基于广义变参Fibonacci混沌系统的压缩感知测量矩阵构造算法

针对常见混沌映射随机性不高、序列元素相关性较强、构造测量矩阵元素需间隔采样来满足数据统计的独立性等问题,通过级联量子Logistic混沌系统和广义Fibonacci数列构造一种新的复合混沌系统.在信息熵、空间特性和相关系数等方面对不同混沌测量矩阵进行定量分析,验证了提出的混沌系统具有遍历性和很强的混沌特性要求,序列元素具有较低相关性,满足数据统计的独立性要求.证明了提出的混沌系统构造的压缩感知测量矩阵满足RIP条件.实验分别对一维稀疏信号和二维图像进行仿真和讨论,结果表明,相较于其他测量矩阵采样率在1/2时,基于所提系统的压缩感知矩阵构造算法的一维稀疏信号重构成功率提高了4％,二维图像重构的信噪比提高了0.2 dB.测量矩阵的构造无需对采样间隔进行提前估计,提高了数据利用率,解决了其他混沌测量矩阵间隔采样造成的极大数据资源浪费的问题.

A compressed sensing measurement matrix construction algorithm based on generalized variable parameter Fibonacci chaotic system

Aiming at the problems that common chaotic mapping has low randomness, sequence elements has strong correlation, and constructing the measurement matrix elements requires interval sampling to satisfy the independence of data statistics, a new composite chaotic system is constructed by cascading quantum Logistic chaotic system and generalized Fibonacci sequence. In terms of information entropy, spatial characteristics and correlation coefficients, different chaotic measurement matrices are quantitatively analyzed to verify that the proposed chaotic system has ergodicity and high chaos. More- over, the sequence elements have low correlation, which satisfies the independence of data statistics. At the same time, it is proved that the compressed sensing measurement matrix constructed by the proposed chaotic system satisfies the RIP condition. Simulation and discussion on one-dimensional sparse signal and two-dimensional image show that, compared with other measurement matrices, when the sampling rate is 1/2, the proposal increases the success rate of reconstructing one-dimensional sparse signals by 4%, and increases the SNR rate of reconstructing two-dimensional images by 0.2dB. It improves the data utilization rate and overcomes the great waste of data resources caused by the interval sampling of other chaotic measurement matrices.