基于混合l_2/l_1范数极小化方法的块稀疏信号重构条件  

Improved Conditions of Block-Sparse Signals Recovery via Mixed l_2/l_1 Norm Minimization

作　　者：王建军[1] 袁建军[1] 王尧[2] 

机构地区：[1]西南大学数学与统计学院,重庆400715 [2]西安交通大学数学与统计学院,西安710049

出　　处：《数学学报（中文版）》2017年第4期619-630,共12页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(61673015;61273020;11501440;11001227);中央高校基本科研业务费资助项目(XDJK2015A007)

摘　　要：研究压缩感知中的块稀疏信号重构问题,主要对混合l_2/l_1极小化方法建立了一类改进的可重构条件.具体地说,本文证明若测量矩阵满足条件δ_k+θ_(k,k)<1,则混合l_2/l_1极小化方法可精确重构(无噪声情形)或鲁棒重构(有噪声情形)原始块k-稀疏信号.进而表明本文给出的新条件弱于现有文献所给出的条件.Abstract We study the block-sparse signal recovery under compressed sensing frame-work. We mainly establish an improved condition on the restricted isometry property in both noiseless and noisy cases for mixed l2/l1 norm minimization. Especially, we prove that under the condition δκ＋θκ,κ〈1 for measurement matrix, any block κ- sparse signals can be exactly recovered in the noiseless case and robustly recovered in the noisy case by mixed l2/l1 minimization method. Finally, we further show that the obtained condition is clearly weaker than existing ones in the literature.

关 键 词：压缩感知 块稀疏信号 混合l2/l1极小化方法 可重构条件 

分 类 号：O177.2[理学—数学]