基于Logistic混沌-贝努力序列的循环压缩测量矩阵构造算法  

A Construction Algorithm of Circulant Compressive Measurement Matrix Based on Logistic Chaotic-Bernoulli Sequence

作　　者：臧华中[1] 

机构地区：[1]三江学院计算机科学与工程学院,南京210012

出　　处：《四川理工学院学报（自然科学版）》2015年第5期31-36,共6页Journal of Sichuan University of Science & Engineering(Natural Science Edition)

摘　　要：作为信号处理的一个新领域,压缩感知的目标是尽量减少信号重构过程中采样点的损失,而压缩感知矩阵的构造是压缩感知的核心工作之一。在前人研究的基础上,将循环矩阵快速算法的优点和混沌序列内在确定性和外在随机性相结合的优点进行有效结合,提出了一种新的压缩感知测量矩阵构造算法,即基于Logistic混沌—贝努利序列和循环矩阵的循环压缩感知测量矩阵构造算法(CCNMM)。大量仿真实验结果表明,对于一维和二维信号的恢复,CCNMM算法优于贝努利随机测量矩阵和高斯测量矩阵,证明了CCNMM的有效性和实用性。Compressed sensing is a new area of signal processing. Its goal is to minimize the loss of sampling site that need to be taken from signal reconstruction. Construction of a compressive sensing matrix is one of the key technologies of compressive sensing. On the basis of the study of the predecessors,a novel construction algorithm of compressive sensing measurement matrix,that is the construction algorithm of circulant compressive sensing measurement matrix based on Logistic chaotic Bernoulli sequence and circulant matrix（ CCNMM）,is presented. This algorithm employs circulant matrix for its advantage in high calculation speed and chaotic sequence for its ability of the effective combination of internal certainty and external randomness. A variety of simulation studies have been done and simulation results demonstrate that,compared with Bernoulli random measurement matrix and Gaussian measurement matrix,one-dimensional and two-dimensional signals can be better reconstructed by CCNMM,which powerfully proved the practicability and effectiveness of the proposed algorithm.

关 键 词：压缩感知 测量矩阵 Logistic混沌 贝努力序列 循环矩阵 

分 类 号：TN911.7[电子电信—通信与信息系统]