基于自适应加速前向后向匹配追踪的压缩感知重构算法

doi:10.11959/j.issn.1000-436x.2020006

通信学报 ›› 2020, Vol. 41 ›› Issue (1): 25-32.doi: 10.11959/j.issn.1000-436x.2020006

基于自适应加速前向后向匹配追踪的压缩感知重构算法

潘作舟,孟宗(),李晶,石颖

燕山大学电气工程学院，河北秦皇岛 066004

修回日期:2019-11-21 出版日期:2020-01-25 发布日期:2020-02-11
作者简介:潘作舟（1994- ），男，安徽巢湖人，燕山大学博士生，主要研究方向为多传感器信号融合与增强、压缩感知重构算法、转子轴承寿命预测等|孟宗（1977- ），男，河北保定人，博士，燕山大学教授、博士生导师，主要研究方向为信号分析与处理、旋转机械故障诊断等|李晶（1990- ），女，河北承德人，燕山大学博士生，主要研究方向为压缩感知稀疏表示方法|石颖（1995- ），女，河北承德人，燕山大学硕士生，主要研究方向为压缩感知重构算法
基金资助:
国家自然科学基金资助项目(51575472);河北省自然科学基金资助项目(E2019203448);河北省创新基金资助项目(CXZZBS2020047)

Compressed sensing reconstruction algorithm based on adaptive acceleration forward-backward pursuit

Zuozhou PAN,Zong MENG(),Jing LI,Ying SHI

School of Electrical Engineering,Yanshan University,Qinhuangdao 066004,China

Revised:2019-11-21 Online:2020-01-25 Published:2020-02-11
Supported by:
The National Natural Science Foundation of China(51575472);The Natural Science Foundation of Hebei Province(E2019203448);Hebei Province Graduate Innovation Funding Project(CXZZBS2020047)

摘要/Abstract

摘要：

针对传统前向后向匹配追踪（FBP）算法运行时间较长的问题，提出了一种自适应加速前向后向匹配追踪（AAFBP）算法。AAFBP算法的重构过程可分为2个阶段，在前向阶段利用自适应阈值来选取适量原子加入支撑集，在后向回溯过程中以原子的投影系数大小作为删除依据，利用自适应删除阈值来进行原子的删除，同时克服了自适应过程中存在的回溯过度现象。所提方法能够保证选入原子数量更具随机性，使每次迭代保留更多的正确原子。一维稀疏信号和二维图像的仿真结果表明，AAFBP算法在重构精度和运算时间上都更具有优势。

关键词: 压缩感知, 匹配追踪, 前向后向搜索, 自适应阈值, 信号重构

Abstract:

Aiming at the long running time problem of the traditional forward-backward pursuit (FBP) algorithm,an adaptive acceleration forward-backward pursuit (AAFBP) algorithm was proposed.The reconstruction process of AAFBP algorithm can be divided into two stages.In the forward stage,the AAFBP algorithm used the adaptive threshold to select the right amount of atoms to join the support set.In the backward stage,based on the projection coefficient of the atoms,the deletion threshold was introduced to remove the atoms adaptively and the excessive backtracking phenomenon in adaptive process was overcome simultaneously.The proposed method can ensure the number of the selected atoms more random,and more right atoms were retained in each iteration.The simulation results of one-dimensional sparse signal and two-dimensional image show that the AAFBP algorithm has more advantages in both the accuracy of reconstruction and the running time.

Key words: compressed sensing, matching pursuit, forward-backward search, adaptive threshold, signal reconstruction

中图分类号:

TN911.7

潘作舟,孟宗,李晶,石颖. 基于自适应加速前向后向匹配追踪的压缩感知重构算法[J]. 通信学报, 2020, 41(1): 25-32.

Zuozhou PAN,Zong MENG,Jing LI,Ying SHI. Compressed sensing reconstruction algorithm based on adaptive acceleration forward-backward pursuit[J]. Journal on Communications, 2020, 41(1): 25-32.

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参考文献 20

[1]	裴立业, 江桦, 麻曰亮 . 基于选择性测量的压缩感知去噪重构算法[J]. 通信学报, 2017,38(2): 106-114.
	PEI L Y , JIANG H , MA Y L . Compressed perceptual denoising reconstruction algorithm based on selective measurement[J]. Journal on Communications, 2017,38(2): 106-114.
[2]	CAND S E , OMBERG J , TAO T . Robust uncertainty principles:exact signal recognition from highly incomplete frequency information[J]. IEEE Transaction on Information Theory, 2006,52(2): 489-509.
[3]	DONOHO D L . Compressed sensing[J]. IEEE Transactions on Information Theory, 2006,52(4): 1289-1306.
[4]	QAISAR S , BILAL R M , LQBAL W ,et al. Compressive sensing:from theory to applications,a survey[J]. Journal of Communications and Networks, 2013,15(5): 443-456.
[5]	CAND S E , TAO T . Near optimal signal recovery from random projection universal encoding Strategies[J]. IEEE Transactions on Information Theory, 2006,52(12): 5406-5425.
[6]	戴琼海, 付长军, 季向阳 . 压缩感知研究[J]. 计算机学报, 2011,34(3): 425-434.
	DAI Q H , FU C J , JI X Y . Compressed sensing research[J]. Chinese Journal of Computers, 2011,34(3): 425-434.
[7]	沈燕飞, 朱珍民, 张勇东 ,等. 基于秩极小化的压缩感知图像恢复算法[J]. 电子学报, 2016,44(3): 453-460.
	SHEN Y F , ZHU Z M , ZHANG Y D ,et al. Compressed sensing image reconstruction algorithm based on rank minimization[J]. Acta Electronica Sinica, 2016,44(3): 453-460.
[8]	宋云, 李雪玉, 沈燕飞 ,等. 基于非局部相似块低秩的压缩感知图像重建算法[J]. 电子学报, 2017,45(3): 695-403.
	SONG Y , LI X Y , SHEN Y F ,et al. Compressed sensing image recon struction based on low rank of non local similar patches[J]. Acta Electronica Sinica, 2017,45(3): 695-403.
[9]	MALLAT S G , ZHANG Z F . Matching pursuits with time frequency dictionaries[J]. IEEE Transactions on Signal Processing, 1993,41(12): 3397-3415.
[10]	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.
[11]	NEEDELL D , VERSHYNIN R . Uniform uncertainty principle and signal recovery via regularized orthogonal matching pursuit[J]. Foundations of Computational Mathematics, 2009,9(3): 317-334.
[12]	刘国海, 吴翃轩, 沈跃 . 正则化自适应匹配追踪电能质量数据重构方法[J]. 仪器仪表学报, 2015,36(8): 1838-1844.
	LIU G H , WU H X , SHEN Y . Novel reconstruction method of power quality data based on regularized adaptive matching pursuit algorithm[J]. Chinese Journal of Scientific Instrument, 2015,36(8): 1838-1844.
[13]	KARAHANOGLU N B , ERDOGAN H . Compressed sensing signal recovery via forward-backward pursuit[J]. Digital Signal Processing, 2013,23(5): 1539-1548.
[14]	王锋, 孙桂玲, 张建平 ,等. 基于压缩感知的加速前向后向匹配追踪算法[J]. 电子与信息学报, 2016,38(10): 2538-2545.
	WANG F , SUN G L , ZHANG J P ,et al. Acceleration forward backward pursuit algorithm based on compressed sensing[J]. Journal of Electronics ＆ Information Technology, 2016,38(10): 2538-2545.
[15]	刘亚新, 赵瑞珍, 胡绍海 . 用于压缩感知信号重建的正则化自适应匹配追踪算法[J]. 电子与信息学报, 2010,32(11): 2713-2717.
	LIU Y X , ZHAO R Z , HU S H . A regularized adaptive matching pursuit algorithm for compressed sensing signal reconstruction[J]. Journal of Electronics ＆ Information Technology, 2010,32(11): 2713-2717.
[16]	周燕, 曾凡智 . 基于二维压缩感知和分层特征的图像检索算法[J]. 电子学报, 2016,44(2): 453-460.
	ZHOU Y , ZENG F Z . An image retrieval algorithm based on two dimensional compressive sensing and hierarchical feature[J]. Acta Electronica Sinica, 2016,44(2): 453-460.
[17]	王天荆, 李秀琴, 白光伟 ,等. 无线传感器网络中基于自适应网格的多目标定位算法[J]. 通信学报, 2019,40(7): 197-207.
	WANG T J , LI X Q , BAI G W ,et al. Multi-target localization algorithm based on adaptive grid in wireless sensor network[J]. Journal on Communications, 2019,40(7): 197-207.
[18]	张奕, 李娟, 张敏 . 基于压缩感知的双麦克风混响多声源定位算法[J]. 通信学报, 2019,40(1): 102-109.
	ZHANG Y , LI J , ZHANG M . Reverberation multi-source localization algorithm based on compressed sensing with dual microphones[J]. Journal on Communications, 2019,40(1): 102-109.
[19]	孟祥瑞, 赵瑞珍, 岑翼刚 . 用于压缩采样信号重建的回溯正则化自适应匹配追踪算法[J]. 信号处理, 2016,32(2): 186-192.
	MENG X R , ZHAO R Z , CEN Y G . A modified regularized adaptive matching pursuit algorithm for compressed sampling signal reconstruction[J]. Signal Processing, 2016,32(2): 186-192.
[20]	刘义颖, 李国瑞, 田丽 . 基于联合稀疏模型的无线传感网数据重构算法[J]. 通信学报, 2016,37(S1): 211-218.
	LIU Y Y , LI G R , TIAN L . Data reconstruction algorithm for wireless sensing network based on joint sparse model[J]. Journal on Communications, 2016,37(S1): 211-218.

算法	PSNR/dB	MSE	重构时间/s
AAFBP	28.99	5.37×10^-6	5.43
AFBP	28.78	5.63×10^-6	22.33
FBP	28.49	6.03×10^-6	27.91
OMP	28.07	6.53×10^-6	4.53
SP	28.54	5.89×10^-6	2.26

基于自适应加速前向后向匹配追踪的压缩感知重构算法

Compressed sensing reconstruction algorithm based on adaptive acceleration forward-backward pursuit

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