Inverse Problems Winter 2007 / 08 Martin Burger

A Level Set Method for Inverse Problems

Inverse Problems Related to Ion Channel Selectivity

Ion channels control many biological processes in cells and consequently a large amount of research is devoted to this topic. Great progress in the understanding of channel function has been made recently using advanced mathematical modeling and simulation. This paper investigates another interesting mathematical topic, namely inverse problems, in connection with ion channels. We concentrate on...

An adaptive inverse scale space method for compressed sensing

In this paper we introduce a novel adaptive approach for solving `-minimization problems as frequently arising in compressed sensing, which is based on the recently introduced inverse scale space method. The scheme allows to efficiently compute minimizers by solving a sequence of low-dimensional nonnegative least-squares problems. We provide a detailed convergence analysis in a general setup as...

Corc Technical Report Tr-2004-03 Using Geometry and Iterated Refinement for Inverse Problems (1): Total Variation Based Image Restoration

We introduce a new iterative regularization procedure for inverse problems based on the use of Bregman distances, with particular focus on problems arising in image processing. We are motivated by the problem of restoring noisy and blurry images via variational methods, specifically by using the BV seminorm. Although our procedure applies in quite general situations it was obtained by geometric...

Using Geometry and Iterated Refinement for Inverse Problems (1): Total Variation Based Image Restoration

We introduce a new iterative regularization procedure for inverse problems based on the use of Bregman distances, with particular focus on problems arising in image processing. We are motivated by the problem of restoring noisy and blurry images via variational methods, specifically by using the BV seminorm. Although our procedure applies in quite general situations it was obtained by geometric...