2020/05/14 by Simone Brugiapaglia, Brugiapaglia, Simone, Sjoerd Dirksen +5 · 1 citation
Economics, Econometrics and Finance · Mathematics · Medicine · #FOS: Computer and information sciences #FOS: Mathematics #Hemodynamic Monitoring and Therapy #Information Theory (cs.IT) #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2005.06994
openalex publication_date 2020/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study sparse recovery with structured random measurement matrices having\nindependent, identically distributed, and uniformly bounded rows and with a\nnontrivial covariance structure. This class of matrices arises from random\nsampling of bounded Riesz systems and generalizes random partial Fourier\nmatrices. Our main result improves the currently available results for the null\nspace and restricted isometry properties of such random matrices. The main\nnovelty of our analysis is a new upper bound for the expectation of the\nsupremum of a Bernoulli process associated with a restricted isometry constant.\nWe apply our result to prove new performance guarantees for the CORSING method,\na recently introduced numerical approximation technique for partial\ndifferential equations (PDEs) based on compressive sensing.\n