Statistical restricted isometry property of orthogonal symmetric Toeplitz matrices

Abstract

Sensing matrices with the restricted isometry property (RIP) play a crucial role in compressed sensing. Although random matrices (i.i.d. Gaussian or Bernoulli) have been proved to satisfy the RIP with high probability, they are heavy in computation and storage. Recently, structurally random matrices or Toeplitz random matrices have been introduced as sensing matrices. Meanwhile, the statistical RIP allows for the usage of deterministic sensing matrices. In this paper, we introduce partial orthogonal symmetric Toeplitz matrices as sensing matrices and prove that this class of matrices satisfies statistical RIP with high probability. Because of the Toeplitz structure, these new sensing matrices can be applied in channel estimation and signal compression with lower computational and storage complexity.