一种基于复合混沌映射的压缩感知测量矩阵构造方法研究  

Construction of Measurement Matrix in Compressive Sensing Based on Composite Chaotic Mapping

作　　者：周伟[1] 景博[1] 张航 黄以锋[1] 李娟[1] 

机构地区：[1]空军工程大学航空航天工程学院,陕西西安710038 [2]北京机电工程研究所,北京100074

出　　处：《电子学报》2017年第9期2177-2183,共7页Acta Electronica Sinica

摘　　要：针对常用随机测量矩阵存在硬件实现困难的不足,提出一种基于复合混沌映射的压缩感知确定性测量矩阵构造方法.首先基于Logistic映射和Tent映射构造随机性和初值敏感性更强的复合混沌映射,然后将复合混沌迭代序列经大间隔采样后进行线性变换得到的结果作为拟构造测量矩阵中的元素,并从理论上证明了该矩阵元素具有非常低的相关性.同时理论证明了所构造复合混沌测量矩阵能以高概率满足压缩感知约束等距性.实验结果表明,所构造复合混沌测量矩阵的性能优于Toeplitz测量矩阵及Logistic映射测量矩阵,与高斯随机测量矩阵的性能相仿.Aiming at the difficult in hardware realization of random measurement matrix,we construct a deterministic measurement matrix based on composite chaotic mapping. The composite chaotic mapping that based on Tent mapping and Logistic mapping,has stronger randomicity and initial value sensitivity. Sampled the composite chaotic mapping sequence with large distance,and then do linear transformation to the sampling sequence. Finally,we construct the measurement matrix with the linear transformation result. We prove that the measurement matrix elements have enough statistically independent,and the measurement matrix can satisfies restricted isometry property（ RIP） with large probability. The simulation result shows that our matrix has the similar performance to Gaussian random matrix,and better than Toeplitz deterministic measurement matrix and Logistic deterministic measurement matrix.

关 键 词：压缩感知 测量矩阵 混沌映射 约束等距性 

分 类 号：TP212.9[自动化与计算机技术—检测技术与自动化装置]