The essential ability of sparse reconstruction of different compressive sensing strategies  

作　　者：ZHANG Hai LIANG Yong GOU HaiLiang XU ZongBen 

机构地区：[1]Institute for Information and System Science,Xi'an Jiaotong University,Xi'an 710049 [2]Department of Mathematics,Northwest University,Xi'an 710069,China [3]University of Science and Technology,Macao 999078,China

出　　处：《Science China(Information Sciences)》2012年第11期2582-2589,共8页中国科学（信息科学）（英文版）

基　　金：supported by National Basic Research Program of China (Grant No. 2007CB311002);National Natural Science Foundation of China (Grant Nos. 60975036,11171272);Macao Science and Technology Development Fund (Grant No. 021/2008/A) of Macao Special Administrative Region of the People’s Republic of China

摘　　要：We show the essential ability of sparse signal reconstruction of different compressive sensing strate- gies,which include the L1 regularization, the L0 regularization（thresholding iteration algorithm and OMP algo- rithm）, the Lq（0 〈 q ≤ 1） regularizations, the Log regularization and the SCAD regularization. Taking phase diagram as the basic tool for analysis, we find that （i） the solutions of the L0 regularization using hard thresh- olding algorithm and OMP algorithm are similar to those of the L1 regularization; （ii） the Lq regularization with the decreasing value of q, the Log regularization and the SCAD regularization can attain sparser solutions than the L1 regularization; （iii） the L1/2 regularization can be taken as a representative of the Lq（0 〈 q 〈 1） regularizations. When 1/2 〈q 〈 1, the LI/2 regularization always yields the sparsest solutions and when 0 〈 q 〈 1/2 the performance of the regularizations takes no significant difference. The results of this paper provide experimental evidence for our previous work.We show the essential ability of sparse signal reconstruction of different compressive sensing strate- gies,which include the L1 regularization, the L0 regularization（thresholding iteration algorithm and OMP algo- rithm）, the Lq（0 〈 q ≤ 1） regularizations, the Log regularization and the SCAD regularization. Taking phase diagram as the basic tool for analysis, we find that （i） the solutions of the L0 regularization using hard thresh- olding algorithm and OMP algorithm are similar to those of the L1 regularization; （ii） the Lq regularization with the decreasing value of q, the Log regularization and the SCAD regularization can attain sparser solutions than the L1 regularization; （iii） the L1/2 regularization can be taken as a representative of the Lq（0 〈 q 〈 1） regularizations. When 1/2 〈q 〈 1, the LI/2 regularization always yields the sparsest solutions and when 0 〈 q 〈 1/2 the performance of the regularizations takes no significant difference. The results of this paper provide experimental evidence for our previous work.

关 键 词：compressive sensing REGULARIZATION SPARSITY L1/2 regularization 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构] TP18[自动化与计算机技术—计算机科学与技术]