基于m序列的压缩感知测量矩阵构造

Construction of Compressed Sensing Matrixs Based on m Sequences

摘要: 测量矩阵作为压缩感知理论的核心内容，对信号的测量和重构会产生重大影响。本文主要基于m序列构造压缩感知测量矩阵。首先，给出一种压缩率为0.5的测量矩阵构造方法，利用该方法构造的测量矩阵元素取值集合较小，具有一定的循环特性。其次，结合有限域的理论，对利用m序列构造的测量矩阵做进一步改进，改进后测量矩阵的压缩率取值范围增大加。仿真结果表明：本文构造的测量矩阵的重构性能优于同大小的Gause测量矩阵，避免了随机性测量矩阵的不确定性，具有一定实用价值。

Abstract: The measurement matrix as the core of the compressed sensing theory, will have a significant im-pact on the measurement and reconstruction. This paper produces a method of compressed sensing measurement matrix through the m sequences. First of all, it gives a method to construct the measurement matrix with compression rate is 0.5; this measurement matrix has small element set and certain cycle characteristics. Secondly, for combining the theory of finite fields, the measure-ment matrix based on m sequence is further improved. The compression rate of the matrix mea-surement range is greatly increased. The simulation results show that the measurement matrix is constructed in this paper which is better than Gause measurement matrix reconstruction perfor-mance of the same size, avoids the random measurement matrix uncertainty and has a certain practical value.