Seminar in Numerical Analysis: Martin Burger (Universität Erlangen)

Nonlinear Spectral Decomposition

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.

For further information about the seminar, please visit this <link de forschung mathematik seminar-in-numerical-analysis internal link in current>webpage.

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