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Nonlinear Eigenanalysis of sparsity-promoting regularisation operators

Presented by: 
Martin Benning
Tuesday 31st October 2017 - 12:00 to 12:50
INI Seminar Room 1
In this talk we analyse Eigenfunctions of nonlinear, variational regularisation operators. We show that they are closely related to a generalisation of singular vectors of compact operators, and demonstrate key mathematical properties. We use them to show how a systematic bias of variational regularisation methods can be corrected with the help of iterative regularisation methods, and discuss conditions that guarantee the decomposition of an additive composition of multiple Eigenfunctions. In the last part of the talk, we focus on utilising the concept of nonlinear Eigenanalysis to learn parametrised regularisations that can effectively separate different geometric structures. This is joint work with Joana Sarah Grah, Guy Gilboa, Carola-Bibiane Schönlieb, Marie Foged Schmidt and Martin Burger.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons