Johannes Maly (Katholische Universitat Eichstatt-Ingolstadt)
Monday, September 27, 2021 - 14:00
MPI fur Mathematik in den Naturwissenschaften Leipzig
Inselstr. 22, 04103 Leipzig, E1 05 (Leibniz-Saal), 1. Etage
We consider the problem of recovering an unknown low-rank matrix X with (possibly) non-orthogonal, effectively sparse rank-1 decomposition from incomplete and inaccurate measurements y gathered in a linear measurement process A. We propose a variational formulation that lends itself to alternating minimization and whose global minimizers provably approximate X from y up to noise level. Working with a variant of robust injectivity, we derive reconstruction guarantees for various choices of A including sub-gaussian, Gaussian rank-1, and heavy-tailed measurements. Numerical experiments support the validity of our theoretical considerations.
submitted by Saskia Gutzschebauch (Saskia.Gutzschebauch@mis.mpg.de, 0341 9959 50)