采样列化的切比雪夫混沌测量矩阵构造算法研究  

Study on construction of Chebyshev chaotic measurement matrix based on sampling columnization

作　　者：赵志俊[1] 许统德[2] 戴晨昱[3] Zhao Zhijun Xu Tongde Dai Chenyu(Sontan College of Guangzhou University, Zengcheng Guangdong 511370, China Guangdong AIB Polytechnic, Guangzhou 510507, China China Mobile Group Guangdong Co. , Ltd, Guangzhou 510000, China)

机构地区：[1]广州大学松田学院 [2]广东农工商职业技术学院 [3]中国移动通信集团广东有限公司

出　　处：《计算机应用研究》2017年第9期2675-2679,共5页Application Research of Computers

基　　金：广东省省级课题资助项目(GDYJSKT16-08);广东省高等职业教育教学改革立项课题(201401154)

摘　　要：压缩感知利用信号的稀疏性,无损地从低维测量信号中恢复高维度稀疏信号。然而,目前存在的测量矩阵中大多存在元素相关性高等问题,无法保证恢复效果的精确性,大大制约了它们的应用前景。针对此问题,通过引入切比雪夫混沌系统,提出一种基于采样列化的切比雪夫混沌感知测量矩阵(SC3M)。不同于经典的相对独立取值的构造方法,SC3M矩阵通过对切比雪夫混沌序列作采样列化及归一化处理等操作来确保矩阵的低列相关性,以优化重构效果;进一步,结合Johnson-Lindenstrauss引理严格证明了其满足约束等距特性(restricted isometric property,RIP),给提出的测量矩阵的应用提供了扎实的理论依据。实验仿真表明,提出的混沌测量矩阵能确保良好的信号和图像重构精度,明显优于纯随机矩阵、伯努利矩阵和高斯矩阵等其他经典测量矩阵。Compressive sensing is a new sampling theory which makes use of the sparsity of signals to recover the high-dimen- sion signal from very few measurements. Unfortunately, most of the existing measurement matrices have high correlation between elements, which can not guarantee exact recovery and has greatly restricted their application prospects. Based on this, this paper proposed a novel Chebyshev chaotic measurement sensing matrix based on sampling columnization（SC3M）. The sampling columnization and normalization guaranteed the low correlation in column of SC3M, which optimized the recovery effect. Moreover, it proved that the proposed SC3M sensing matrix satisfies the RIP with overwhelming probability from the Johnson-Lindenstrauss lemma. Numerical simulations show that the SC3M is sufficient to guarantee exact recovery, which shows better effect compared to other popular measurement matrixes such as the fully random matrix, Bernoulli matrix and Gaussian sensing matrix.

关 键 词：压缩感知 测量矩阵 切比雪夫 混沌系统 约束等距特性 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]