Design of a Dynamic Sparse Circulant Measurement Matrix Based on a New Compound Sine Chaotic Map
Design of a Dynamic Sparse Circulant Measurement Matrix Based on a New Compound Sine Chaotic Map
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基于新型复合正弦混沌映射的动态稀疏循环测量矩阵设计
DOI：
10.1109/access.2022.3142535
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发表时间：
2022-01-01
期刊：
影响因子：
3.9
通讯作者：
Zhou, Zhenxiong
中科院分区：
文献类型：
--
作者：
Jin, Jiliang;Xing, Liyun;Zhou, Zhenxiong
测量矩阵的性能一直是影响压缩感知在工程实践中应用的关键因素。基于混沌映射设计的测量矩阵易于在物理电路中实现，但常见的一维混沌映射的弱混沌行为和小混沌间隔直接影响信号重建的精度。针对这一问题，利用Logistic混沌映射与简单二次混沌映射的比值形式对正弦混沌映射进行改进，得到了一种新的复合正弦（NC-sine）混沌映射。通过分岔图、李雅普诺夫指数和复杂性分析，验证了该模型良好的混沌行为和混沌区间扩展特性。基于NC正弦混沌映射，设计了一种具有自适应置零元素的动态稀疏循环（DSC）测量矩阵。仿真结果表明，与正弦测量矩阵相比，当测量值和稀疏度发生变化时，对于一维信号，DSC测量矩阵的重构成功率平均提高了5%和9.69%。不同压缩率下重建的二维信号峰值信噪比平均提高0.92 dB以上，重建效率更高。不同初始值下重构信号的平均结构相似度比高斯测量矩阵的平均结构相似度提高了0.027以上。因此，可以利用该矩阵来提高信号传输的速率和准确性。
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.