关键词: 压缩感知, 稀疏表示, 观测矩阵, 重构算法, 奇异值分解

Abstract:

In recent years,the emergence of compressed sensing has broken the limit of Nyquist sampling.The original signal can be recovered accurately by observed values,which is much less than the length of original signal.But now the theory of compressed sensing is not mature enough,and the image reconstruction accuracy is not ideal.In this paper,the design method for the observation matrix has been improved by firstly giving weights to the observation matrix according to the characteristics of sparse signal and then making all the elements on the diagonal of the diagonal matrix obtained by the singular value of weighted matrix to be 1.Experimental results show that the value of PSNR has increased by about 1~2 dB at large compression ratios,by almost 8~9 dB at small compression ratios with the improved matrix used as observation matrix of compressed sensing.

Key words: compressed sensing;sparse representation;observation matrix;reconstruction algorithm;singular value decomposition