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BEGIN:VEVENT
SUMMARY:Andras Vasy (Stanford University)
DTSTART;VALUE=DATE-TIME:20200521T160000Z
DTEND;VALUE=DATE-TIME:20200521T170000Z
DTSTAMP;VALUE=DATE-TIME:20210419T091831Z
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;VALUE=DATE-TIME:20200528T160000Z
DTEND;VALUE=DATE-TIME:20200528T170000Z
DTSTAMP;VALUE=DATE-TIME:20210419T091831Z
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;VALUE=DATE-TIME:20200604T160000Z
DTEND;VALUE=DATE-TIME:20200604T170000Z
DTSTAMP;VALUE=DATE-TIME:20210419T091831Z
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;VALUE=DATE-TIME:20200611T160000Z
DTEND;VALUE=DATE-TIME:20200611T170000Z
DTSTAMP;VALUE=DATE-TIME:20210419T091831Z
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;VALUE=DATE-TIME:20200702T160000Z
DTEND;VALUE=DATE-TIME:20200702T170000Z
DTSTAMP;VALUE=DATE-TIME:20210419T091831Z
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;VALUE=DATE-TIME:20200723T160000Z
DTEND;VALUE=DATE-TIME:20200723T170000Z
DTSTAMP;VALUE=DATE-TIME:20210419T091831Z
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;VALUE=DATE-TIME:20200625T160000Z
DTEND;VALUE=DATE-TIME:20200625T170000Z
DTSTAMP;VALUE=DATE-TIME:20210419T091831Z
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;VALUE=DATE-TIME:20200730T160000Z
DTEND;VALUE=DATE-TIME:20200730T170000Z
DTSTAMP;VALUE=DATE-TIME:20210419T091831Z
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;VALUE=DATE-TIME:20200813T160000Z
DTEND;VALUE=DATE-TIME:20200813T170000Z
DTSTAMP;VALUE=DATE-TIME:20210419T091831Z
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;VALUE=DATE-TIME:20200618T160000Z
DTEND;VALUE=DATE-TIME:20200618T170000Z
DTSTAMP;VALUE=DATE-TIME:20210419T091831Z
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;VALUE=DATE-TIME:20200709T160000Z
DTEND;VALUE=DATE-TIME:20200709T170000Z
DTSTAMP;VALUE=DATE-TIME:20210419T091831Z
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;VALUE=DATE-TIME:20200716T160000Z
DTEND;VALUE=DATE-TIME:20200716T170000Z
DTSTAMP;VALUE=DATE-TIME:20210419T091831Z
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;VALUE=DATE-TIME:20200820T160000Z
DTEND;VALUE=DATE-TIME:20200820T170000Z
DTSTAMP;VALUE=DATE-TIME:20210419T091831Z
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;VALUE=DATE-TIME:20200806T160000Z
DTEND;VALUE=DATE-TIME:20200806T170000Z
DTSTAMP;VALUE=DATE-TIME:20210419T091831Z
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;VALUE=DATE-TIME:20200903T160000Z
DTEND;VALUE=DATE-TIME:20200903T170000Z
DTSTAMP;VALUE=DATE-TIME:20210419T091831Z
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;VALUE=DATE-TIME:20200910T160000Z
DTEND;VALUE=DATE-TIME:20200910T170000Z
DTSTAMP;VALUE=DATE-TIME:20210419T091831Z
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;VALUE=DATE-TIME:20200917T160000Z
DTEND;VALUE=DATE-TIME:20200917T170000Z
DTSTAMP;VALUE=DATE-TIME:20210419T091831Z
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;VALUE=DATE-TIME:20200924T160000Z
DTEND;VALUE=DATE-TIME:20200924T170000Z
DTSTAMP;VALUE=DATE-TIME:20210419T091831Z
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;VALUE=DATE-TIME:20201008T160000Z
DTEND;VALUE=DATE-TIME:20201008T170000Z
DTSTAMP;VALUE=DATE-TIME:20210419T091831Z
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;VALUE=DATE-TIME:20201022T160000Z
DTEND;VALUE=DATE-TIME:20201022T170000Z
DTSTAMP;VALUE=DATE-TIME:20210419T091831Z
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;VALUE=DATE-TIME:20201029T160000Z
DTEND;VALUE=DATE-TIME:20201029T170000Z
DTSTAMP;VALUE=DATE-TIME:20210419T091831Z
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;VALUE=DATE-TIME:20201203T170000Z
DTEND;VALUE=DATE-TIME:20201203T180000Z
DTSTAMP;VALUE=DATE-TIME:20210419T091831Z
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;VALUE=DATE-TIME:20201001T160000Z
DTEND;VALUE=DATE-TIME:20201001T170000Z
DTSTAMP;VALUE=DATE-TIME:20210419T091831Z
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;VALUE=DATE-TIME:20201105T170000Z
DTEND;VALUE=DATE-TIME:20201105T180000Z
DTSTAMP;VALUE=DATE-TIME:20210419T091831Z
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;VALUE=DATE-TIME:20201112T170000Z
DTEND;VALUE=DATE-TIME:20201112T180000Z
DTSTAMP;VALUE=DATE-TIME:20210419T091831Z
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;VALUE=DATE-TIME:20201015T160000Z
DTEND;VALUE=DATE-TIME:20201015T170000Z
DTSTAMP;VALUE=DATE-TIME:20210419T091831Z
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;VALUE=DATE-TIME:20201210T170000Z
DTEND;VALUE=DATE-TIME:20201210T180000Z
DTSTAMP;VALUE=DATE-TIME:20210419T091831Z
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;VALUE=DATE-TIME:20201119T170000Z
DTEND;VALUE=DATE-TIME:20201119T180000Z
DTSTAMP;VALUE=DATE-TIME:20210419T091831Z
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;VALUE=DATE-TIME:20210121T170000Z
DTEND;VALUE=DATE-TIME:20210121T180000Z
DTSTAMP;VALUE=DATE-TIME:20210419T091831Z
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;VALUE=DATE-TIME:20210211T170000Z
DTEND;VALUE=DATE-TIME:20210211T180000Z
DTSTAMP;VALUE=DATE-TIME:20210419T091831Z
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;VALUE=DATE-TIME:20210114T170000Z
DTEND;VALUE=DATE-TIME:20210114T180000Z
DTSTAMP;VALUE=DATE-TIME:20210419T091831Z
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;VALUE=DATE-TIME:20210128T170000Z
DTEND;VALUE=DATE-TIME:20210128T180000Z
DTSTAMP;VALUE=DATE-TIME:20210419T091831Z
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;VALUE=DATE-TIME:20210204T170000Z
DTEND;VALUE=DATE-TIME:20210204T180000Z
DTSTAMP;VALUE=DATE-TIME:20210419T091831Z
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;VALUE=DATE-TIME:20210218T170000Z
DTEND;VALUE=DATE-TIME:20210218T180000Z
DTSTAMP;VALUE=DATE-TIME:20210419T091831Z
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;VALUE=DATE-TIME:20210225T170000Z
DTEND;VALUE=DATE-TIME:20210225T180000Z
DTSTAMP;VALUE=DATE-TIME:20210419T091831Z
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;VALUE=DATE-TIME:20210304T170000Z
DTEND;VALUE=DATE-TIME:20210304T180000Z
DTSTAMP;VALUE=DATE-TIME:20210419T091831Z
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;VALUE=DATE-TIME:20210311T170000Z
DTEND;VALUE=DATE-TIME:20210311T180000Z
DTSTAMP;VALUE=DATE-TIME:20210419T091831Z
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;VALUE=DATE-TIME:20210318T160000Z
DTEND;VALUE=DATE-TIME:20210318T170000Z
DTSTAMP;VALUE=DATE-TIME:20210419T091831Z
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;VALUE=DATE-TIME:20210325T160000Z
DTEND;VALUE=DATE-TIME:20210325T170000Z
DTSTAMP;VALUE=DATE-TIME:20210419T091831Z
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;VALUE=DATE-TIME:20210401T160000Z
DTEND;VALUE=DATE-TIME:20210401T170000Z
DTSTAMP;VALUE=DATE-TIME:20210419T091831Z
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;VALUE=DATE-TIME:20210408T160000Z
DTEND;VALUE=DATE-TIME:20210408T170000Z
DTSTAMP;VALUE=DATE-TIME:20210419T091831Z
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;VALUE=DATE-TIME:20210415T160000Z
DTEND;VALUE=DATE-TIME:20210415T170000Z
DTSTAMP;VALUE=DATE-TIME:20210419T091831Z
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
END:VCALENDAR