LAUSR

The performance of the measurement matrix is always the key to affecting the application of compressed sensing in engineering practice. The measurement matrix designed based on the 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 affects 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 the bifurcation diagram, the Lyapunov exponent, and the 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 rate of the DSC measurement matrix is 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 under 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 the Gaussian measurement matrix. This can then be utilized for the promotion of signal transmission in rate and accuracy.