Abstract: Measurement matrix is an important part of the compressed sensing theory,and is related to the reconstructed accuracy of original signals.To address the low reconstruction accuracy of common measurement matrixes,this paper proposes a random measurement matrix based on Markov Chain.Firstly,M random numbers are generated by using the randomness of Markov Chain,and respectively mapped to -1 and 1 based on certain rules to serve as the elements of an M×M diagonal matrix.Secondly,M×(N-M) random numbers are generated by using Markov Chain,and mapped to 0 and 1 respectively to form an M×(N-M) matrix.Finally,the two matrixes are combined to form an M×N measurement matrix.Simulation results show that the proposed matrix has a simple structure,and can significantly improve the reconstruction accuracy compared with commonly used measurement matrixes and Toeplitz structure matrixes based on singular value decomposition.The proposed matrix also reduces the amount of calculation and saves storage space.

Key words: compressed sensing, measurement matrix, Markov chain, random number, mapping

摘要： 测量矩阵是压缩感知理论中的重要组成部分，其将直接影响原始信号的重构精度。针对常用测量矩阵重构精度较低的问题，构造一种基于马尔科夫链的随机测量矩阵。利用马尔科夫链的随机性生成M个随机数，将随机数按照规则分别映射为-1和1后作为M×M维对角矩阵的元素，采用马尔科夫链生成M×（N-M）个随机数并按照规则分别映射为0和1，构成包含0和1元素的M×（N-M）维矩阵，并将这两部分矩阵相结合形成M×N的测量矩阵。仿真结果表明，该矩阵结构简单，相比常用测量矩阵和基于奇异值分解的Toeplitz结构矩阵重构精度得到明显提升，并且减少了运算量与存储空间。

关键词: 压缩感知, 测量矩阵, 马尔科夫链, 随机数, 映射

CLC Number: 

• TN911.7