The Restricted Isometry Property of Block Diagonal Matrices Generated by $\varphi$-Sub-Gaussian Variables

TL;DR

This paper proves the restricted isometry property for block diagonal matrices with $\, extphi$-sub-Gaussian entries, extending known results and introducing an improved Hanson-Wright inequality of independent interest.

Contribution

It extends the RIP results to $\, extphi$-sub-Gaussian matrices and develops a novel Hanson-Wright deviation inequality.

Findings

RIP holds for block diagonal matrices with $\, extphi$-sub-Gaussian entries

Introduces an improved Hanson-Wright deviation inequality

Extends previous sub-Gaussian RIP results

Abstract

In this paper, we prove the restricted isometry property of block diagonal random matrices with elements from $\varphi$-sub-Gaussian variables, which extends the previously known results for the sub-Gaussian case. A crucial ingredient of our proof is an improved uniform Hanson-Wright deviation inequality, which should be of independent interest.