基于两次分段弱选择的压缩感知子空间追踪算法  

Compressed sensing subspace pursuit algorithm based on two stagewise weak selection

作　　者：王博伟 谭劲 WANG Bowei;TAN Jin(College o f Information Engineering,China Ji Liang University,Hangzhou 310018,China)

机构地区：[1]中国计量大学信息工程学院,浙江杭州310018

出　　处：《电信科学》2020年第5期83-92,共10页Telecommunications Science

基　　金：浙江省自然科学基金资助项目(No.LY16F020013)。

摘　　要：压缩感知是一种新的信号采样和数据压缩方式,子空间追踪算法在压缩感知重构算法中兼具较高的效率和精度,但是它需要将信号的稀疏度作为先验信息,如果稀疏度估计不够准确会降低算法重构效果。针对这个问题,提出一种基于两次分段弱选择的子空间追踪算法,它不需要预先知道信号的稀疏度,第一次弱选择自适应地选择初始原子候选集,第二次弱选择自适应地从当前原子支撑集中剔除之前可能选择的错误原子,最后通过回溯法从当前原子候选集中选择多个相关原子加入原子支撑集。仿真分析表明,该算法可以在稀疏度未知的情况下实现一维随机信号和二维图像信号的精确重构,且具有较高的稳定性;与OMP算法、SWOMP算法、BAOMP算法、SAMP算法和SP算法相比,均方误差降低了60.5%~99.1%,峰值信噪比提高了2.1%~34.3%。Compressed sensing is a new way of signal sampling and data compression. The subspace pursuit algorithm has higher efficiency and precision in the compressed sensing reconstruction algorithms, but it needs the sparsity of the signal as a priori information. And if the sparsity estimation is not accurate enough, it will reduce the algorithm reconstruction effect. Aiming at this problem, a two stagewise weak selection-based subspace pursuit(TSWSP) algorithm was proposed, which didn’t need to know the sparsity of the signal in advance. The first weak selection adaptively selected the initial atom candidate set, and the second weak selection adaptively culled the wrong atoms that may had been previously selected from the current atom support set, and finally it selected a plurality of related atoms from the current atom candidate set to join the atom support set by the backtracking method. Simulation analysis shows that the proposed algorithm can reconstruct one-dimensional random signals and two-dimensional image signals accurately with unknown sparsity, and it has high stability, compared with OMP, SWOMP, BAOMP, SAMP and SP algorithm, the mean-square erroris reduced by 60.5% to 99.1%, the peak signal-to-noise ratio is improved by 2.1% to 34.3%.

关 键 词：压缩感知 子空间追踪 分段弱选择 信号重构 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]