Construction of a Class of Logistic Chaotic Measurement Matrices for Compressed Sensing

Abstract

The construction of the measurement matrix is the key technology for accurate recovery of compressed sensing. In this paper, we demonstrated correlation properties of nonpiecewise and piecewise logistic chaos system to follow Gaussian distribution. The correlation properties can generate a class of logistic chaotic measurement matrices with simple structure, easy hardware implementation and ideal measurement efficiency. Specifically, spread spectrum sequences generated by the correlation properties follow Gaussian distribution. Thus, the proposed algorithm constructs chaos-Gaussian matrices by the sequences. Simulation results of one-dimensional signals and two-dimensional images show that chaos-Gaussian measurement matrices can provide comparable performance against common random measurement matrices. In addition, chaos-Gaussian matrices are deterministic measurement matrices.