Design of a Dynamic Sparse Circulant Measurement Matrix Based on a New Compound Sine Chaotic Map

The performance of a measurement matrix is always the key factor affecting the application of compressed sensing in engineering practice. A measurement matrix designed based on a chaotic map is easy to implement in physical circuits, but the weak chaotic behavior and small chaotic interval of the common one-dimensional chaotic map directly affect the signal reconstruction accuracy. To solve this problem, this paper uses the ratio form of the logistic chaotic map to the simple quadratic chaotic map to improve the sine chaotic map and obtain a new type of compound sine (NC-sine) chaotic map. Its good chaotic behavior and chaotic interval expansion characteristics are verified by a bifurcation diagram, the Lyapunov exponent, and complexity analysis. Based on the NC-sine chaotic map, a dynamic sparse circulant (DSC) measurement matrix with adaptive zero-setting elements is designed. The simulation results show that compared with the sine measurement matrix, the reconstruction success rates of the DSC measurement matrix are increased by 5% and 9.69% on average for a one-dimensional signal when the measurements and sparsity change, respectively. The peak signal-to-noise ratio of the reconstructed two-dimensional signals at different compression rates is improved by more than 0.92 dB on average, and the reconstruction efficiency is higher. The average structural similarity of the reconstructed signals at different initial values is improved by more than 0.027 compared to that of the Gaussian measurement matrix. This matrix can thus be utilized to promote the rate and accuracy of signal transmission.