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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:X-ray Tomography and Discretization of Inverse Pro
blems - Lassas\, M (University of Helsinki)
DTSTART;TZID=Europe/London:20110825T094500
DTEND;TZID=Europe/London:20110825T103000
UID:TALK32488AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/32488
DESCRIPTION:In this talk we consider the question how inverse
problems posed for continuous objects\, for instan
ce for continuous functions\, can be discretized.
This means the approximation of the problem by inf
inite dimensional inverse problems. We will consid
er linear inverse problems of the form $m=Af+psil
on$. Here\, the function $m$ is the measurement\,
$A$ is a ill-conditioned linear operator\, $u$ is
an unknown function\, and $psilon$ is random nois
e.\nThe inverse problem means determination of $u$
when $m$ is given.\nIn particular\, we consider t
he X-ray tomography with sparse or limited angle m
easurements where $A$ corresponds to integrals of
the attenuation function $u(x)$ over lines in a fa
mily $Gamma$.\nThe traditional solutions for the p
roblem include the generalized Tikhonov regulariza
tion and the estimation of $u$ using Bayesian meth
ods. To solve the problem in practice $u$ and $m$
are discretized\, that is\, approximated by vector
s in an infinite dimensional vector space. We show
positive results when this approximation can succ
essfully be done and consider examples of problems
that can appear. As an example\, we consider the
total variation (TV) and Besov norm penalty regula
rization\, the Bayesian analysis based on total va
riation prior and Besov priors.\n\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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