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SUMMARY:Data driven regularization by projection - Otmar Scherzer (Univers
 ität Wien)
DTSTART:20230131T114500Z
DTEND:20230131T123000Z
UID:TALK194521@talks.cam.ac.uk
DESCRIPTION:We start by deriving a new variant of the iteratively regulari
 zed Landweber iteration for solving linear and nonlinear ill-posed inverse
  problems. The method takes into account training data\, which forms the c
 ore of the new iteration process. We prove convergence and stability for t
 he scheme in infinite dimensional Hilbert spaces.&nbsp\;In the second part
  of the talk we study the solution of linear inverse problems under the pr
 emise that the forward operator&nbsp\;is not at hand but given indirectly 
 through some input-output training pairs. We demonstrate that regularizati
 on by projection and variational regularization can be implemented without
  making use of the forward operator. Convergence and stability of the regu
 larized solutions are studied in view of a famous non-convergence statemen
 t of Seidman. We show\, analytically and numerically\, that regularization
  by projection is indeed capable of learning linear operators\, such as th
 e Radon transform.\nThis is joint work with A. Aspri\, S. Banert\, L. Fris
 chauf\, Y. Korolev\, O. &Ouml\;ktem.
LOCATION:Seminar Room 1\, Newton Institute
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