一种新非单调法求解压缩感知问题

›› 2015, Vol. 28 ›› Issue (2): 14-.

一种新非单调法求解压缩感知问题

王文,李永

(西安电子科技大学数学与统计学院,陕西西安 710126)

出版日期:2015-02-15 发布日期:2015-02-16
作者简介:王文(1990—),女,硕士研究生。研究方向:压缩感知重构算法。E-mail:1019463474@qq.com。李永(1988—),男,硕士研究生。研究方向:基于Kriging模型的优化算法。
基金资助:
中央高校基本科研业务费专项基金资助项目(K50513100007)

New Non-monotone Algorithm for Compressed Sensing

WANG Wen,LI Yong

(School of Mathematics and Statistics,Xidian University,Xi'an 710126,China)

Online:2015-02-15 Published:2015-02-16

摘要/Abstract

摘要：

提出了一种新的非单调线搜索Barzilai-Borwein梯度法,并证明了该算法的全局收敛性。通过Matlab数值试验表明,该算法对重构稀疏信号是可行有效的,与其他算法相比,具有迭代次数少,计算用时短等优点。

关键词: 压缩感知, 信号处理, 重构算法, Barzilai-Borwein步长, 非单调线搜索

Abstract:

This paper proposes a new non-monotone Barzilai-Borwein gradient method,and proves the global convergence of the algorithm.Matlab numerical experiments show that the algorithm for sparse signal reconstruction is feasible and effective with the advantages of fewer iterations and less computation time over other algorithms.

Key words: compressed sensing;signal processing;reconstruction algorithm;Barzilai-Borwein step;non-monotone line search

中图分类号:

TN919.8

王文,李永. 一种新非单调法求解压缩感知问题[J]. , 2015, 28(2): 14-.

WANG Wen,LI Yong. New Non-monotone Algorithm for Compressed Sensing[J]. , 2015, 28(2): 14-.

参考文献

［1］石光明,刘丹华,高大化,等.压缩感知理论及其研究进展［J］.电子学报,2009,37(5):1070-1081.

［2］Donoho D L.Compressed sensing［J］.IEEE Transactions on Information Theory,2006,52(4):1289-1306.

［3］Candes E J,Romberg J K,Tao T.Stable signal recovery from incomplete and inaccurate measurements［J］.Communications on Pure and Applied Mathematics,2006,59(8):1207-1223.

［4］Candès E J,Romberg J,Tao T.Robust uncertainty principles:Exact signal reconstruction from highly incomplete frequency information［J］.IEEE Transactions on Information Theory,2006,52(2):489-509.

［5］Mallat S G,Zhang Z.Matching pursuits with time-frequency dictionaries［J］.IEEE Transactions on Signal Processing,1993,41(12):3397-3415.

［6］Tropp J A,Gilbert A C.Signal recovery from random measurements via orthogonal matching pursuit［J］.IEEE Transactions on Information Theory,2007,53(12):4655-4666.

［7］Do T T,Gan L,Nguyen N,et al.Sparsity adaptive matching pursuit algorithm for practical compressed sensing［C］.2008 42nd Asilomar Conference on Signals,Systems and Computers,IEEE,2008:581-587.

［8］Needell D,Vershynin R.Signal recovery from incomplete and inaccurate measurements via regularized orthogonal matching pursuit［J］.IEEE Journal of Selected Topics in Signal Processing,2010,4(2):310-316.

［9］Chen S S,Donoho D L,Saunders M A.Atomic decomposition by basis pursuit［J］.SIAM Journal on Scientific Computing,1998,20(1):33-61.

［10］Figueiredo M A T,Nowak R D,Wright S J.Gradient projection for sparse reconstruction:application to compressed sensing and other inverse problems［J］.IEEE Journal of Selected Topics in Signal Processing,2007,1(4):586-597.

［11］Hale E T,Yin W,Zhang Y.Fixed-point continuation for 1-minimization:Methodology and convergence［J］.SIAM Journal on Optimization,2008,19(3):1107-1130.

［12］Yun S,Toh K C.A coordinate gradient descent method for 1-regularized convex minimization［J］.Computational Optimization and Applications,2011,48(2):273-307.

［13］Yang J,Zhang Y.Alternating direction algorithms for 1-problems in compressive sensing［J］,SIAM Journal on Scientific Computing,2011,33(3):250-278.

［14］Wright S J,Nowak R D,Figueiredo M A T.Sparse reconstruction by separable approximation［J］.IEEE Transactions on Signal Processing,2009,57(7):2479-2493.

［15］Kim S,Koh K,Lustig M,et al.An interior-point method for large-scale 1-regularized leastsquares［J］.IEEE Journal of Selected Topics in Signal Processing,2007(1):606-617.

［16］Xiao Y H,Wu S Y,Qi L Q.Nonmonotone Barzilai-Borwein gradient algorithm for 1-regularized
nonsmooth minimization in compressive sensing［J］.Journal of Scientiic Computing,2014(1):6-10.

［17］Huang S,Wan Z,Chen X.A new nonmonotone line search technique for unconstrained optimization［J］.Journal of Computational and Applied Mathematics,2008,219(1):134-144.

［18］Grippo L,Lampariello F,Lucidi S.A nonmonotone line search technique for Newton's method［J］.SIAM Journal on Numerical Analysis,1986,23(8):707-716.

［19］Toint P L.An assessment of nonmonotone linesearch techniques for unconstrained optimization［J］.SIAM Journal of Science Computer,1996,17(3):725-739.

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