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We study sparse recovery with structured random measurement matrices havingindependent, identically distributed, and uniformly bounded rows and with anontrivial covariance structure. This class of matrices arises from randomsampling of bounded Riesz systems and generalizes random partial Fouriermatrices. Our main result improves the currently available results for the nullspace and restricted isometry properties of such random matrices. The mainnovelty of our analysis is a new upper bound for the expectation of thesupremum 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 partialdifferential equations (PDEs) based on compressive sensing.

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