| 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 |
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| 引用本文： | 王建军,袁建军,王尧.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[J].数学学报,2017,60(4):619-630. |
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| 作者姓名： | 王建军 袁建军 王尧 |
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| 作者单位： | 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 |
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| 基金项目： | 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） |
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| 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.
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| 关 键 词： | 压缩感知 块稀疏信号 混合l_2/l_1极小化方法 可重构条件 |
Improved Conditions of Block-Sparse Signals Recovery via Mixed l2/l1 Norm Minimization |
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| Jian Jun WANG,Jian Jun YUAN,Yao WANG.Improved Conditions of Block-Sparse Signals Recovery via Mixed l2/l1 Norm Minimization[J].Acta Mathematica Sinica,2017,60(4):619-630. |
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| Authors: | Jian Jun WANG Jian Jun YUAN Yao WANG |
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| Institution: | 1. School of Mathematics and Statistics, Southwest University, Chongqing 400715, P. R. China;
2. School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, P. R. China |
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| Abstract: | We study the block-sparse signal recovery under compressed sensing framework.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 δk+θk,k < 1 for measurement matrix,any block k-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. |
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| Keywords: | compressed sensing block-sparse signal mixed l2/l1 norm minimization recovery condition |
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