[1]ZHENG Xiao,BO Hua,SUN Qiang.An algorithm for measurement matrix based on QR decomposition and eigenvalue optimizatio[J].CAAI Transactions on Intelligent Systems,2015,10(1):149-155.[doi:10.3969/j.issn.2013-0934.201309034]
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An algorithm for measurement matrix based on QR decomposition and eigenvalue optimizatio

CAAI Transactions on Intelligent Systems[ISSN 1673-4785/CN 23-1538/TP] Volume: 10 Number of periods: 2015 1 Page number: 149-155 Column: 学术论文—机器学习 Public date: 2015-03-25
Title:
An algorithm for measurement matrix based on QR decomposition and eigenvalue optimizatio
Author(s):
ZHENG Xiao1;  BO Hua1;  SUN Qiang2
1. College of Information Engineering, Shanghai Maritime University, Shanghai 201306, China;
2. Automation and Information Engineering College, Xi’an University of Technology, Xi’an, 710000, China
Keywords:
compressed sensing; sparse basis; measurement matrix; reconstruction algorithm; QR decomposition; eigenvalue; column independence; incoherenc
CLC:
TP391.9
DOI:
10.3969/j.issn.2013-0934.201309034
Abstract:
Measurement matrix is a core part of compressed sensing. The column independence of measurement matrix and the incoherence between measurement matrix and sparse basis have a major impact on the quality of a reconstructed image. This paper proposes a new algorithm of measurement matrix based on QR decomposition and eigenvalue. The column independence of the measurement matrix is increased by QR decomposition and at the same time the Gram matrix is optimized. Therefore, the eigenvalue of the normalized Gram matrix approximates to N/M so as to increases the incoherence between measurement matrix and sparse basis. The simulation results showed that the proposed method has excellent results on the aspects of increasing the quality of reconstructed image. In addition, the stability of the reconstructed results had more apparent advantages than other algorithms in the case of less number of observed values.
References:
[1] ELAD M.Optimized projections for compressed sensing[J].IEEE Transaction on Signal Processing, 2007, 55(12): 5695-5702.
[2] DINH M N. Efficientprojection for compressed sensing[C]//7th ACIS International CONFerence on Computer and Information Science.Oregon, America,2008:322-327.
[3] JULIO M D,GUILLERMO S. Learning to sense sparse signals:Simultaneous sensing matrix and sparsifying dictionary optimization[J]. IEEE Transactions on Image Processing, 2009, 18(7):1395-1408.
[4] CAO Z.Optimized projection matrix for compressive sensing[J]. EURAIP Journal Advances in Signal Processing, 2010(43):55-60.
[5] YU Lifeng, LI Gang, CHANG Liping.Optimizing projection matrix for compressed sensing systems[C]//8th International Conference on Communnicationand Signal Processing, 2011: 1-5.
[6] EVAGGLIAT,LISIMACHOS P K, AGGELOS K K.Useof tight frames for optimized compressed sensing[C]//20th European Signal Processing Conference, Bucharest, 2012: 1439-1443.
[7] VAHID A, SAIDEH F, SAEID S. A gradient-based alternating minimization approach for optimization of measurement matrix in compressive sensing[J].Signal Processing, 2012, 92(4): 999-1009.
[8] THONG T D, LU Gan, NAM H N,et al.Fast and efficientcompressive sensing using structurally random matrices[J].IEEE Transactions on Signal Processing, 2012, 60(1): 139-154.
[9] WEI Chen, MIGUEL R D. On the use of unit-norm tight frames to improve the use of MSE performance in compressive sensing application[J].Transactions on Signal Processing Letter, 2012, 19(1): 8-11.
[10] TSILIGIANNI E, KONDI L P, KATSAGGELOS A K. Use of tight frames for optimized compressed sensing[C]//20th European Signal Processing ConferenceBucharest, 2012: 1439-1443.
[11] 赵瑞珍,秦周,胡绍海.一种基于特征值分解的测量矩阵优化方法[J].信号处理, 2012, 28(5): 653-658.Zhao Ruizhen, QIN Zhou. An method based on eigenvalue decomposition to optimize measurement matrix[J]. Signal Processing, 2012, 28 (5): 653-658.
[12] 傅迎华.可压缩传感重构算法与近似QR分解[J]. 计算机应用, 2008, 28(9): 2300-2302.FU Ying hua. Reconstruction algorithm of compressed sensing and QR decomposition [J]. Computer Applications, 2008, 28(9): 2300-2302.
[13] 彭玉楼,何怡刚,林斌.基于奇异值分解的压缩感知噪声信号重构算法[J].仪器仪表学报, 2012, 33(12): 2655-2660.PENG Yulou, YI Gang, LIN Bin. Reconstruction algorithm of compressed sensing noise signal based on singular value decomposition[J]. Journal of Scientific Instrument, 2012,33 (12): 2655-2660.
[14] DONOHO. Compressed sensing[J].IEEE Trans on Information Theory,2006,52(4):1289-1306.
[15] YAAKOV TSAIG,DAVID L. Extensions of Compressed sensing[J]. Signal Processing, 2006, 86(3):533-548.
[16] DAVID L. Compressed sensing[J]. Information Theory, 2006, 52(4): 1289-1306.
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