Orthogonal symmetric Toeplitz matrices for compressed sensing: Statistical isometry property
Abstract
Recently, the statistical restricted isometry property (RIP) has been formulated to analyze the performance of deterministic sampling matrices for compressed sensing. In this paper, we propose the usage of orthogonal symmetric Toeplitz matrices (OSTM) for compressed sensing and study their statistical RIP by taking advantage of Stein's method. In particular, we derive the statistical RIP performance bound in terms of the largest value of the sampling matrix and the sparsity level of the input signal. Based on such connections, we show that OSTM can satisfy the statistical RIP for an overwhelming majority of signals with given sparsity level, if a Golay sequence used to generate the OSTM. Such sensing matrices are deterministic, Toeplitz, and efficient to implement. Simulation results show that OSTM can offer reconstruction performance similar to that of random matrices.
Keywords
Cite
@article{arxiv.1012.5947,
title = {Orthogonal symmetric Toeplitz matrices for compressed sensing: Statistical isometry property},
author = {Kezhi Li and Lu Gan and Cong Ling},
journal= {arXiv preprint arXiv:1012.5947},
year = {2015}
}
Comments
This paper has been withdrawn by the authors due to an error. It will be replaced with a new paper shortly