压缩感知测量矩阵综述

Overview of compressed sensing measurement matrices

压缩感知是一种新的采样和重建数字信号的方法,可以在低于奈奎斯特采样率的条件下实现原始信号的精确恢复。在稀疏信号的精确重建中,测量矩阵十分关键。性能良好的测量矩阵可确保信号恢复的精确性,改善重建算法的性能。为比较在压缩感知中各矩阵性能的差异,本文使用两步迭代收缩阈值算法,比较高斯矩阵、伯努利矩阵、混沌矩阵、稀疏矩阵、托普利兹矩阵、循环矩阵、部分哈达玛矩阵在不同测量数目、信号稀疏度、噪声的大小对于信号重建成功率的影响。由实验结果可得,这七类矩阵中混沌矩阵为最优测量矩阵。

Compressed sensing theory is a new method for sampling and reconstruction of digital signals.It can recover the original signal accurately with lower than Nyquist sampling rate.The measurement matrix plays a crucial role in the process of sparse signal reconstruction.The measurement matrix with good performance can ensure the accuracy of signal reconstruction and improve the performance of reconstruction algorithm.In order to compare the difference in performance of each matrix in compressed sensing,the experiment uses a two-step iterative shrinkage threshold algorithm.Then we compare the influence of Gaussian Matrix,Bernoulli Matrix,Partial Hadamard Matrix,Toeplitz Matrix,Circulant Matrix,Chaotic Matrix and Sparse matrix on the number of different measurements,the signal sparsity,and the magnitude of the noise on the signal reconstruction success rate.The experimental results show that the performance of the chaotic random measurement matrix is optimal in these seven types of measurement matrices.