Sparse recovery in bounded Riesz systems with applications to numerical methods for PDEs

Brugiapaglia, Simone; Dirksen, Sjoerd; Jung, Hans Christian und Rauhut, Holger (July 2021): Sparse recovery in bounded Riesz systems with applications to numerical methods for PDEs. In: Applied and Computational Harmonic Analysis, Vol. 53: pp. 231-269

Abstract

We study sparse recovery with structured random measurement matrices having independent, identically distributed, and uniformly bounded rows and with a nontrivial covariance structure. This class of matrices arises from random sampling of bounded Riesz systems and generalizes random partial Fourier matrices. Our main result improves the currently available results for the null space and restricted isometry properties of such random matrices. The main novelty of our analysis is a new upper bound for the expectation of the supremum of a Bernoulli process associated with a restricted isometry constant. We apply our result to prove new performance guarantees for the CORSING method, a recently introduced numerical approximation technique for partial differential equations (PDEs) based on compressive sensing.

• Item Type: Journal article
• Keywords: Compressive sensing; Restricted isometry constants; Bounded Riesz systems; Numerical PDEsCORSING method; Generic chaining
• Faculties: Mathematics, Computer Science and Statistics > Mathematics > Chair of Mathematics of Information Processing
• Subjects: 500 Science > 510 Mathematics
• ISSN: 10635203
• Language: English