Computer Science ›› 2019, Vol. 46 ›› Issue (6A): 133-137.

• Intelligent Computing • Previous Articles     Next Articles

Alternate Random Search Algorithm of Objective Penalty Function for Compressed Sensing Problem

JIANG Min1, MENG Zhi-qing1, SHEN Rui2   

  1. School of Management,Zhejiang University of Technology,Hangzhou 310023,China1;
    School of Economics,Zhejiang University of Technology,Hangzhou 310023,China2
  • Online:2019-06-14 Published:2019-07-02

Abstract: The compressed sensing optimization problem was defined as a biconvex optimization problem.It is proved that the optimal solution of the equivalent biconvex optimization problem is also the optimal solution of the compressed sensing optimization problem.Then a smooth objective penalty function and its corresponding alternating sub-problem were defined.An iterative algorithm for solving the sub-problem was given.The convergence theorem of alternating algorithm was proved theoretically.The expression of the optimal solution for compression perception was derived.An alternating random search algorithm was designed,which is effective for a specific type of compressed sensing problem.This method provides a new design idea for studying and solving the actual compressed sensing problem.

Key words: Alternating random search algorithm, Compressive sensing, Equivalent representation, Object penalty function, Sparse optimization

CLC Number: 

  • TP391.4
[1]CANDÈS E,TAO T.Near optimal signal recovery from random projections:Universal encoding strategies [J].IEEE Trans. Info.Theory,2006,52(12):5406-5425.
[2]CANDÈS E J,WAKIN M B,BOYD S P.Enhancing Sparsity by Reweighted l1 Minimization[J].J. Fourier Anal. Appl.,2008,14:877-905.
[3]CHARTRAND R,YIN W.Iteratively reweighted algorithms for compressive sensing[C]∥Proc.IEEE Int.Conf.Acoust,Speech,Signal Process.2008:3869-3872.
[4]MOHIMANI H,BABIE-ZADEH M,JUTTEN C.A fast ap-proach for overcomplete sparse decomposition based on smoothed l0-norm[J].IEEE Trans.Signal Process.,2009,57(1):289-301.
[5]FOUCART S,RAUHUT H.A Mathematical Introduction to Compressive Sensing[M].Springer,New York,2013.
[6]PANT J K,LU W S,ANTONIOU A.New Improved Algo-rithms for Compressive Sensing Based on lp Norm[J].IEEE Transactions on Circuits and Systems-II:Express Briefs,2014,61(3):198-202.
[7]WANG Y,WANG J J,XU Z B.Restricted p-isometry properties of nonconvex block-sparse compressed sensing[J].Signal Processing,2014,104:188-196.
[8]ZHU Y,WU J,YU G H.A fast proximal point algorithm for l1-minimization problem mincompressed sensing[J].Applied Mathematics and Computation,2015,270:777-784.
[9]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.
[10]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.
[11]MENG Z Q,DANG C Y,JIANG M,et al.Exactness and algorithm of an objective penalty function.Journal Globel Optimization,2013,56:691-711.
[12]GORSKI J,PFEUFFER F,KLAMROTH K.Biconvex sets and optimization with biconvex functions:a survey and extensions[J].Math. Meth. Oper. Res.,2007,66:373-407.
[13]孟志青,徐蕾艳,蒋敏,等.压缩感知优化问题的等价表示及其目标罚函数方法[J].计算机科学,2017,44(S1):97-99.
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