On Compressed Sensing Matrices Breaking the Square-Root Bottleneck
Information Theory
2020-10-29 v2 Combinatorics
math.IT
Number Theory
Abstract
Compressed sensing is a celebrated framework in signal processing and has many practical applications. One of challenging problems in compressed sensing is to construct deterministic matrices having restricted isometry property (RIP). So far, there are only a few publications providing deterministic RIP matrices beating the square-root bottleneck on the sparsity level. In this paper, we investigate RIP of certain matrices defined by higher power residues modulo primes. Moreover, we prove that the widely-believed generalized Paley graph conjecture implies that these matrices have RIP breaking the square-root bottleneck.
Keywords
Cite
@article{arxiv.2010.11179,
title = {On Compressed Sensing Matrices Breaking the Square-Root Bottleneck},
author = {Shohei Satake and Yujie Gu},
journal= {arXiv preprint arXiv:2010.11179},
year = {2020}
}