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SUMMARY:François Monard (UC Santa Cruz)
DTSTART:20200806T160000Z
DTEND:20200806T170000Z
DTSTAMP:20260423T021156Z
UID:Inverse/14
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Inverse/14/"
 >Abelian and Non-Abelian X-ray transforms. Sharp mapping properties and Ba
 yesian inversion</a>\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/
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