Performance Analysis of Toeplitz Block Sampling Matrix in Compressed Sensing

This paper analyzes the recovery performance when a Toeplitz block matrix is used for sampling in compressed sensing. Different from current work that mainly discusses the restricted isometry property and the applications of such matrix, we provide an upper bound for the mean squared reconstruction error. By comparing with the random matrix in which its entries are drawn independently from certain probability distributions, the results show that the Toeplitz block matrix is efficient for compressed sampling. Simulation results validate that the sampling performance of Toeplitz block matrix can approach that of random matrix by choosing its parameters properly.