低相干高鲁棒性观测矩阵优化

doi:10.19665/j.issn1001-2400.2019.06.024

西安电子科技大学学报 ›› 2019, Vol. 46 ›› Issue (6): 171-178.doi: 10.19665/j.issn1001-2400.2019.06.024

• • 上一篇

低相干高鲁棒性观测矩阵优化

赵辉^1,²,张乐^1,²,刘莹莉^1,²,张静^1,²,张天骐^1,²

^1. 重庆邮电大学通信与信息工程学院重庆 400065
^2. 重庆邮电大学信号与信息处理重庆市重点实验室重庆 400065

收稿日期:2019-01-25 出版日期:2019-12-20 发布日期:2019-12-21
作者简介:赵辉(1980—),女,教授,E-mail:zhaohui@cqupt.edu.cn
基金资助:
国家自然科学基金(6167095)

Optimization of the low coherence and high robustness observation matrix

ZHAO Hui^1,²,ZHANG Le^1,²,LIU Yingli^1,²,ZHANG Jing^1,²,ZHANG Tianqi^1,²

^1. School of Communication and Information Engineering,Chongqing University of Posts and Telecommunications , Chongqing 400065, China
^2. Chongqing Key Laboratory of Signal and Information Processing, Chongqing University of Posts and Telecommunications, Chongqing 400065, China

Received:2019-01-25 Online:2019-12-20 Published:2019-12-21

摘要/Abstract

摘要：

针对目前压缩感知观测矩阵普适性低和优化算法鲁棒性不足的问题,提出了一种基于紧框架和稀疏表示误差的观测矩阵优化算法。该算法首先将格拉姆矩阵同时逼近单位矩阵和紧框架,以降低感知矩阵的平均互相干性;然后将稀疏表示误差作为正则项加入传统优化模型中,来提高观测矩阵的鲁棒性;最后利用解析法求解观测矩阵,保证算法的收敛性。实验结果表明,与现有的优化矩阵相比,所构造观测矩阵的平均互相干系数至少可降低0.03,且具有更强的鲁棒性。

关键词: 观测矩阵, 平均互相干性, 紧框架, 稀疏表示误差

Abstract:

An observation matrix optimization algorithm based on the tight frame and sparse representation error is proposed. First, the average mutual coherence of the sensing matrix is reduced by the Glam matrix which approximates the unit matrix and the constructed tight frame. Second, the sparse representation error as a regularization term is added to the conventional optimization model to improve the robustness of the observation matrix. Finally,the analytical method is applied to solve the observation matrix to ensure the convergence of the algorithm. Experimental results show that, compared with the contrast optimization matrix, the average mutual coherence of the proposed sensing matrix can be reduced by at least 0.03 with more robustness.

Key words: observation matrix, average mutual coherence, tight frame, sparse representation error

中图分类号:

TN911.7

赵辉,张乐,刘莹莉,张静,张天骐. 低相干高鲁棒性观测矩阵优化[J]. 西安电子科技大学学报, 2019, 46(6): 171-178.

ZHAO Hui,ZHANG Le,LIU Yingli,ZHANG Jing,ZHANG Tianqi. Optimization of the low coherence and high robustness observation matrix[J]. Journal of Xidian University, 2019, 46(6): 171-178.

图/表 6

表1

低维不同优化矩阵相关性对比"

参数	原始投影矩阵	Elad优化矩阵	Li优化矩阵	Bai优化矩阵	文中优化矩阵
$‖ I L - G ‖ F 2$	5.669×10⁵	465	125	265	125
μ	0.76	0.64	0.58	0.88	0.91
μ_av	0.31	0.26	0.26	0.25	0.22

表1

表2

高维不同优化矩阵相关性对比"

参数	原始投影矩阵	Elad优化矩阵	Li优化矩阵	Bai优化矩阵	文中优化矩阵
$‖ I L - G ‖ F 2$	7.389×10⁶	654	220	438	220
μ	0.54	0.37	0.33	0.72	0.83
μ_av	0.18	0.14	0.14	0.15	0.12

表2

图1

图2

图3

图4

参考文献 17

[1]	DONOHO D L . Compressed Sensing[J]. IEEE Transactions on Information Theory, 2006,52(4):1289-1306. doi: 10.1002/mrm.28135 pmid: 31863516
[2]	王峰, 向新, 易克初 , 等. 支撑驱动的非凸压缩感知恢复算法[J]. 西安电子科技大学学报, 2016,43(2):1-5.
	WANG Feng, XIANG Xin, YI Kechu , et al. Support Driven Recovery Algorithm for Non-convex Compressed Sensing[J]. Journal of Xidian University, 2016,43(2):1-5.
[3]	BANITALBI-DEHKORDI M, BANITALBI-DEHKORDI A, ABOUEI J , et al. Face Recognition Using a New Compressive Sensing-based Feature Extraction Method[J]. Multimedia Tools and Applications, 2018,77(11):14007-14027. doi: 10.1007/s11042-017-5007-0
[4]	LI L C, LI D J, PAN Z H . Compressed Sensing Application in Interferometric Synthetic Aperture Radar[J]. Science China Information Sciences, 2017,60(10):102305. doi: 10.1007/s11432-016-9017-6
[5]	SEITZER M, YANG G, SCHLEMPER J , et al. Adversarial and Perceptual Refinement for Compressed Sensing MRI Reconstruction[C]//Lecture Notes in Computer Science: 11070LNCS. Heidelberg: Springer Verlag, 2018: 232-240.
[6]	刘学文, 肖嵩, 薛晓 . 经验模态分解构造观测矩阵的方法[J]. 西安电子科技大学学报, 2018,45(1):35-41.
	LIU Xuewen, XIAO Song, XUE Xiao . Measurement Matrix Construction Based on Empirical ModeDecomposition[J]. Journal of Xidian University, 2018,45(1):35-41.
[7]	EMMANUEL J C . The Restricted Isometry Property and Its Implications for Compressed Sensing[J]. Comptes Rendus Mathématique, 2008,346(9/10):589-592. doi: 10.1073/pnas.1700203114 pmid: 28611224
[8]	ELAD M . Optimized Projections for Compressed Sensing[J]. IEEE Transactions on Signal Processing, 2007,55(12):5695-5702. doi: 10.1002/mrm.27678 pmid: 30773679
[9]	ABOLGHASEMI V, FERDOWSI S, SANEI S . A Gradient-based Alternating Minimization Approach for Optimization of the Measurement Matrix in Compressive Sensing[J]. Signal Processing, 2012,92(4):999-1009. doi: 10.1016/j.sigpro.2011.10.012
[10]	LI Q W, ZHU Z H, LI G , et al. Robust Projection Matrix Optimization from the MSE View for Compressive Sensing Systems[C]// IEEE International Conference on Signal Processing. Kunming: IEEE Press, 2013: 6663992.
[11]	LI G, ZHU Z, YANG D , et al. On Projection Matrix Optimization for Compressive Sensing Systems[J]. IEEE Transactions on Signal Processing, 2013,61(11):2887-2898. doi: 10.1109/TSP.2013.2253776
[12]	BAI H, LI S, HE X X . Sensing Matrix Optimization Based on Equiangular Tight Frames with Consideration of Sparse Representation Error[J]. IEEE Transactions on Multimedia, 2016,18(10):2040-2053. doi: 10.1109/TMM.2016.2595261
[13]	WELCH L . Lower Bounds on the Maximum Cross Correlation of Signals[J]. IEEE Transactions on Information Theory, 1974,20(3):397-399. doi: 10.1109/TIT.1974.1055219
[14]	HONG T, ZHU Z . An Efficient Method for Robust Projection Matrix Design[J]. Signal Processing, 2018,143:200-210. doi: 10.1016/j.sigpro.2017.09.007
[15]	HONG T, ZHU Z . Online Learning Sensing Matrix and Sparsifying Dictionary Simultaneously for Compressive Sensing[J]. Signal Processing, 2018,153:188-196. doi: 10.1016/j.sigpro.2018.05.021
[16]	LI G, ZHU Z H, WU X M , et al. On Joint Optimization of Sensing Matrix and Sparsifying Dictionary for Robust Compressed Sensing Systems[J]. Digital Signal Processing: A Review Journal, 2018,73:62-71. doi: 10.1016/j.dsp.2017.10.023
[17]	RUSU C, GONZALEZ-PRELCIC N . Designing Incoherent Frames through Convex Techniques for Optimized Compressed Sensing[J]. IEEE Transactions on Signal Processing, 2016,64(9):2334-2344. doi: 10.1109/TSP.2016.2521607

低相干高鲁棒性观测矩阵优化

Optimization of the low coherence and high robustness observation matrix

RichHTML

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

图/表 6

参考文献 17

相关文章 5

Metrics

本文评价

推荐阅读 0

[1]	刘学文;肖嵩;薛晓. 经验模态分解构造观测矩阵的方法[J]. 西安电子科技大学学报, 2018, 45(1): 35-41.
[2]	吴玉莲;冯象初. 利用平衡方法的非凸图像修复[J]. J4, 2014, 41(5): 141-147.
[3]	宋晓霞;石光明. 低冗余的压缩感知观测[J]. J4, 2012, 39(4): 144-148+171.
[4]	李万社;刘志国. 一种有效的小波紧框架设计[J]. J4, 2006, 33(4): 665-669.
[5]	赵瑞珍;宋国乡;王卫卫. 基于紧框架的规范正交小波基[J]. J4, 2000, 27(1): 49-52.