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Nonlinear Spectral Decomposition

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VMVW01 - Variational methods, new optimisation techniques and new fast numerical algorithms

In this talk we will discuss nonlinear spectral decompositions in Banach spaces, which shed a new light on multiscale methods in imaging and open new possibilities of filtering techniques. We provide a novel geometric interpretation of nonlinear eigenvalue problems in Banach spaces and provide conditions under which gradient flows for norms or seminorms yield a spectral decomposition. We will see that under these conditions standard variational schemes are equivalent to the gradient flows for arbitrary large time step, recovering previous results e.g. for the one dimensional total variation flow as special cases. 

The talk is based on joint work with Guy Gilboa, Michael Moeller, Martin Benning, Daniel Cremers, Lina Eckardt

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

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