University of Cambridge) as part of International Zo
om Inverse Problems Seminar\, UC Irvine\n\n\nAbstract\nInverse problems ar
e about the reconstruction of an unknown physical quantity from indirect m
easurements. Most inverse problems of interest are ill-posed and require a
ppropriate mathematical treatment for recovering meaningful solutions. Reg
ularization is one of the main mechanisms to turn inverse problems into we
ll-posed ones by adding prior information about the unknown quantity to th
e problem\, often in the form of assumed regularity of solutions. Classica
lly\, such regularization approaches are handcrafted. Examples include Tik
honov regularization\, the total variation and several sparsity-promoting
regularizers such as the L1 norm of Wavelet coefficients of the solution.
While such handcrafted approaches deliver mathematically and computational
ly robust solutions to inverse problems\, providing a universal approach t
o their solution\, they are also limited by our ability to model solution
properties and to realise these regularization approaches computationally.
Recently\, a new paradigm has been introduced to the regularization of in
verse problems\, which derives regularization approaches for inverse probl
ems in a data driven way. Here\, regularization is not mathematically mode
lled in the classical sense\, but modelled by highly over-parametrised mod
els\, typically deep neural networks\, that are adapted to the inverse pro
blems at hand by appropriately selected (and usually plenty of) training d
ata. In this talk\, I will review some machine learning based regularizati
on techniques\, present some work on unsupervised and deeply learned conve
x regularisers and their application to image reconstruction from tomograp
hic and blurred measurements\, and finish by discussing some open mathemat
ical problems.\n
LOCATION:https://researchseminars.org/talk/Inverse/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Houssem Haddar (Ecole Polytechnique)
DTSTART:20210225T170000Z
DTEND:20210225T180000Z
DTSTAMP:20260422T225802Z
UID:Inverse/35
DESCRIPTION:by Houssem Haddar (Ecole Polytechnique) as part of Internation
al Zoom Inverse Problems Seminar\, UC Irvine\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Inverse/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samuli Siltanen (University of Helsinki)
DTSTART:20210304T170000Z
DTEND:20210304T180000Z
DTSTAMP:20260422T225802Z
UID:Inverse/36
DESCRIPTION:Title: Learning from electric X-ray images: the new EIT\nby Samuli Siltanen
(University of Helsinki) as part of International Zoom Inverse Problems Se
minar\, UC Irvine\n\n\nAbstract\nA fundamental connection between Electric
al Impedance Tomography (EIT) and classical X-ray tomography was found in
[Greenleaf et al 2018]. There it was shown that a one-dimensional Fourier
transform applied to the spectral parameter of Complex Geometric Optics (C
GO) solutions to a Beltrami equation is a useful technique. Microlocal ana
lysis of the involved complex principal type operators reveals singulariti
es propagating in curious ways. They enable a novel filtered back-projecti
on type nonlinear reconstruction algorithm for EIT. This approach is calle
d Virtual Hybrid Edge Detection (VHED). \n\nOne of the medically most prom
ising applications of EIT is stroke imaging. There are two main types of s
troke: (1) brain hemorrhage and (2) ischemic stroke caused by a blood clot
. The symptoms for those two conditions are the same\, but the treatments
are completely the opposite. There are two main uses for EIT here: (a) cla
ssifying the type of stroke already in the ambulance with a cost-effective
portable device\, and (b) monitoring the state of recovering stroke patie
nts in the intensive care unit. \n\nThe main difficulty in using EIT for h
ead imaging is the resistive skull. Because of that\, the relevant signal
from the brain is weak and almost buried in noise. Given the extreme ill-p
osedness of the inverse conductivity problem\, it is quite a challenge to
design a robust EIT algorithm for either (a) or (b). \n\nVHED offers a way
to divide the information in EIT measurements into geometrically understo
od pieces. One could wish that those pieces are less sensitive to noise th
an a full reconstructed image of the conductivity. This presentation shows
how machine learning can be used for classifying stroke (problem (a)) abo
ve based on VHED profiles. Examined are fully connected neural networks (F
CNN)\, convolutional neural networks (CNN) and recurrent neural networks (
RNN). Perhaps surprisingly\, CNNs offer the worst performance\, while RNNs
are slightly better than FCNNs.\n
LOCATION:https://researchseminars.org/talk/Inverse/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gitta Kutyniok (Ludwig-Maximilians-Universität München)
DTSTART:20210311T170000Z
DTEND:20210311T180000Z
DTSTAMP:20260422T225802Z
UID:Inverse/37
DESCRIPTION:Title: Graph Convolutional Neural Networks: The Mystery of Generalization\nb
y Gitta Kutyniok (Ludwig-Maximilians-Universität München) as part of Int
ernational Zoom Inverse Problems Seminar\, UC Irvine\n\n\nAbstract\nThe tr
emendous importance of graph structured data due to\nrecommender systems o
r social networks led to the introduction of\ngraph convolutional neural n
etworks (GCN). Those split into spatial\nand spectral GCNs\, where in the
later case filters are defined as\nelementwise multiplication in the frequ
ency domain of a graph.\nSince often the dataset consists of signals defin
ed on many\ndifferent graphs\, the trained network should generalize to si
gnals\non graphs unseen in the training set. One instance of this problem\
nis the transferability of a GCN\, which refers to the condition that\na s
ingle filter or the entire network have similar repercussions on\nboth gra
phs\, if two graphs describe the same phenomenon. However\,\nfor a long ti
me it was believed that spectral filters are not\ntransferable.\n\nIn this
talk we aim at debunking this common misconception by\nshowing that if tw
o graphs discretize the same continuous metric\nspace\, then a spectral fi
lter or GCN has approximately the same\nrepercussion on both graphs. Our a
nalysis also accounts for large\ngraph perturbations as well as allows gra
phs to have completely\ndifferent dimensions and topologies\, only requiri
ng that both\ngraphs discretize the same underlying continuous space. Nume
rical\nresults then even imply that spectral GCNs are superior to spatial\
nGCNs if the dataset consists of signals defined on many different\ngraphs
.\n
LOCATION:https://researchseminars.org/talk/Inverse/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victor Isakov (Wichita State University)
DTSTART:20210318T160000Z
DTEND:20210318T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/38
DESCRIPTION:Title: On increasing stability and minimal data in inverse problems\nby Vict
or Isakov (Wichita State University) as part of International Zoom Inverse
Problems Seminar\, UC Irvine\n\n\nAbstract\nWe expose (with basic ideas o
f proofs) recent results about improving stability in the Cauchy problem f
or general elliptic partial differential equations of second order of Helm
holtz type without any geometrical assumptions on domains and operators w
hen the wave number is growing. The next topic is better stability in in t
he inverse source scattering problems with the boundary data at an interv
al of wave numbers when this interval is getting larger. We give rather co
mplete theory for the Helmholtz equation (based on sharp bounds of analyt
ic and exact observability for the wave equation)\, as well as convincing
numerical examples. Similarly we discuss recovery of the Schroedinger pote
ntial from the Dirichlet-to Neumann map. Finally\, we report on first resu
lts on the inverse problems where the wave number is zero (or small)\, sho
wing that in the two dimensional case of inverse gravimetry in a realistic
practical situation one can stably find only 5 real parameters of gravity
force at the boundary and with this data uniquely determine an ellipse.\n
LOCATION:https://researchseminars.org/talk/Inverse/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Angkana Rüland (Heidelberg University)
DTSTART:20210325T160000Z
DTEND:20210325T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/39
DESCRIPTION:Title: On instability mechanisms in inverse problems\nby Angkana Rüland (He
idelberg University) as part of International Zoom Inverse Problems Semina
r\, UC Irvine\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Inverse/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gaik Ambartsoumian (University of Texas at Arlington)
DTSTART:20210401T160000Z
DTEND:20210401T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/40
DESCRIPTION:Title: 2D vector tomography with broken rays and stars\nby Gaik Ambartsoumia
n (University of Texas at Arlington) as part of International Zoom Inverse
Problems Seminar\, UC Irvine\n\n\nAbstract\nMultiple classical works of i
ntegral geometry have been dedicated to the reconstruction of vector field
s from various integral transforms of such fields\, including the longitud
inal ray transform (Doppler transform)\, transverse ray transform\, and th
eir integral moments. We consider a generalization of these transforms\, i
n which the straight-line path of integration is substituted either by bro
ken rays or by stars (a finite union of rays emanating from a common verte
x). We present several exact closed-form inversion formulas for certain pa
irs of these transforms on 2D compactly supported vector fields in the pla
ne\, discuss their properties and present results of numerical simulations
. The talk is based on joint work with Mohammad Latifi (University of Ariz
ona) and Rohit Mishra (University of Texas at Arlington).\n
LOCATION:https://researchseminars.org/talk/Inverse/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mourad Bellassoued (University of Tunis El Manar\, Tunisia)
DTSTART:20210408T160000Z
DTEND:20210408T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/41
DESCRIPTION:Title: Stable recovery of a metric tensor from the partial hyperbolic Dirichlet
to Neumann map\nby Mourad Bellassoued (University of Tunis El Manar\,
Tunisia) as part of International Zoom Inverse Problems Seminar\, UC Irvin
e\n\n\nAbstract\nIn this talk we consider the inverse problem of determini
ng on a compact Riemannian manifold the metric tensor in the wave equation
with Dirichlet data from measured Neumann sub-boundary observations. Thi
s information is enclosed in the dynamical partial Dirichlet-to-Neumann ma
p associated to the wave equation. We prove in dimension $n\\geq 2$ that
the knowledge of the partial Dirichlet-to-Neumann map for the wave equatio
n uniquely determines the metric tensor and we establish logarithm-type st
ability.\n
LOCATION:https://researchseminars.org/talk/Inverse/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antônio Sá Barreto (Purdue University)
DTSTART:20210415T160000Z
DTEND:20210415T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/42
DESCRIPTION:Title: Inverse Scattering for Critical Semilinear Wave Equations\nby Antôni
o Sá Barreto (Purdue University) as part of International Zoom Inverse Pr
oblems Seminar\, UC Irvine\n\n\nAbstract\nWe show that the scattering oper
ator for defocusing energy critical semilinear wave equations $\\square u
+f(u)=0\,$ $f\\in C^\\infty(\\mr)$ and $f\\sim u^5\,$ in three space dime
nsions\, determines $f$. This is joint work with Gunther Uhlmann and Yiran
Wang.\n
LOCATION:https://researchseminars.org/talk/Inverse/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ting Zhou (Northeastern University)
DTSTART:20210422T160000Z
DTEND:20210422T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/43
DESCRIPTION:Title: Inverse Problems for Nonlinear PDEs\nby Ting Zhou (Northeastern Unive
rsity) as part of International Zoom Inverse Problems Seminar\, UC Irvine\
n\n\nAbstract\nIn this talk\, I will demonstrate the higher order lineariz
ation approach to solve several inverse boundary value problems for nonlin
ear PDEs modeling nonlinear electromagnetic optics including nonlinear tim
e-harmonic Maxwell’s equations with Kerr-type and second harmonic genera
tion nonlinearity. The problem will be reduced to solving for the coeffici
ent functions from their integrals against multiple linear solutions. We w
ill focus our discussion on different choices of linear solutions. A simil
ar problem for nonlinear magnetic Schrodinger equation will be considered
as a comparison.\n
LOCATION:https://researchseminars.org/talk/Inverse/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hanming Zhou (UC Santa Barbara)
DTSTART:20210429T160000Z
DTEND:20210429T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/44
DESCRIPTION:Title: Travel time tomography in stationary spacetimes\nby Hanming Zhou (UC
Santa Barbara) as part of International Zoom Inverse Problems Seminar\, UC
Irvine\n\n\nAbstract\nIn this talk\, I will discuss the boundary rigidity
problem on a cylindrical domain in $\\mathbb R^{1+n}$\, $n\\geq 2$\, equi
pped with a stationary (time-invariant) Lorentzian metric. We show that th
e time separation function between pairs of points on the boundary of the
cylindrical domain determines the stationary spacetime\, up to some time-i
nvariant diffeomorphism\, assuming that the metric is close to the Minkows
ki metric\, and satisfies some a-priori conditions. The talk is based on j
oint work with Gunther Uhlmann (UW) and Yang Yang (MSU).\n
LOCATION:https://researchseminars.org/talk/Inverse/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joonas Ilmavirta (Tampere University)
DTSTART:20210506T160000Z
DTEND:20210506T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/45
DESCRIPTION:Title: Geometric inverse problems arising from geophysics\nby Joonas Ilmavir
ta (Tampere University) as part of International Zoom Inverse Problems Sem
inar\, UC Irvine\n\n\nAbstract\nI will describe how geometrization of some
seismological problems leads to geometric inverse problems\, focusing on
broader ideas rather than specific details or theorems. The talk will most
ly revolve around seismology\, modelling\, PDEs\, differential geometry\,
and inverse problems.\n
LOCATION:https://researchseminars.org/talk/Inverse/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tony Liimatainen (University of Helsinki)
DTSTART:20210513T160000Z
DTEND:20210513T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/46
DESCRIPTION:Title: Linearized Calderón problem and exponentially accurate quasimodes for an
alytic manifolds\nby Tony Liimatainen (University of Helsinki) as part
of International Zoom Inverse Problems Seminar\, UC Irvine\n\n\nAbstract\
nI will discuss a new method for the linearized anisotropic Calderón prob
lem on cylindrical Riemannian manifolds. I will present our recent result
with Katya Krupchyk and Mikko Salo\, https://arxiv.org/abs/2009.05699. Cru
cial ingredients in the proof of our result are the construction of Gaussi
an beam quasimodes with exponentially small errors\, as well as the FBI tr
ansform characterization of the analytic wave front set. These might have
applications in other inverse problems as well.\n
LOCATION:https://researchseminars.org/talk/Inverse/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ru-Yu Lai (University of Minnesota)
DTSTART:20210520T160000Z
DTEND:20210520T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/47
DESCRIPTION:Title: An inverse problem for the Boltzmann equation\nby Ru-Yu Lai (Universi
ty of Minnesota) as part of International Zoom Inverse Problems Seminar\,
UC Irvine\n\n\nAbstract\nThe Inverse problem for the Boltzmann equation fi
nds applications in many fields such as optical imaging. It seeks to recon
struct certain physical properties of a medium from the data measured on t
he boundary. In this talk\, I will discuss an inverse problem for the Bolt
zmann equation with nonlinear collision operator. We show that the collisi
on kernel can be reconstructed from the incoming-to-outgoing mappings on t
he boundary of the domain. This talk is based on a joint work with Gunther
Uhlmann (UW) and Yang Yang (MSU).\n
LOCATION:https://researchseminars.org/talk/Inverse/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexei Novikov (Penn State University)
DTSTART:20210527T160000Z
DTEND:20210527T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/48
DESCRIPTION:Title: Imaging with highly incomplete and corrupted data\nby Alexei Novikov
(Penn State University) as part of International Zoom Inverse Problems Sem
inar\, UC Irvine\n\n\nAbstract\nWe consider the problem of imaging sparse
scenes from a few noisy data using an l1-minimization approach. This probl
em can be cast as a linear system of the form Ax=b. The dimension of the u
nknown sparse vector x is much larger than the dimension of the data vecto
r b. The l1-minimization alone\, however\, is not robust for imaging with
noisy data. To improve its performance we propose to solve instead the aug
mented linear system [A|C]x=b\, where the matrix C is a noise collector. I
t is constructed so as its column vectors provide a frame on which the noi
se of the data can be well approximated with high probability. This approa
ch gives rise to a new hyper-parameter free imaging method that has a zer
o false discovery rate for any level of noise. We further apply the idea o
f the noise collector to signal recovery from cross-correlated data matrix
bb’. Cross-correlations naturally arise in many fields of imaging\, suc
h as optics\, holography and seismic interferometry. The unknown is now a
matrix xx’ formed by the cross correlation of the unknown signal. Henc
e\, the bottleneck for inversion is the number of unknowns that grows quad
ratically with dimension of x. The noise collector helps to reduce the dim
ensionality of the problem by recovering only the diagonal of xx’\, whos
e dimension grows linearly with the size of x. I will demonstrate the effe
ctiveness of our approach for radar imaging. The method itself\, however\,
can be applied in\, among others\, medical imaging\, structural biology\,
geophysics and high-dimensional linear regression in statistics. This is
a joint work with M. Moscoso\, G.Papanicolaou and C. Tsogka.\n
LOCATION:https://researchseminars.org/talk/Inverse/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francis Chung (University of Kentucky)
DTSTART:20210603T160000Z
DTEND:20210603T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/49
DESCRIPTION:Title: Optical Inverse Problems with Local Data\nby Francis Chung (Universit
y of Kentucky) as part of International Zoom Inverse Problems Seminar\, UC
Irvine\n\n\nAbstract\nOptical tomography is the process of reconstructing
internal properties of an object by making optical measurements at the bo
undary. By considering both diffusion and transport models for light propa
gation\, this process gives rise to a number of interesting inverse proble
ms. Although many of these problems are solved in the case of full boundar
y data\, most are still at least partially open in the case of local data\
, where measurements are restricted to a fixed subset of the boundary. In
this talk I will describe four of these problems\, and discuss some of wha
t is known in each case.\n
LOCATION:https://researchseminars.org/talk/Inverse/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Albert Fannjiang (UC Davis)
DTSTART:20210610T160000Z
DTEND:20210610T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/50
DESCRIPTION:Title: Ptychography: Theory and Algorithms\nby Albert Fannjiang (UC Davis) a
s part of International Zoom Inverse Problems Seminar\, UC Irvine\n\n\nAbs
tract\nPtychography is a scanning version of coded-aperture phase retrieva
l\, a versatile method that finds its way to many applications in molecula
r and materials imaging. Its operating principle is that measurement redun
dancy due to overlap of scanning probe removes the usual ambiguities in st
andard phase retrieval by providing extra constraint for unique characteri
zation of the underlying extended object. \n\nA remarkable effect of ptych
ography emerged in physics experiments more than 10 years ago that the cod
ed aperture can be recovered along with the unknown object\, up to a const
ant phase factor\, for certain measurement schemes with sufficient probe o
verlap (i.e. blind ptychography). We review recent progress in mathematica
l theory and algorithms developed for blind ptychography operating at real
istic level of measurement resources.\n
LOCATION:https://researchseminars.org/talk/Inverse/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kenneth Golden (University of Utah)
DTSTART:20210617T160000Z
DTEND:20210617T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/51
DESCRIPTION:Title: On Thinning Ice: Modeling and monitoring sea ice in a warming climate
\nby Kenneth Golden (University of Utah) as part of International Zoom Inv
erse Problems Seminar\, UC Irvine\n\n\nAbstract\nPolar sea ice is a key co
mponent of Earth’s climate system. As a material it is a composite which
is structured on length scales ranging over ten orders of magnitude. A pr
incipal challenge in modeling sea ice is how to use information on small s
cale structure to find the effective or homogenized properties on larger s
cales relevant to climate models. Moreover\, the inverse problem of estima
ting parameters controlling small scale processes from large scale observa
tions is also of interest. For example\, electromagnetic remote sensing of
sea ice is central to assessing the impact of climate change. We will dis
cuss recent results on forward and inverse homogenization for sea ice over
a broad range of scales. We consider electromagnetic and fluid transport
through the brine and polycrystalline microstructure\, advection diffusion
processes\, ocean wave propagation through the ice pack\, melt ponds\, an
d the sea ice concentration field over the Arctic Ocean. This work is help
ing to advance how sea ice is represented in climate models\, and to impro
ve projections of the fate of Earth’s sea ice packs and the ecosystems t
hey support.\n
LOCATION:https://researchseminars.org/talk/Inverse/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Faraco Hurtado (Universidad Autónoma de Madrid)
DTSTART:20210624T160000Z
DTEND:20210624T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/52
DESCRIPTION:Title: Mathematics with Slava Kurylev: Homogenization and Inverse Problems\
nby Daniel Faraco Hurtado (Universidad Autónoma de Madrid) as part of Int
ernational Zoom Inverse Problems Seminar\, UC Irvine\n\n\nAbstract\nI wil
describe two theorems of Y. Kurylev with the Madrid group in relation wit
h homogenization and inverse problems. In between those theorems I will re
visit the relation between quasiconformal maps and the stability of Calder
ón problemand how a suitable average of the time dependent non elliptic
Schrödinger equation provides a seemly stable Buckgheim type recovery al
gorthim for irregular potentials. The talk is aimed to be not technical an
d highlighting the new viewpoints.\n
LOCATION:https://researchseminars.org/talk/Inverse/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gunther Uhlmann (University of Washington)
DTSTART:20210819T160000Z
DTEND:20210819T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/53
DESCRIPTION:Title: The Dirichlet-to-Neumann Map\, the Boundary Distance Function\, and the G
eodesic X-Ray Transform\nby Gunther Uhlmann (University of Washington)
as part of International Zoom Inverse Problems Seminar\, UC Irvine\n\n\nA
bstract\nWe will discuss some connections between these three topics.\n
LOCATION:https://researchseminars.org/talk/Inverse/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adrian Nachman (University of Toronto)
DTSTART:20210826T160000Z
DTEND:20210826T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/54
DESCRIPTION:Title: A nonlinear Plancherel Theorem with applications to global well-posedness
for the Defocusing Davey-Stewartson Equation and to the Calderón Inverse
Problem in dimension 2\nby Adrian Nachman (University of Toronto) as
part of International Zoom Inverse Problems Seminar\, UC Irvine\n\n\nAbstr
act\nI’ll describe a well-studied nonlinear Fourier transform in two dim
ensions for which a proof of the Plancherel theorem had been a challenging
open problem. I’ll sketch out the main ideas of the solution of this pr
oblem\, as well as the solution of two other problems that motivated it: g
lobal well-posedness for the Defocusing DSII Equation in the mass critical
case\, and global uniqueness for the Inverse Boundary Value Problem of Ca
lderón for a class of unbounded conductivities. On the way\, there will a
lso be new estimates for classical fractional integrals\, and a new result
on L^2 boundedness of pseudodifferential operators with non-smooth symbol
s. (This is joint work with Idan Regev and Daniel Tataru.)\n
LOCATION:https://researchseminars.org/talk/Inverse/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:William Rundell (Texas A&M University)
DTSTART:20210902T160000Z
DTEND:20210902T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/55
DESCRIPTION:Title: Inverse Problems for Fractional Partial Differential Equations\nby Wi
lliam Rundell (Texas A&M University) as part of International Zoom Inverse
Problems Seminar\, UC Irvine\n\n\nAbstract\nFractional derivatives and po
wers of operators have been a well-studied topic over the last decade —
and for good reason. Not only is there interesting mathematics involved bu
t a myriad of applications have shown that such operators have definitely
left any curiousity-level label. Also\, many inverse problems for PDE are
characterised by the fact that their solution is often highly ill-posed. I
n this talk we shall look at several inverse problems involving both class
ical derivatives and some of their fractional counterparts. The recurring
question\, which will come with some answers\, is whether these two paradi
gms give similar uniqueness results and if the levels of ill-posedness are
the same and\, of course\, why this should be so.\n
LOCATION:https://researchseminars.org/talk/Inverse/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leonid Kunyansky (University of Arizona)
DTSTART:20210909T160000Z
DTEND:20210909T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/56
DESCRIPTION:Title: Parametrix for the inverse source problem of thermoacoustic tomography wi
th reduced data\nby Leonid Kunyansky (University of Arizona) as part o
f International Zoom Inverse Problems Seminar\, UC Irvine\n\n\nAbstract\nW
e consider the inverse source problem of thermo- and photoacoustic tomogra
phy\, with data registered on an open surface partially surrounding the so
urce of acoustic waves. Our goal is to find efficient non-iterative\nsolut
ions to this problem.\n\nI will present two different methods:\n\n(1) A pr
ocedure based on solving the exterior Dirichlet problem and computing the
Radon transform of the solution. This technique works under assumption of
a constant speed of sound.\n\n(2) A procedure based on modifying the time-
reversed solution by two Hilbert transforms\, one in time and one in a cer
tain spatial variable. This techniques works for a smooth known speed of s
ound\, subject to an additional geometric condition.\n\nBoth techniques pr
oduce microlocally accurate approximations to the sought initial condition
. In certain geometries these methods can be implemented as fast algorithm
s. Performance of these techniques will be demonstrated in numerical simul
ations.\n\nJoint work with M. Eller and P. Hoskins\n
LOCATION:https://researchseminars.org/talk/Inverse/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tracey Balehowsky (University of Helsinki)
DTSTART:20210916T160000Z
DTEND:20210916T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/57
DESCRIPTION:Title: Determining a Riemannian metric from least-area data\nby Tracey Baleh
owsky (University of Helsinki) as part of International Zoom Inverse Probl
ems Seminar\, UC Irvine\n\n\nAbstract\nIn this talk\, we address the follo
wing question: Given any simple closed curve $\\gamma$ on the boundary of
a Riemannian 3-manifold $(M\,g)$\, suppose the area of the least-area surf
aces bounded by $\\gamma$ are known. From this data may we uniquely recove
r $g$? \n\nIn several settings\, we show the the answer is yes. In fact\,
we prove both global and local uniqueness results given least-area data fo
r a much smaller class of curves on the boundary. We demonstrate uniquenes
s for $g$ by reformulating parts of the problem as a 2-dimensional inverse
problem on an area-minimizing surface. In particular\, we relate our leas
t-area information to knowledge of the Dirichlet-to-Neumann map for the st
ability operator on a minimal surface. \n\nBroadly speaking\, the question
we address is a dimension 2 version of the classical boundary rigidity pr
oblem for simply connected\, Riemannian 3-manifolds with boundary. We will
briefly review this problem of boundary rigidity as it relates to aspects
of our question of recovering $g$ from knowledge of areas. \n\nThis is jo
int work with S. Alexakis and A. Nachman.\n
LOCATION:https://researchseminars.org/talk/Inverse/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mihajlo Cekić (Université Paris-Saclay)
DTSTART:20210923T160000Z
DTEND:20210923T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/58
DESCRIPTION:Title: The Holonomy Inverse Problem\nby Mihajlo Cekić (Université Paris-Sa
clay) as part of International Zoom Inverse Problems Seminar\, UC Irvine\n
\n\nAbstract\nGiven a compact Riemannian manifold (M\, g) and a vector bun
dle over M equipped with a connection\, we consider the following question
: does the holonomy along closed geodesics determine the gauge (equivalenc
e) class of the connection? If (M\, g) has negative curvature or more gene
rally its geodesic flow is Anosov\, in this talk I will explain how in fac
t\, only the traces of the holonomy along closed geodesics locally determi
ne a generic connection\; global uniqueness results are obtained in some c
ases. A direct consequence is an inverse spectral result for the connectio
n (magnetic) Laplacian. The proof relies on two new ingredients: a Livšic
type theorem in hyperbolic dynamics for unitary cocycles\, and the interp
lay between the local geometry of the moduli space of connections with Pol
licott-Ruelle resonances of a certain natural transport operator. Joint wo
rk with Thibault Lefeuvre.\n
LOCATION:https://researchseminars.org/talk/Inverse/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elena Cherkaev (University of Utah)
DTSTART:20210930T160000Z
DTEND:20210930T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/59
DESCRIPTION:Title: Inverse homogenization: Can one hear the structure of a composite?\nb
y Elena Cherkaev (University of Utah) as part of International Zoom Invers
e Problems Seminar\, UC Irvine\n\n\nAbstract\nInverse homogenization is a
problem of deriving information about the microgeometry of a finely struct
ured medium from its known effective properties. I will discuss an approac
h to this problem based on reconstructing the matrix-valued spectral measu
re in the Stieltjes integral representation of the effective properties of
a two-component composite. This integral representation relates the n-poi
nt correlation functions of the microstructure to the moments of the spect
ral measure of an operator depending on the composite’s geometry. I will
show that the spectral measure which contains all information about the m
icrostructure\, can be uniquely recovered from frequency dependent effecti
ve data\; this allows to view the problem as an inverse spectral problem.
In particular\, the moments of the measure and the spectral gaps at the en
ds of the spectral interval can be uniquely reconstructed\, which results
in the unique identification of the volume fractions of materials in the c
omposite and estimates for the connectedness of its phases. I will discuss
the recovery of microstructural parameters from electromagnetic and visco
elastic effective measurements and show that the resulting spectroscopic i
maging method provides an efficient way to construct spectrally matched mi
crostructures.\n
LOCATION:https://researchseminars.org/talk/Inverse/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fioralba Cakoni (Rutgers University)
DTSTART:20211007T160000Z
DTEND:20211007T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/60
DESCRIPTION:Title: Singularities Almost Always Scatter: Regularity Results for Non-scatterin
g Inhomogeneities\nby Fioralba Cakoni (Rutgers University) as part of
International Zoom Inverse Problems Seminar\, UC Irvine\n\n\nAbstract\nA p
erplexing question in scattering theory is whether there are incoming tim
e harmonic waves\, at particular frequencies\, that are not scattered by a
given inhomogeneity\, in other words the inhomogeneity is invisible to pr
obing by such waves. We refer to wave numbers\, that correspond to freque
ncies for which there exists a non-scattering incoming wave\, as non-scatt
ering. This question is inherently related to the solution of inverse scat
tering problem for inhomogeneous media. The attempt to provide an answer
to this question has led to the so-called transmission eigenvalue problem
with the wave number as the eigen-parameter. This is non-selfadjoint eige
nvalue problem with challenging mathematical structure. The non-scattering
wave numbers form a subset of real transmission eigenvalues. A positive
answer to the existence of non-scattering wave numbers is already known fo
r spherical inhomogeneities and a negative answer was given for inhomog
eneities with corners. Up to very recently little was known about non-scat
tering inhomogeneities that are neither spherical symmetric nor having sup
port that contains a corner. In this presentation we discuss some new res
ults for general inhomogeneities. More specifically we examine necessary c
onditions for an inhomogeneity to be non-scattering\, or equivalently\, by
negation\, sufficient conditions for it to be scattering. These condition
s are formulated in terms of the regularity of the boundary and refractive
index of the inhomogeneity. Our approach makes a connection between non-s
cattering configuration and free boundary methods. \n\nThis presentation i
s based on a joint work with Michael Vogelius.\n
LOCATION:https://researchseminars.org/talk/Inverse/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elena Beretta (Politecnico di Milano)
DTSTART:20211014T160000Z
DTEND:20211014T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/61
DESCRIPTION:Title: Title: Identification of cavities in a nonlinear model arising from cardi
ac electrophysiology via Gamma-convergence\nby Elena Beretta (Politecn
ico di Milano) as part of International Zoom Inverse Problems Seminar\, UC
Irvine\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Inverse/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jingni Xiao (Rutgers University)
DTSTART:20211021T160000Z
DTEND:20211021T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/62
DESCRIPTION:Title: Nonscattering Wavenumbers\nby Jingni Xiao (Rutgers University) as par
t of International Zoom Inverse Problems Seminar\, UC Irvine\n\n\nAbstract
\nIn this talk\, I will survey some recent results on the existence or non
existence of nonscattering wavenumbers under various settings\, including
medium scatterers with corners or with regular boundaries. This talk is pa
rtially based on joint papers with F. Cakoni\, M. Vogelius\, H. Liu\, and
E. Blåsten.\n
LOCATION:https://researchseminars.org/talk/Inverse/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Otmar Scherzer (University of Vienna & RICAM)
DTSTART:20211028T160000Z
DTEND:20211028T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/63
DESCRIPTION:Title: Projection and Diffraction Tomography of Particles in a Trap\nby Otma
r Scherzer (University of Vienna & RICAM) as part of International Zoom In
verse Problems Seminar\, UC Irvine\n\n\nAbstract\nTomographic imaging of p
articles in a trap is a recent research topic in microscopy. There a parti
cle is moved by tweezers for tomographic imaging. Mathematically\, this re
sults in a tomographic imaging problem with irregular movement. Typically
the problem is split up into two problems: The first is motion detection a
nd the second is 3D tomographic imaging. We consider motion detection base
d on optical projection imaging and 3D tomographic imaging based on a diff
raction forward model. Open problems and relations to mathematical problem
s in Cryo imaging are discussed.\n\nThis is joint work with Peter Elbau\,
Florian Faucher\, Clemens Kirisits\, Michael Quellmalz\, Monika Ritsch-Ma
rte\, Eric Setterqvist\, Gabriele Steidl.\n
LOCATION:https://researchseminars.org/talk/Inverse/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jorge Passamani Zubelli (Khalifa University)
DTSTART:20211104T160000Z
DTEND:20211104T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/64
DESCRIPTION:Title: A Splitting Strategy for the Calibration of Jump-Diffusion Models\nby
Jorge Passamani Zubelli (Khalifa University) as part of International Zoo
m Inverse Problems Seminar\, UC Irvine\n\n\nAbstract\nThis talk concerns t
he calibration of Dupire’s model in the presence of jumps. This leads to
an integro-differential equation whose parameters have to be calibrated s
o as to fit market data. We present a detailed analysis and implementation
of a splitting strategy to identify simultaneously the local-volatility s
urface and the jump-size distribution from quoted European prices. The und
erlying model consists of a jump-diffusion driven asset with\ntime and pri
ce dependent volatility. Our approach uses a forward Dupire-type partial-i
ntegro-differential equation for the option prices to produce a parameter-
to-solution map. The ill-posed inverse problem for such a map is then solv
ed by means of a Tikhonov-type convex regularization. We present numerical
examples that substantiate the robustness of the method both for synthet
ic and real data. This is joint work with Vinicius Albani (UFSC) that appe
ared in Finance and Stochastics.\n
LOCATION:https://researchseminars.org/talk/Inverse/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fernando Guevara Vasquez (University of Utah)
DTSTART:20211118T170000Z
DTEND:20211118T180000Z
DTSTAMP:20260422T225802Z
UID:Inverse/65
DESCRIPTION:Title: Active thermal cloaking and mimicking\nby Fernando Guevara Vasquez (U
niversity of Utah) as part of International Zoom Inverse Problems Seminar\
, UC Irvine\n\n\nAbstract\nWe show how to hide objects or sources by using
an active source and dipole distribution on a surface enclosing the regio
n to be cloaked\, allowing for cloaking even in transient regimes. This te
chnique does assume a homogeneous medium and knowledge of the probing fiel
d\, but applies to a variety of physical phenomena that can be modeled by
the heat equation (including mass or light diffusion). The same idea can b
e used to make an object (or source) appear as another one. This is work i
n collaboration with Maxence Cassier\, Trent DeGiovanni and Sebastien Guen
neau.\n
LOCATION:https://researchseminars.org/talk/Inverse/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xue-Cheng Tai (Hong Kong Baptist University)
DTSTART:20211209T170000Z
DTEND:20211209T180000Z
DTSTAMP:20260422T225802Z
UID:Inverse/66
DESCRIPTION:Title: Deep neural networks in image processing\nby Xue-Cheng Tai (Hong Kong
Baptist University) as part of International Zoom Inverse Problems Semina
r\, UC Irvine\n\n\nAbstract\nIn this talk\, we present our recent research
on using variational models as layers for deep neural networks (DNNs). We
use image segmentation as an example. The technique can also be used for
high dimensional data classification as well. Through this technique\, we
could integrate many well-know variational models for image segmentation i
nto deep neural networks. The new networks will have the advantages of tra
ditional DNNs. At the same time\, the outputs from the new networks can al
so have many good properties of variational models for image segmentation.
We will present some techniques to incorporate shape priors into the netw
orks through the variational layers. We will show how to design networks w
ith spatial regularization and volume preservation. We can also design net
works with guarantee that the output shapes from the network for image seg
mentation must be convex shapes/star-shapes. It is numerically verified th
at these techniques can improve the performance when the true shapes satis
fy these priors. \n\nThe ideas of these new networks is based on some rela
tionship between the softmax function\, the Potts models and the structure
of traditional DNNs. We will explain this in detail which leads naturally
to the newly designed networks. \n\nThis talk is based on joint works wit
h Jun Liu\, S. Luo and several other collaborators.\n
LOCATION:https://researchseminars.org/talk/Inverse/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yi-Hsuan Lin (National Yang Ming Chiao Tung University)
DTSTART:20211202T170000Z
DTEND:20211202T180000Z
DTSTAMP:20260422T225802Z
UID:Inverse/67
DESCRIPTION:Title: Simultaneous recovery inverse problems for nonlinear and nonlocal equatio
ns\nby Yi-Hsuan Lin (National Yang Ming Chiao Tung University) as part
of International Zoom Inverse Problems Seminar\, UC Irvine\n\n\nAbstract\
nWe study inverse problems associated with semilinear parabolic and hyperb
olic systems in several scenarios where both the nonlinearities and the in
itial data can be unknown. We also show that some simultaneous recovery re
sults hold for both nonlocal and nonlinear elliptic equations. It turns ou
t that the nonlinearity and nonlocality play critical roles in deriving th
ese simultaneous recovery results.\n
LOCATION:https://researchseminars.org/talk/Inverse/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giovanni Covi (Heidelberg University)
DTSTART:20211216T170000Z
DTEND:20211216T180000Z
DTSTAMP:20260422T225802Z
UID:Inverse/68
DESCRIPTION:Title: Uniqueness for the fractional Calderon problem with quasilocal perturbati
ons\nby Giovanni Covi (Heidelberg University) as part of International
Zoom Inverse Problems Seminar\, UC Irvine\n\n\nAbstract\nWe will be talki
ng about the fractional Schrodinger equation with quasilocal perturbations
. Quasilocal operators are a special kind of nonlocal operators transformi
ng compactly supported functions into functions of unbounded support with
a decay estimate at infinity. These include\, among the others\, convoluti
ons operators against Schwartz functions. We will show that both qualitati
ve and quantitative unique continuation and Runge approximation properties
hold in the assumption of sufficient decay. The results are then used to
show uniqueness in the inverse problem of retrieving a quasilocal perturba
tion from DN data under suitable geometric assumptions. This work generali
zes recent results regarding the locally perturbed fractional Calderon pro
blem\, and is based on the following paper: https://arxiv.org/abs/2110.110
63\n
LOCATION:https://researchseminars.org/talk/Inverse/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlos Kenig (University of Chicago)
DTSTART:20220113T170000Z
DTEND:20220113T180000Z
DTSTAMP:20260422T225802Z
UID:Inverse/69
DESCRIPTION:Title: Wave maps into the sphere\nby Carlos Kenig (University of Chicago) as
part of International Zoom Inverse Problems Seminar\, UC Irvine\n\n\nAbst
ract\nWe will introduce wave maps and discuss some of their basic properti
es\, leading to recent works on the soliton resolution conjecture for crit
ical wave maps and related equations.\n
LOCATION:https://researchseminars.org/talk/Inverse/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Mazzucato (Penn State University)
DTSTART:20220120T170000Z
DTEND:20220120T180000Z
DTSTAMP:20260422T225802Z
UID:Inverse/70
DESCRIPTION:Title: An inverse problem in fault detection\nby Anna Mazzucato (Penn State
University) as part of International Zoom Inverse Problems Seminar\, UC Ir
vine\n\n\nAbstract\nI will discuss a model for dislocations in an elastic
medium\, modeling faults in the Earth’s crust. The direct problem consis
ts in solving a non-standard boundary value/interface problem for isotropi
c linear elasticity with piecewise Lipschitz Lame’ parameters. The inver
se problem consists in determining the fault surface and slip vector from
displacement measurements made at the surface. We prove uniqueness under s
ome geometric conditions\, using unique continuation results. The results
extend to certain anisotropic media in 2 dimensions.\nWe also establish s
hape derivative formulas under infinitesimal movements of the fault and ch
anges in the slip. . This is joint work with Andrea Aspri (Milan Universit
y)\, Elena Beretta (NYU-Abu Dhabi)\, and Maarten de Hoop (Rice University)
.\n
LOCATION:https://researchseminars.org/talk/Inverse/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Steve Zelditch (Northwestern University)
DTSTART:20220127T170000Z
DTEND:20220127T180000Z
DTSTAMP:20260422T225802Z
UID:Inverse/71
DESCRIPTION:Title: Spatial and Fourier restriction problems for eigenfunctions\nby Steve
Zelditch (Northwestern University) as part of International Zoom Inverse
Problems Seminar\, UC Irvine\n\n\nAbstract\nThere are two different types
of “restriction theorems” for Laplace (or related) operators. One type
is “Fourier restriction theorems” where the Fourier transform is rest
ricted to a hypersurface or submanifold. Another type is spatial restricti
on theorems\, where an eigenfunction $\\phi$ of the Laplacian $\\Delta_M$
of a Riemannian manifold is restricted to a submanifold $H$. My talk is ab
out joint restriction theorems: one first restricts an eigenfunction $\\ph
i$ to a submanifold $H$\, expands it in eigenfunctions $e_k$ of $\\Delta_
H$\, and then studies the Fourier restriction of $\\phi |_H$ to short wind
ow of Fourier coefficients w.r.t. $H$. How much of the $L^2$-mass of $\\p
hi |_H$ lies in a short window of frequencies of $H$? This kind of proble
m arises in several branches of analysis. My talk is in part a survey of j
oint restriction phenomena and in part a description of recent results\, p
artly in collaboration with Yakun Xi and Emmett Wyman.\n
LOCATION:https://researchseminars.org/talk/Inverse/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Teemu Tyni (University of Toronto)
DTSTART:20220210T170000Z
DTEND:20220210T180000Z
DTSTAMP:20260422T225802Z
UID:Inverse/72
DESCRIPTION:Title: Stability of an inverse problem for a semi-linear wave equation\nby T
eemu Tyni (University of Toronto) as part of International Zoom Inverse Pr
oblems Seminar\, UC Irvine\n\n\nAbstract\nStability of an inverse problem
deals with the question about whether small errors in the measurement lead
only to small errors in the reconstruction. I will discuss the stability
and unique recovery of a potential function in a semi-linear wave equation
. The inverse problem is formulated on a Lorentzian manifold. Using the no
nlinearity of the wave equation\, we show that the potential function can
be recovered in a H\\"older stable way from the Dirichlet-to-Neumann map.
This talk is based on a joint work with Matti Lassas\, Tony Liimatainen an
d Leyter Potenciano-Machado.\n
LOCATION:https://researchseminars.org/talk/Inverse/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ruchi Guo (UC Irvine)
DTSTART:20220303T170000Z
DTEND:20220303T180000Z
DTSTAMP:20260422T225802Z
UID:Inverse/73
DESCRIPTION:Title: A Deep Direct Sampling Method for Electrical Impedance and Diffuse Optica
l Tomography\nby Ruchi Guo (UC Irvine) as part of International Zoom I
nverse Problems Seminar\, UC Irvine\n\n\nAbstract\nElectrical impedance to
mography (EIT) and Diffuse Optical Tomography (DOT) are promising techniqu
es for non-invasive and radiation-free type of medical imaging. They all c
an be considered as inverse boundary value problems to identify PDE coeffi
cients. But a high-quality reconstruction is always challenging due to its
severe ill-posedness. Based on the idea of direct sampling methods (DSMs)
\, we present a framework to construct deep neural networks for solving th
ese two problems. It is able to capture the underlying mathematical struct
ure from background projection of boundary measurement to coefficient dist
ribution. The resulting Deep DSM (DDSM) is easy for implementation and its
offline-online decomposition inherits efficiency from the original DSM th
at does not need any optimization process in reconstruction. Additionally\
, it is capable of systematically incorporating multiple Cauchy data pairs
to achieve high-quality reconstruction and is also highly robust to large
noise.\n
LOCATION:https://researchseminars.org/talk/Inverse/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yang Zhang (University of Washington)
DTSTART:20220310T170000Z
DTEND:20220310T180000Z
DTSTAMP:20260422T225802Z
UID:Inverse/74
DESCRIPTION:Title: Inverse boundary value problems for a quasilinear wave equation on Lorent
zian manifolds\nby Yang Zhang (University of Washington) as part of In
ternational Zoom Inverse Problems Seminar\, UC Irvine\n\n\nAbstract\nInver
se problems of recovering the metric and nonlinear terms were originated i
n the work by Kurylev\, Lassas\, and Uhlmann for the semilinear wave equat
ion $\\square_g u(x) + a(x)u^2(x) = f(x)$ in a manifold without boundary.
The idea is to use the linearization and the nonlinear interactions of dis
torted planes waves to produce point source like singularities in an obser
vable set. In this talk\, I will discuss the joint work with Gunther Uhlma
nn which considers the recovery of the metric and the nonlinear term for a
quadratic derivative nonlinear wave equation on a Lorentzian manifold wit
h boundary. The main difficulty that we need to handle here is caused by t
he presence of the boundary. Our work builds on the previous results and I
will discuss the methods to overcome these difficulties.\n
LOCATION:https://researchseminars.org/talk/Inverse/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Erkki Somersalo (Case Western Reserve University)
DTSTART:20220224T170000Z
DTEND:20220224T180000Z
DTSTAMP:20260422T225802Z
UID:Inverse/75
DESCRIPTION:Title: Bayesian inversion and data science methods to identify changes in brain
activity during meditation from MEG measurements\nby Erkki Somersalo (
Case Western Reserve University) as part of International Zoom Inverse Pro
blems Seminar\, UC Irvine\n\n\nAbstract\nMeditation as a potential alterna
tive for pharmaceutical intervention to mitigate conditions such as chron
ic pain or clinical depression continues to obtain significant attention.
One of the problems is that often the positive effects of meditation that
have been reported are anecdotal or are based on self reporting. To quanti
fy the effects of meditation\, it is therefore important to develop method
s based on medical imaging to identify brain regions that are involved in
the meditation practice. In this talk\, we review some recent results abou
t this topic\, addressed by using magnetoencephalography (MEG) to map brai
n activity during meditation. One of the difficulties here is that the dat
a are less sensitive to activity taking place in the deep brain regions\,
including the limbic system that is believed to play an important role in
meditation. The MEG inverse problem is addressed by using novel Bayesian m
ethods combined with advanced numerical techniques\, applied on data from
professional Buddhist meditators. The reconstructed activity is then analy
zed using data science techniques to distill the information about the act
ivation changes during meditation.\n
LOCATION:https://researchseminars.org/talk/Inverse/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Barbara Kaltenbacher (University of Klagenfurt)
DTSTART:20220428T160000Z
DTEND:20220428T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/76
DESCRIPTION:Title: Imaging with nonlinear and fractionally damped waves\nby Barbara Kalt
enbacher (University of Klagenfurt) as part of International Zoom Inverse
Problems Seminar\, UC Irvine\n\n\nAbstract\nThe importance of ultrasound i
s well established in the imaging of human tissue. In order to enhance ima
ge quality by exploiting nonlinear effects\, recently techniques such as h
armonic imaging and nonlinearity parameter tomography have been put forwar
d. The latter leads to a coefficient identification problem for a quasilin
ear wave equation. Another characteristic property of ultrasound propagati
ng in human tissue is frequency power law attenuation leading to fractiona
l derivative damping models in time domain. In this talk we will first of
all dwell on modeling of nonlinearity on one hand and fractional damping o
n the other hand. Then we will discuss the linear inverse problem of photo
acoustic tomography with fractional damping. Finally we return to the inve
rse problem of nonlinearity parameter imaging and show some first results.
\n
LOCATION:https://researchseminars.org/talk/Inverse/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Vogelius (Rutgers University)
DTSTART:20220331T160000Z
DTEND:20220331T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/77
DESCRIPTION:Title: Recent results concerning ``small" change in boundary conditions\nby
Michael Vogelius (Rutgers University) as part of International Zoom Invers
e Problems Seminar\, UC Irvine\n\n\nAbstract\nThe study of the effect of (
volumetric) small changes of material parameters is an area of research th
at has had significant impact on inverse problems\, and in addition to the
very recent (boundary) results\, I will attempt to give a brief survey o
f some of the earlier work.\n
LOCATION:https://researchseminars.org/talk/Inverse/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bastian von Harrach (Goethe University Frankfurt)
DTSTART:20220407T160000Z
DTEND:20220407T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/78
DESCRIPTION:Title: Uniqueness and convex reformulation for inverse coefficient problems with
finitely many measurements\nby Bastian von Harrach (Goethe University
Frankfurt) as part of International Zoom Inverse Problems Seminar\, UC Ir
vine\n\n\nAbstract\nSeveral applications in medical imaging and non-destru
ctive material testing lead to inverse elliptic coefficient problems\, whe
re an unknown coefficient function in an elliptic PDE is to be determined
from partial knowledge of its solutions. This is usually a highly non-line
ar ill-posed inverse problem\, for which unique reconstructability results
\, stability estimates and global convergence of numerical methods are ver
y hard to achieve.\n\nIn this talk we will consider an inverse coefficient
problem with finitely many measurements and a finite desired resolution.
We will present a criterion based on monotonicity\, convexity and localize
d potentials arguments that allows us to explicitly estimate the number of
measurements that is required to achieve the desired resolution. We also
obtain an error estimate for noisy data\, and overcome the problem of loca
l minima by rewriting the problem as an equivalent uniquely solvable conve
x non-linear semidefinite optimization problem.\n\nReferences\n\nB. Harrac
h\, Uniqueness\, stability and global convergence for a discrete inverse e
lliptic Robin transmission problem\, Numer. Math. 147 (2021)\, pp. 29-70\,
https://doi.org/10.1007/s00211-020-01162-8\n\nB. Harrach\, Solving an inv
erse elliptic coefficient problem by convex non-linear semidefinite progra
mming\, Optim Lett (2021)\, arXiv preprint (2021)\, https://doi.org/10.100
7/s11590-021-01802-4\n
LOCATION:https://researchseminars.org/talk/Inverse/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yimin Zhong (Duke University)
DTSTART:20220203T170000Z
DTEND:20220203T180000Z
DTSTAMP:20260422T225802Z
UID:Inverse/79
DESCRIPTION:Title: Quantitative PAT with simplified PN approximation\nby Yimin Zhong (Du
ke University) as part of International Zoom Inverse Problems Seminar\, UC
Irvine\n\n\nAbstract\nThe photoacoustic tomography (PAT) is a hybrid moda
lity that combines the optics and\nacoustics to obtain high resolution and
high contrast imaging of heterogeneous media. In this\nwork\, our objecti
ve is to study the inverse problem in the quantitative step of PAT which a
ims\nto reconstruct the optical coefficients of the governing radiative tr
ansport equation from the\nultrasound measurements. In our analysis\, we t
ake the simplified PN approximation of the\nradiative transport equation a
s the physical model and then show the uniqueness and stability\nfor this
modified inverse problem. Numerical simulations based on synthetic data ar
e presented\nto validate our analysis.\n
LOCATION:https://researchseminars.org/talk/Inverse/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikolas Eptaminitakis (Purdue University)
DTSTART:20220217T170000Z
DTEND:20220217T180000Z
DTSTAMP:20260422T225802Z
UID:Inverse/80
DESCRIPTION:Title: The Solid-Fluid Transmission Problem\nby Nikolas Eptaminitakis (Purdu
e University) as part of International Zoom Inverse Problems Seminar\, UC
Irvine\n\n\nAbstract\nWe will discuss a problem motivated from geophysics\
, where one is interested in understanding the propagation of seismic wave
s in the interior of the Earth. It is known that the interior of the Earth
consists of several layers\, some of which are solid and some of which ar
e fluid. When a seismic wave meets the interface between two layers\, part
of its energy is reflected back (possibly with mode conversion)\, and\, i
f the angle of incidence is not too large\, part of it is transmitted to t
he other side of the interface. We are particularly interestred in underst
anding reflection\, transmission and mode conversion of waves at the inter
face between a linear elastic solid and an inviscid fluid. For simplicity\
, we consider the case of two layers\, with the fluid layer being enclosed
by the solid one. The two media are described by a system of PDEs modelin
g the displacement in the solid and pressure-velocity in the fluid\, with
these quantities being coupled at the interface by transmission conditions
. We study the problem microlocally: to understand the behavior of singula
rities of solutions of the system\, we construct a parametrix for it (appr
oximate solution up to smooth error) using geometric optics. As an applica
tion of our study\, we consider the inverse problem of recovering the wave
speeds in the two layers and the material density in the solid outer laye
r from the Neumann-to-Dirichlet map for the solid-fluid system correspondi
ng to the exterior boundary. Based on joint work with Plamen Stefanov.\n
LOCATION:https://researchseminars.org/talk/Inverse/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuzhou (Joey) Zou (UC Santa Cruz)
DTSTART:20220421T160000Z
DTEND:20220421T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/81
DESCRIPTION:Title: The $C^\\infty$-isomorphism property for a class of singularly-weighted X
-ray transforms\nby Yuzhou (Joey) Zou (UC Santa Cruz) as part of Inter
national Zoom Inverse Problems Seminar\, UC Irvine\n\n\nAbstract\nWe consi
der the mapping properties of singularly-weighted normal operators associa
ted to X-ray transforms on manifolds with boundary. While normal operators
associated to geodesic X-ray transforms in "simple" settings are known to
be elliptic pseudodifferential operators in the interior\, their behavior
near the boundary is more subtle\; in particular the normal operators nee
d to be precomposed with weights in order to even map $C^\\infty$ of a man
ifold with boundary back to itself. This motivates asking which choice of
weights guarantee the normal operator to be an isomorphism of $C^\\infty$\
; such questions arise in considering theoretical guarantees for the consi
stency and uncertainty quantification of statistical recovery algorithms\,
where one needs to know on what spaces the operator can be considered inv
ertible. In this talk\, we will show that a particular family of weights o
n the Euclidean disk and on simple disks of constant curvature do give ris
e to normal operators which are isomorphisms on $C^\\infty$. The proof inv
olves deriving the Singular Value Decomposition of a weighted X-ray transf
orm and studying certain function spaces based on the singular vectors of
the X-ray transform\, which coincides with the eigenfunctions of a particu
lar degenerately elliptic Kimura-type differential operator. Joint work wi
th Rohit Kumar Mishra and Francois Monard.\n
LOCATION:https://researchseminars.org/talk/Inverse/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Li Li (Institute for Pure and Applied Mathematics\, UCLA)
DTSTART:20220512T160000Z
DTEND:20220512T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/82
DESCRIPTION:Title: Inverse problems for fractional parabolic equations with power type nonli
nearities\nby Li Li (Institute for Pure and Applied Mathematics\, UCLA
) as part of International Zoom Inverse Problems Seminar\, UC Irvine\n\n\n
Abstract\nI will first introduce classical and fractional Calderón proble
ms. Then I will focus on two inverse problems for fractional parabolic equ
ations with power type nonlinearities. Both can be viewed as nonlinear par
abolic variants of the fractional Calderón problem. The goal is to determ
ine nonlinearities/coefficients in fractional equations from exterior part
ial measurements of the Dirichlet-to-Neumann map. The approach relies on t
he unique continuation property of the fractional operator as well as tech
niques relating nonlinear problems to linear ones.\n
LOCATION:https://researchseminars.org/talk/Inverse/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jared Wunsch (Northwestern University)
DTSTART:20220317T160000Z
DTEND:20220317T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/83
DESCRIPTION:Title: Semiclassical analysis and the convergence of the finite element method\nby Jared Wunsch (Northwestern University) as part of International Zoo
m Inverse Problems Seminar\, UC Irvine\n\n\nAbstract\nAn important problem
in numerical analysis is the solution of the Helmholtz equation in exteri
or domains\, in variable media\; this models the scattering of time-harmon
ic waves. The Finite Element Method (FEM) is a flexible and powerful tool
for obtaining numerical solutions\, but difficulties are known to arise i
n obtaining convergence estimates for FEM that are uniform as the frequenc
y of waves tends to infinity. I will describe some recent joint work with
David Lafontaine and Euan Spence that yields new convergence results for
the FEM which are uniform in the frequency parameter. The essential new t
ools come from semiclassical microlocal analysis. No knowledge of either
FEM or semiclassical analysis will be assumed in the talk\, however.\n
LOCATION:https://researchseminars.org/talk/Inverse/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gunther Uhlmann (University of Washington)
DTSTART:20220616T160000Z
DTEND:20220616T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/84
DESCRIPTION:by Gunther Uhlmann (University of Washington) as part of Inter
national Zoom Inverse Problems Seminar\, UC Irvine\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Inverse/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tanya Christiansen (University of Missouri)
DTSTART:20220324T160000Z
DTEND:20220324T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/85
DESCRIPTION:Title: The semiclassical structure of the scattering matrix for a manifold with
infinite cylindrical end\nby Tanya Christiansen (University of Missour
i) as part of International Zoom Inverse Problems Seminar\, UC Irvine\n\n\
nAbstract\nWe study the microlocal properties of the scattering\nmatrix as
sociated to the semiclassical \nSchr\\"odinger operator $P=h^2\\Delta_X+V$
on a Riemannian\nmanifold with an infinite cylindrical end. Let $Y$ deno
te the cross section of the end\, which is not necessarily connected. We
show that under suitable hypotheses\, microlocally the scattering matrix
is a Fourier integral operator associated to the graph of the scattering m
ap $\\kappa:\\mathcal{D}_{\\kappa}\\to T^*Y$\, with $\\mathcal{D}_\\kappa\
\subset T^*Y$. The scattering map\n$\\kappa$ and its domain $\\mathcal{D}
_\\kappa$ are \ndetermined by the Hamilton flow of the principal symbol of
$P$.\nAs an application we prove that\, under additional hypotheses on th
e scattering map\,\nthe eigenvalues of the associated unitary scattering m
atrix are equidistributed on the unit circle.\n\nThis talk is based on joi
nt work with A. Uribe.\n
LOCATION:https://researchseminars.org/talk/Inverse/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Per Christian Hansen (Technical University of Denmark)
DTSTART:20220519T160000Z
DTEND:20220519T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/86
DESCRIPTION:by Per Christian Hansen (Technical University of Denmark) as p
art of International Zoom Inverse Problems Seminar\, UC Irvine\n\nAbstract
: TBA\n
LOCATION:https://researchseminars.org/talk/Inverse/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yang Yang (Michigan State University)
DTSTART:20220602T160000Z
DTEND:20220602T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/87
DESCRIPTION:by Yang Yang (Michigan State University) as part of Internatio
nal Zoom Inverse Problems Seminar\, UC Irvine\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Inverse/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Isaac Harris (Purdue University)
DTSTART:20220414T160000Z
DTEND:20220414T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/88
DESCRIPTION:Title: Regularization of the Factorization Method with Applications\nby Isaa
c Harris (Purdue University) as part of International Zoom Inverse Problem
s Seminar\, UC Irvine\n\n\nAbstract\nIn this talk\, we discuss a new regul
arized version of the Factorization Method. The Factorization Method uses
Picard’s Criteria to define an indicator function to image an unknown re
gion. In most applications\, the data operator is compact which gives that
the singular values can tend to zero rapidly which can cause numerical in
stabilities. The regularization of the Factorization Method presented here
seeks to avoid the numerical instabilities in applying Picard’s Criteri
a. This method allows one to image the interior structure of an object wit
h little a priori information in a computationally simple and analytically
rigorous way. Here we will focus on an application of this method to diff
use optical tomography which will prove that this method can be used to re
cover an unknown subregion from the Dirichlet-to-Neumann mapping.\n
LOCATION:https://researchseminars.org/talk/Inverse/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthias Eller (Georgetown University)
DTSTART:20220505T160000Z
DTEND:20220505T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/89
DESCRIPTION:Title: Hyperbolic boundary problems\, Carleman estimates\, and the Kreiss-Sakamo
to-Tataru condition\nby Matthias Eller (Georgetown University) as part
of International Zoom Inverse Problems Seminar\, UC Irvine\n\n\nAbstract\
nA review of the theory of hyperbolic initial-boundary value problems is p
resented. Since the 1970s there are two competing theories\, one for symme
tric hyperbolic systems mainly due to Friedrichs and one for strictly hype
rbolic systems due to Kreiss and Sakamoto. The relationship of these two t
heories has been clarified only during the last decade. A central part of
both theories is played by a priori estimates. Carleman estimates share so
me similarities with hyperbolic a priori estimates. Initially establish fo
r functions with compact support and as a tool for proving unique continua
tion for operators with non-analytic coefficients\, they have found applic
ations in Inverse Problems and Control Theory. Boundary data were included
in Carleman estimates by Lebeau\, Robbiano\, and Tataru established a con
dition similar to the one used by Kreiss and Sakamoto for hyperbolic probl
ems. The case of scalar second-order operators will be discussed.\n
LOCATION:https://researchseminars.org/talk/Inverse/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gregory Eskin (UCLA)
DTSTART:20220526T160000Z
DTEND:20220526T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/90
DESCRIPTION:Title: Rigidity for Lorentzian metrics having the same length of null-geodesics<
/a>\nby Gregory Eskin (UCLA) as part of International Zoom Inverse Problem
s Seminar\, UC Irvine\n\n\nAbstract\nWe study the Lorentzian metric inde
pendent of the time variable in the cylinder $\\R\\times\\Omega$ wher
e $x_0\\in\\R$ is the time variable and $\\Omega$ is a bounded smoo
th domain in $\\R^n$.\n\nWe consider forward null-geodesics in $\\R\\t
imes \\Omega$ starting on $\\R\\times\\partial\\Omega$ at $t=0$ a
nd leaving $\\R\\times\\Omega$ at some later time. We prove the followi
ng rigidity result:\n\nIf two Lorentzian metrics are close enough
in some norm and if corresponding null-geodesics have equal lengths
in $(x_0\,x)$ space then the metrics are equal.\n
LOCATION:https://researchseminars.org/talk/Inverse/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Todd Quinto (Tufts University)
DTSTART:20220609T160000Z
DTEND:20220609T170000Z
DTSTAMP:20260422T225802Z
UID:Inverse/91
DESCRIPTION:Title: Seismic imaging with generalized Radon transforms.\nby Todd Quinto (T
ufts University) as part of International Zoom Inverse Problems Seminar\,
UC Irvine\n\n\nAbstract\nGeneralized Radon transforms are Fourier integral
operators which are used\, for instance\, as imaging models in geophysica
l exploration. They appear naturally when linearizing about a known backgr
ound compression wave speed. In this work we consider seismic operators wi
th two scanning geometries: zero-offset (the source and receiver are at th
e same point and translated over the surface of the earth) and common-offs
et (the source and receiver are offset a fixed distance from each other an
d translated together). We first analyze the model with a linearly increas
ing background velocity in two spatial dimensions. We verify the Bolker co
ndition for the zero-offset scanning geometry and provide meaningful argum
ents for it to hold even if the common-offset is positive. The Bolker cond
ition allows us to infer that the normal operator is a pseudodifferential
operator. We calculate its top order symbol in the zero-offset case to stu
dy how it maps singularities. Second\, to support the usage of background
models obtained from linear regression\, we prove that the Bolker conditio
n is stable under sufficiently small perturbations of the background veloc
ity or of the offset.\n\nAuthors: Peer Christian Kunstmann and Andreas Rie
der\, Department of Mathematics\, Karlsruhe Institute of Technology (KIT)\
, D-76128\, Karlsruhe\, Germany\, Eric Todd Quinto\, Department of Mathema
tics\, Tufts University\, Medford\, MA 02155\, USA.\n
LOCATION:https://researchseminars.org/talk/Inverse/91/
END:VEVENT
END:VCALENDAR