Computer Science ›› 2017, Vol. 44 ›› Issue (Z6): 97-98.doi: 10.11896/j.issn.1002-137X.2017.6A.020

Previous Articles     Next Articles

Equivalent Representation of Compressed Sensing Optimization Problem and Its Penalty Function Method

MENG Zhi-qing, XU Lei-yan, JIANG Min and SHEN Rui   

  • Online:2017-12-01 Published:2018-12-01

Abstract: Firstly,the definition of an equivalent representation for compressed sensing optimization problem was given.It is proved that an optimal solution to the equivalent representation problem is an optimal solution to compressed sen-sing problem.Then an objective penalty function was defined,which has more than 2 order of smoothness,and its iterative algorithm was given.The convergence of the algorithm was proved.By solving the objective penalty function,the approximate optimal solution of compressed sensing optimization problem can be obtained.This method provides a new tool for us to study and solve the actual compressed sensing.

Key words: Compressive sensing,Equivalent representation,Sparse optimization,Object penalty function

[1] CANDS E,TAO T.Near optimal signal recovery from random projections:Universal encoding strategies [J].IEEE Trans Info.Theory,2006,52(12):5406-5425.
[2] 文再文,印卧涛,刘歆,等.压缩感知和稀疏优化简介[J].运筹学学报,2012,6(3):49-65.
[3] 邵文泽,韦志辉.压缩感知基本理论:回顾与展望[J].中国图象图形学报,2012,7(1):1-12.
[4] 宋长明,惠庆磊.压缩感知中图像重构的模型综述[J].中原工学院学报,2016,7(4):80-84.
[5] 陶卿,高乾坤,姜纪远,等.稀疏学习优化问题的求解综述[J],软件学报,2013,24(11):2498-2507.
[6] 于春梅.稀疏优化算法综述[J].计算机工程与应用,2014,0(11):210-217.
[7] 兰美辉.基于惩罚似然优化模型的本体稀疏向量计算算法[J].云南师范大学学报(自然科学版),2015,35(4):51-55.
[8] 张海,梁勇,徐宗本,等.基于SCAD罚函数的有噪压缩感知[J].数学学报,2013,6(5):767-776.
[9] WANG Y,WANG J J,XU Z B.Restricted p-isometry properties of nonconvex block-sparse compressed sensing[J].Signal Processing,2014,4:188-196.
[10] ZHU Y,WU J,YU G H.A Fast Proximal Point Algorithm for l1-Minimization Proble Mincompressed Sensing[J].Applied Mathematics and Computation,2015,270:777-784.
[11] 文婷婷,马兆楠,裴炳.基于拟牛顿法的压缩感知重构零范数平滑算法[J].计算机应用,2015,35(S2):17-19,23.
[12] 杜卓明,李洪安,康宝生,等.二阶收敛的光滑正则化压缩感知信号重构方法[J].中国图象图形学报,2016,21(4):490-498.
[13] MENG Z Q,DANG C Y,JIANG M,et al.Exactness and Algorithm of an Objective Penalty Function[J].Journal Globel Optimization,2013,56:691-711.
[14] HENG Y,MENG Z Q,SHEN R.An M-Objective Penalty Func-tion Algorithm Under Big Penalty Parameters[J].J Syst Sci Complex,2016,29:455-471.

No related articles found!
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!