Title: Sparsity enhanced solutions to inverse and ill-posed problems
Organizer(s): Simon Arridge, University College London
Marta Betcke, University College London
Speakers: Martin Benning, Westfaelische Wilhelms Universitaet Muenster
An adaptive inverse scale space method for compressed sensing

Ignace Loris, Universite Libre de Bruxelles
On a generalization of the iterative soft-thresholding algorithm for the case of non-separable penalty

Marta Betcke, University College London
Applications of mesh wavelets in diffuse optical tomography

Matti Lassas, University of Helsinki
Sparsity in inverse problems and the discretization of continuous inverse problems
Abstract: We believe that this topic is of considerable interest to the Inverse Problems community and it presents very different challenges than the widely considered problem of sparse recovery from an underdetermined system of equations satisfying one of the common assumptions using coherence or restricted isometry property of the system matrix. In any case, such properties are very restrictive and in practical setting rarely provable. Moreover, the conditions are in most cases not necessary and hence the obtained bounds are very pessimistic. However, for many interesting real life applications the issue is much more fundamental, namely the ill-posedness of the underlying inverse problem. Due to the strongly (e.g. exponentially) decaying spectrum there is no hope of carrying over results obtained for problems with full spectrum, up to a cutoff from the undersampling. Nonetheless, there are ways in which sparsity can be used to enhance the solution of ill-posed inverse problems and corresponding results will be presented in this minisymposium.

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