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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Data driven regularization by projection - Otmar S
cherzer (Universität Wien)
DTSTART;TZID=Europe/London:20230131T114500
DTEND;TZID=Europe/London:20230131T123000
UID:TALK194521AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/194521
DESCRIPTION:We start by deriving a new variant of the iterativ
ely regularized Landweber iteration for solving li
near and nonlinear ill-posed inverse problems. The
method takes into account training data\, which f
orms the core of the new iteration process. We pro
ve convergence and stability for the scheme in inf
inite dimensional Hilbert spaces. \;In the sec
ond part of the talk we study the solution of line
ar inverse problems under the premise that the for
ward operator \;is not at hand but given indir
ectly through some input-output training pairs. We
demonstrate that regularization by projection and
variational regularization can be implemented wit
hout making use of the forward operator. Convergen
ce and stability of the regularized solutions are
studied in view of a famous non-convergence statem
ent of Seidman. We show\, analytically and numeric
ally\, that regularization by projection is indeed
capable of learning linear operators\, such as th
e Radon transform.\nThis is joint work with A. Asp
ri\, S. Banert\, L. Frischauf\, Y. Korolev\, O. &O
uml\;ktem.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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