基于冗余紧框架的?2/?1极小化块稀疏压缩感知  

Block-sparse compressed densing with redundant tight frames via ?2/?1-minimization

作　　者：张枫 王建军[1] Zhang Feng;Wang Jianjun(School of Mathematics and Statistic,Southwest University,Chongqing 400715,China)

机构地区：[1]西南大学数学与统计学院

出　　处：《纯粹数学与应用数学》2019年第2期138-150,共13页Pure and Applied Mathematics

基　　金：国家自然科学基金(61673015,61273020);西南大学实验技术研究项目(SYJ2019031);中央高校基本业务费专项(XDJK2018C076,SWU1809002)

摘　　要：压缩感知是(近似)稀疏信号处理的研究热点之一,它突破了Nyquist/Shannon采样率,实现了信号的高效采集和鲁棒重构.本文采用l2/l1极小化方法和BlockD-RIP理论研究了在冗余紧框架下的块稀疏信号,所获结果表明,当BlockD-RIP常数δ2k/τ满足0<δ2k/τ<0.2时,l2/l1极小化方法能够鲁棒重构原始信号,同时改进了已有的重构条件和误差上界.基于离散傅里叶变换(DFT)字典,执行了一系列仿真实验充分证实了理论结果.Compressed sensing is one of the hot research theories for (approximately) sparse signal processing which breaks through Nyquist/Shannon sampling theory, and makes it into reality that one can efficiently acquire and exactly reconstruct a signal. This paper mainly investigated the signals which are block-sparse under redundant tight frames based on l2/l1-minimization method and Block DRIP theory. Under the condition 0 <δ2k/τ < 0.2, the obtained results show that l2/l1-minimization method can robustly reconstruct the original signal, meanwhile, improve the existing reconstruction condition and error upper bound.Using the discrete Fourier transform dictionary, we conducted a series of simulation experiments which sufficiently verified the theoretical results.

关 键 词：压缩感知 l2/l1极小化方法 BlockD-RIP 冗余紧框架 块稀疏信号 

分 类 号：O29[理学—应用数学]