Abstract
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.
Highlights
Compressive sensing (CS) [1], which breaks through the Nyquist sampling theorem, has outstanding advantages for reducing signal storage space, as well as improving signal transmission in real-time and high efficiency
When dynamic sparse circulant (DSC) is used to process twodimensional signals, the peak signal-to-noise ratio (PSNR) and reconstruction time of the reconstructed signals at different compression rates are compared with other measurement matrices used in the experiments
When the compression rate is between 0.6 and 0.8, the PSNR of the reconstructed image by the DSC measurement matrix is similar to the sine circulant measurement matrix, and is larger than other measurement matrices used in the experiment
Summary
OF THE CS THEORY AND PROPOSAL OF NC-SINE CHAOTIC MAP CS theory is first introduced in detail. The NC-sine chaotic map is proposed based on the logistic chaotic map, the simple quadratic chaotic map, and the sine chaotic map. The performance of the proposed chaotic map is analyzed
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