Date: Wed. March 31, 2021
Organized by: FAU DCN-AvH, Chair in Applied Analysis – Alexander von Humboldt Professorship at FAU Erlangen-Nürnberg (Germany)
Title: Adaptive Computation of Sparse Solutions

Speaker: Prof. Dr. Martin Burger
Affiliation: FAU Erlangen-Nürnberg, Germany

Abstract. In this talk we will discuss approaches of adaptivity to the computation of sparse solutions in an underlying continuum setting. A canonical application of interest and the guiding is the deconvolution problem in superresolution microscopy, but there are several other relevant applications, e.g. the efficient design of imaging techniques for exploration robots or the training of compact neural networks. Our approach is based on convexified variational formulations of sparsity, which allows for a rigorous mathematical analysis. A key idea we discuss is the adaptive refinement on grids based on a-posteriori error estimation, a second one the superresolved estimation of peak locations from multiple nonzero entries in adjacent grid points.

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