Data driven regularization by projection

Add to your list(s) Download to your calendar using vCal

• Otmar Scherzer (Universität Wien)
• Tuesday 31 January 2023, 11:45-12:30
• Seminar Room 1, Newton Institute.

If you have a question about this talk, please contact nobody.

RNTW01 - Rich and Nonlinear Tomography (RNT) in Radar, Astronomy and Geophysics

We start by deriving a new variant of the iteratively regularized Landweber iteration for solving linear and nonlinear ill-posed inverse problems. The method takes into account training data, which forms the core of the new iteration process. We prove convergence and stability for the scheme in infinite dimensional Hilbert spaces. In the second part of the talk we study the solution of linear inverse problems under the premise that the forward operator is not at hand but given indirectly through some input-output training pairs. We demonstrate that regularization by projection and variational regularization can be implemented without making use of the forward operator. Convergence and stability of the regularized solutions are studied in view of a famous non-convergence statement of Seidman. We show, analytically and numerically, that regularization by projection is indeed capable of learning linear operators, such as the Radon transform. This is joint work with A. Aspri, S. Banert, L. Frischauf, Y. Korolev, O. Öktem.

This talk is part of the Isaac Newton Institute Seminar Series series.

This talk is included in these lists:

• All CMS events
• Featured lists
• INI info aggregator
• Isaac Newton Institute Seminar Series
• School of Physical Sciences
• Seminar Room 1, Newton Institute
• bld31

Note that ex-directory lists are not shown.