梯度投影法求解压缩感知信号重构问题

doi:10.13190/jbupt.201204.112.heyb

北京邮电大学学报 ›› 2012, Vol. 35 ›› Issue (4): 112-115.doi: 10.13190/jbupt.201204.112.heyb

梯度投影法求解压缩感知信号重构问题

何宜宝1，毕笃彦1，马时平1，岳耀帅2

1空军工程大学航空航天工程学院2空军驻甘肃地区军事代表室

收稿日期:2011-03-11 修回日期:2012-02-14 出版日期:2012-08-28 发布日期:2012-07-08
通讯作者: 何宜宝 E-mail:gudujianboboo@yahoo.com.cn
作者简介:何宜宝（1985-），男，博士生，Email：gudujianboboo@yahoo.com.cn 毕笃彦（1962-），男，教授，博士生导师
基金资助:
国防科技重点实验室基金项目（9140c610301080c6106,9140c6001070801）；航空科学基金项目（20101996009）

Problem of Signal Reconstruction of Compressive Sensing Solved by Gradient Projection

HE Yi-bao1, BI Du-yan1, MA Shi-ping1, YUE Yao-shuai2

1Aeronautics and Astronautics Engineering College, Air Force Engineering University2Gansu Ministry Delegate Office of Air Force of the Peoples Liberation Army

Received:2011-03-11 Revised:2012-02-14 Online:2012-08-28 Published:2012-07-08

摘要/Abstract

摘要：

将结合Barzilai-Borwein步长和非单调线搜索的梯度投影法用于压缩感知信号重构. 分析了Barzilai-Borwein步长计算方法，结合其特点给出了非单调线搜索方法，为降低线搜索对算法性能的影响，引入了自适应的策略，最后给出了算法收敛性分析. 实验结果表明，该算法能很好地重构不同稀疏度的信号，且在相同条件下，计算效率优于经典的基追踪法、正交匹配追踪和其他梯度投影法.

关键词: 压缩感知, 信号重构, 梯度投影, Barzilai-Borwein步长, 非单调线搜索

Abstract:

A gradient projection method combining Barzilai-Borwein stepsize and nonmonotone line search is proposed and applied to signal reconstruction in compressive sensing. The computation of Barzilai-Borwein stepsize is analyzed, A corresponding nonmonotone line search method is introduced. To reduce influence of line search, an adaptive nonmonotone line search is designed. Convergence analysis of the algorithm is given. Experiment shows that the proposed algorithm can get good performances of signal reconstruction with different sparsity, seems better than Basis Pursuit, Orthogonal Matching Pursuit and other gradient projection algorithms. 

Key words: compressive sensing, signal reconstruction, gradient projection, Barzilai-Borwein stepsize, nonmonotone line search

中图分类号:

TN911.7

何宜宝毕笃彦马时平岳耀帅. 梯度投影法求解压缩感知信号重构问题[J]. 北京邮电大学学报, 2012, 35(4): 112-115.

HE Yi-bao, BI Du-yan, MA Shi-ping, YUE Yao-shuai. Problem of Signal Reconstruction of Compressive Sensing Solved by Gradient Projection[J]. JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM, 2012, 35(4): 112-115.

参考文献

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梯度投影法求解压缩感知信号重构问题

Problem of Signal Reconstruction of Compressive Sensing Solved by Gradient Projection

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