基于支撑集保护的回环匹配算法

doi:10.11959/j.issn.1000-436x.2015243

通信学报 ›› 2015, Vol. 36 ›› Issue (9): 127-134.doi: 10.11959/j.issn.1000-436x.2015243

基于支撑集保护的回环匹配算法

田淑娟^1,²,樊晓平^1,³,裴廷睿²,杨术²,李哲涛²

¹ 中南大学信息科学与工程学院，湖南长沙 410075
² 湘潭大学信息工程学院，湖南湘潭 411105
³ 湖南财政经济学院网络化系统研究所，湖南长沙 410205

出版日期:2015-09-25 发布日期:2017-09-15
基金资助:
国家自然科学基金资助项目;国家自然科学基金资助项目;国家自然科学基金资助项目;国家自然科学基金资助项目;湖南省自然科学基金资助项目;湖南省自然科学基金资助项目;湖南省自然科学基金资助项目;湖南省科技计划基金资助项目;湖南省重点学科建设基金资助项目

Loopback matching algorithm with support set protection

Shu-juan TIAN^1,²,Xiao-ping FAN^1,³,Ting-rui PEI²,Shu YANG²,Zhe-tao LI²

¹ School of Information Science and Engineering,Central South University,Changsha 410075,China
² College of Information Engineering,Xiangtan University,Xiangtan 411105,China
³ Laboratory of Networked Systems,Hunan University of Finance and Economics,Changsha 410205,China

Online:2015-09-25 Published:2017-09-15
Supported by:
The National Natural Science Foundation of China;The National Natural Science Foundation of China;The National Natural Science Foundation of China;The National Natural Science Foundation of China;The Natu-ral Science Foundation of Hunan Province;The Natu-ral Science Foundation of Hunan Province;The Natu-ral Science Foundation of Hunan Province;Hunan Provincial Science and Technology Project;The Construct Program of the Key Discipline in Hunan Province

摘要/Abstract

摘要：

针对部分压缩感知贪婪迭代类重构算法中误删正确支撑集元素的缺点，提出了一种基于支撑集保护的回环匹配算法（LM-P）。该算法依据最小残差内积初始化非受保护支撑集元素，然后依据观测向量在非受保护支撑集对应观测子矩阵上的投影，选择对应投影绝对值最大的元素添加到受保护支撑集，迭代获得受保护支撑集，从而重构原始信号。实验结果表明，对于非零值服从正态分布且稀疏度小于观测值一半数目的稀疏信号，LM-P算法的重构准确率超过86%；对于低信噪比稀疏信号，该算法的重构准确率能够维持在99%以上；与OMP、CoSaMP、SP和 GPA算法相比，LM-P精确重构所需观测值数更少；此外，LM-P算法在二维图像信号的重构中也有较好性能。

关键词: 压缩感知, 贪婪迭代, 支撑集, 稀疏信号, LM-P

Abstract:

There was a drawback of deleting right support elements in some greedy iterative reconstruction algorithms.To resolve this problem,loopback matching algorithm with support set protection (LM-P) was proposed.First,LM-P ini-tialized elements of non-protected support set based on minimum residual inner product.Second,it computed the projec-tions of observations on the observation sub-matrix corresponding to non-protected support set elements.Then,an ele-ment in non-protected support set with the largest projection was added to the protected support set.An alternative multi-plicative iteration method was employed to obtain the whole protected support set.As to reconstruct a sparse signal whose nonzero elements are normally distributed and the signal sparsity is less than half the number of measurements,experimental results show that the reconstruction accuracy of LM-P algorithm exceeds 86%.For sparse signals with small noise,the reconstruction accuracy of LM-P can maintain over 99 %.Compared with OMP,CoSaMP,SP and GPA algo-rithms,LM-P's observations are smaller.LM-P also has good performance for image reconstruction.greedy iteration;support set;sparse signal;LM-P

田淑娟,樊晓平,裴廷睿,杨术,李哲涛. 基于支撑集保护的回环匹配算法[J]. 通信学报, 2015, 36(9): 127-134.

Shu-juan TIAN,Xiao-ping FAN,Ting-rui PEI,Shu YANG,Zhe-tao LI. Loopback matching algorithm with support set protection[J]. Journal on Communications, 2015, 36(9): 127-134.

图/表 6

表1

部分贪婪重构类算法性能对比"

重构算法	算法优势	算法缺陷	算法复杂度
OMP	算法简易	稀疏度范围受限	O(KMN)
CoSaMP	自适应修正支撑集	稀疏度存在 $\frac{M}{3}$ 门限效应	O(MN)
SP	自适应修正支撑集	稀疏度存在 $\frac{M}{2}$ 门限效应	O(KMN)
GPA	收敛性优于OMP、CoSaMP	稀疏度存在 $\frac{M}{2}$ 门限效应，计算复杂度高	O(M ²N)

表1

图1

图2

图3

图4

表2

参考文献 15

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算法名称		PSNR
算法名称	K=64	K=49	K=36
OMP	31.013 7	32.013 7	30.608 9
CoSaMP	12.706 8	21.020 9	30.606 2
SP	22.853 1	31.515 0	30.610 2
GPA	31.949 0	32.067 0	30.610 5
LM-P	33.410 5	32.068 4	30.614 7

基于支撑集保护的回环匹配算法

Loopback matching algorithm with support set protection

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