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CATEGORIES:Applied and Computational Analysis
SUMMARY:Some approaches to sparse solutions of linear ill-
posed problems - Elena Resmerita (Alpen-Adria Univ
ersity of Klagenfurt)
DTSTART;TZID=Europe/London:20180712T150000
DTEND;TZID=Europe/London:20180712T160000
UID:TALK108013AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/108013
DESCRIPTION:During the past two decades it has become clear t
hat $lp$ spaces with $p \\in (0\,2)$ and correspo
nding (quasi)norms are appropriate settings for d
ealing with reconstruction of sparse solutions of
ill-posed problems. In this context\, the focus of
our presentation is twofold. Firstly\, since the
question of how to choose the exponent $p$ in such
settings has been not only a numerical issue\, bu
t also a philosophical one\, we present a more fl
exible way of (performing/achieving) sparse regula
rization by varying exponents. Rather than using n
orms or quasinorms\, we employ F-norms on infinit
e dimensional spaces. Secondly\, we approach the i
ll-posed problem $Au=f$ by appropriate discretiza
tion in the image space. We formulate the so-calle
d least error method in an $l1$ setting and perfo
rm the convergence analysis by choosing the discre
tization level according to both a priori and a po
steriori rules.\nConvergence rates are obtained
under source condition (usually) yielding sparsity
of the solution.\n\n\nJoint research with Kristia
n Bredies\, Barbara Kaltenbacher and Dirk Lorenz
LOCATION:MR 14
CONTACT:Carola-Bibiane Schoenlieb
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