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

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.