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Robust Sensing of Low-Rank Matrices With Non-Orthogonal Sparse Decomposition

MCML Authors

Johannes Maly

Prof. Dr.

Associate

Mathematical Data Science and Artificial Intelligence

Abstract

We consider the problem of recovering an unknown low-rank matrix with (possibly) non-orthogonal, effectively sparse rank-1 decomposition from measurements y gathered in a linear measurement process . We propose a variational formulation that lends itself to alternating minimization and whose global minimizers provably approximate up to noise level. Working with a variant of robust injectivity, we derive reconstruction guarantees for various choices of including sub-gaussian, Gaussian rank-1, and heavy-tailed measurements. Numerical experiments support the validity of our theoretical considerations.

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