Robust sensing of low-rank matrices with non-orthogonal sparse decomposition

Maly, Johannes (2023): Robust sensing of low-rank matrices with non-orthogonal sparse decomposition. In: Applied and Computational Harmonic Analysis, Vol. 67, 101569

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.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics > Bavarian Chair for Mathematical Foundations of Artificial Intelligence
• Subjects: 500 Science > 510 Mathematics
• ISSN: 10635203
• Language: English