CSMP:基于约束等距的压缩感知匹配追踪

压缩感知包括压缩采样与稀疏重构,是一种计算欠定线性方程组稀疏解的方法.大规模快速重构方法是压缩感知的研究热点.提出一种匹配追踪算法CSMP,采用迭代式框架和最佳s项逼近以逐步更新信号的支集与幅度.基于约束等距性质进行收敛分析,算法收敛的充分条件为3s阶约束等距常数小于0.23,松弛了匹配追踪重构s稀疏信号的约束等距条件,加快了收敛速度.为适用于大规模稀疏信号重构,提供了可进行随机投影测量子集与稀疏基子集选择的矩阵向量乘算子,可利用离散余弦变换与小波变换,避免了大规模矩阵的显式存储.在2+{20}随机支集的稀疏高斯信号,512×512 Lenna图像上进行压缩采样与稀疏重构实验并与其他算法进行比较,结果表明所提算法快速稳健,适用于大规模稀疏信号重构.

CSMP: Compressive Sensing Matching Pursuit Based on Restricted Isometry Property

Compressive sensing consists of compressed sampling and sparse reconstruction,which is a method to compute sparse solution for underdetermined linear systems.Large scale and fast reconstruction method has become an active research topic of compressive sensing.In this paper,a matching pursuit algorithm is presented and named CSMP.It adopts iterative framework and best s term approximation to update signal support and magnitude.Convergence analysis is developed based on restricted isometry properties(RIP).The sufficient condition for the convergence of CSMP is established with 3s order restricted isometry constant(RIC) less than 0.23,which relaxes the RIC condition for recovering s sparse signal by matching pursuit and improves the convergence speed.In order to adapt for large scale sparse signal reconstruction,the proposed method is equipped with matrix-vector multiplication operator which can select subsets of both random projection measurements and sparse bases,therefore becoming able to utilize discrete cosine transform and wavelet transform,avoiding explicit storage of large scale matrix.Compressive sampling and reconstruction experiments are conducted on 220 sparse Gaussian signal with random support and on 512 by 512 Lenna image.Comparisons with other algorithms demonstrate that the proposed method is stable and fast for large scale sparse signal reconstruction in compressive sensing.