低冗余的压缩感知观测

doi:10.3969/j.issn.1001-2400.2012.04.026

J4 ›› 2012, Vol. 39 ›› Issue (4): 144-148+171.doi: 10.3969/j.issn.1001-2400.2012.04.026

低冗余的压缩感知观测

宋晓霞^1,2;石光明¹

(1. 西安电子科技大学智能感知与图像理解教育部重点实验室，陕西西安 710071；
2. 山西大同大学物理与电子科学学院，山西大同 037009)

收稿日期:2011-05-21 出版日期:2012-08-20 发布日期:2012-10-08
通讯作者: 宋晓霞
作者简介:宋晓霞(1975-)，女，副教授，西安电子科技大学博士研究生，E-mail: xxsong@mail.xidian.edu.cn．
基金资助:
国家自然科学基金资助项目(61033004, 61072104，61070138, 60902031);高等学校博士学科点专项科研基金资助项目(20090203110003)

Low-redundancy compressed sensing measurements

SONG Xiaoxia^1,2;SHI Guangming¹

(1. Ministry of Education Key Lab. of Intelligent Perception and Image Understanding, Xidian Univ., Xi'an 710071， China;
2. School of Physics ＆ Electronics, Shanxi Datong Univ., Datong 037009， China)

Received:2011-05-21 Online:2012-08-20 Published:2012-10-08
Contact: SONG Xiaoxia

摘要/Abstract

摘要：

为了解决传统压缩方法很难有效地减少压缩感知观测的难题，基于互相关理论、集合论和序列压缩感知方法，提出了一种获取低冗余压缩感知观测的方法．在所提方法中，依据互相关理论，在保证信号完全重构的前提下，尽可能去除原观测集中的一些冗余观测，获得一个较小的观测集．然后，在已获得的较小观测集中，基于每个观测对于信号重构的重要程度，将其分为关键观测和非关键观测，在保证信号完全重构的前提下，迭代剔除一些非关键观测，直到观测集中不再包含非关键观测为止．实验结果表明，所提方法仅用原观测集中40％～70％的观测就可以获得与原观测集几乎相同的信号重构质量．

关键词: 压缩感知, 互相关, 信号重构, 稀疏表示, 观测矩阵

Abstract:

To solve the difficult problem that it is difficult for traditional compression methods to efficiently reduce compressed sensing measurements, this paper proposes a method for obtaining the low-redundancy compressed sensing measurements based on the mutual coherence theory, set theory and sequential compressed sensing. In the proposed method, according to the mutual coherence theory, a smaller measurement set is obtained by removing some redundant measurements from the original measurement set in the premise of ensuring signal reconstruction. Then, the smaller measurement set obtained above is classified into the key set (only including key measurement) or the non-key set (only including non-key measurement) according to the important degree of each measurement for signal reconstruction. And some non-key measurements are eliminated iteratively in the premise of ensuring signal reconstruction until the measurement set does not contain a non-key measurement again. Experimental results show that the proposed method can only take 40 to 70 percent of the original measurement set to obtain almost the same reconstruction quality as that by the original measurement set.

Key words: compressed sensing, mutual coherence, signal reconstruction, sparse representation, measurement matrix

中图分类号:

TN911. 72

宋晓霞;石光明. 低冗余的压缩感知观测[J]. J4, 2012, 39(4): 144-148+171.

SONG Xiaoxia;SHI Guangming. Low-redundancy compressed sensing measurements[J]. J4, 2012, 39(4): 144-148+171.

参考文献

［1］ Donoho D. Compressed Sensing ［J］. IEEE Trans on Information Theory, 2006, 52(4): 1289-1306.
［2］ Candes E, Romberg J, Tao T. Near Optimal Signal Recovery from Random Projections: Universal Encoding Strategies? ［J］. IEEE Trans on Information Theory, 2006, 52(12): 5406-5425.
［3］ Candes E, Wakin M. An Introduction to Compressive Sampling ［J］. IEEE Signal Processing Magazine, 2008, 25(2): 21-30.
［4］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.
Shi Guangming, Liu Danhua, Gao Dahua, et al. Advances in Theory and Application of Compressed Sensing ［J］. Acta Electronic Sinica, 2009, 37(5): 1070-1081.
［5］ Shannon C E. A Mathematical Theory of Communication ［J］. Bell System Tech Journal, 1948, 27(3): 379-423.
［6］ Ward R. Compressed Sensing with Cross Validation ［J］. IEEE Trans on Information Theory, 2009, 55(12): 5773-5782.
［7］ Malioutov D M, Sanghavi S R, Willsky A S. Sequential Compressed Sensing ［J］. IEEE J Sel Top Sig Proc, 2010, 4(2): 435-444.
［8］ Blelloch G E. Introduction to Data Compression［M］. Pittsburgh: Carnegie Mellon University, 2010.
［9］ Lustig M, Donoho D, Santos J, et al. Compressed Sensing MRI ［J］. IEEE Signal Processing Magazine, 2008, 25(2): 72-82.
［10］ Shi G M, Gao D H, Song X X, et al. High-resolution Imaging Via Moving Random Exposure and Its Simulation ［J］. IEEE Trans on Image Processing, 2011, 20(1): 276-282.
［11］ Haupt J, Bajwa W U, Rabbat M, et al. Compressed Sensing for Networked Data ［J］. IEEE Signal Processing Magazine, 2008, 25(2): 92-101.
［12］ Bajwa W U, Haupt J, Sayeed A M, et al. Compressed Channel Sensing: a New Approach to Estimating Sparse Multipath Channels ［J］. Proceedings of the IEEE, 2010, 98(6): 1058-1076.
［13］臧博, 张磊, 唐禹, 等. 利用压缩感知的逆合成孔径激光雷达成像新方法［J］. 西安电子科技大学学报, 2010, 37(6): 1027-1032.
Zang Bo, Zhang Lei, Tang Yu, et al. Novel Imaging Method Using Compressed Sensing for the Inverse Synthetic Aperture Imaging Ladar ［J］. Journal of Xidian University, 2010, 37(6): 1027-1032.
［14］全英汇, 张磊, 刘亚波, 等. 利用压缩感知的短孔径高分辨ISAR成像方法［J］. 西安电子科技大学学报, 2010, 37(6): 1022-1026.
Quan Yinghui, Zhang Lei, Liu Yabo, et al. Method for Achieving High Resolution ISAR Imaging with Short Aperture Data via Compressed Sensing ［J］. Journal of Xidian University, 2010, 37(6): 1022-1026.
［15］李军, 邢孟道, 张磊, 等. 一种高分辨的稀疏孔径ISAR成像方法［J］. 西安电子科技大学学报, 2010, 37(3): 441-446.
Li Jun, Xing Mengdao, Zhang Lei, et al. High Resolution Imaging Method for the Sparse Aperture of ISAR ［J］. Journal of Xidian University, 2010, 37(3): 441-446.
［16］ Candes E, Romberg J. Sparsity and Incoherence in Compressive Sampling ［J］. Inverse Problems, 2007, 23(3): 969-985.

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低冗余的压缩感知观测

Low-redundancy compressed sensing measurements

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