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| Novel Optimization Method for Projection Matrix in Compress Sensing Theory |
| Wu Guang-wen①② Zhang Ai-jun① Wang Chang-ming① |
①(School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China)
②(Department of Electronic Engineering, East China Institute of Technology, Fuzhou 344000, China) |
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Abstract Considering the influence of the projection matrix on Compressed Censing (CS), a novel method is proposed to optimize the projection matrix. In order to improve the signal’s reconstruction precise and the stability of the optimization algorithm of the projection matrix, the proposed method adopts a differentiable threshold function to shrink the off-diagonal items of a Gram matrix corresponding to the mutual coherence between the projection matrix and sparse dictionary, and introduces a gradient descent approach based on the Wolf’s-conditions to solve the optimization projection matrix. The Basis-Pursuit (BP) algorithm and the Orthogonal Matching Pursuit (OMP) algorithm are applied to find the solution of the minimum l0-norm optimization issue and the compressed sensing are utilized to sense and reconstruct the random vectors, wavelet’s noise test signals and pictures. The results of the simulation show the proposed method based on the projection matrix optimization is able to improve the quality of the reconstruction performance.
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Received: 20 November 2014
Published: 02 June 2015
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Corresponding Authors:
Wu Guang-wen
E-mail: wu_gw@163.com
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| [1] |
Donoho D L, Elad M, and Temlyakov V N. Stable recovery of sparse overcomplete representations in the presence of noise[J]. IEEE Transactions on Information Theory, 2006, 52(1): 6-18.
|
| [2] |
Candes E J, Romberg J K, and Tao T. Stable signal recovery from incomplete and inaccurate measurements[J]. Communications on Pure and Applied Mathematics, 2006, 59(8): 1207-1223
|
| [3] |
Candes E J and Tao T. Near-optimal signal recovery from random projections: universal encoding strategies[J]. IEEE Transactions on Information Theory, 2006, 52(12): 5406-5425.
|
| [4] |
郑红, 李振. 压缩感知理论投影矩阵优化方法综述[J]. 数据采集与处理, 2014, 52(1): 43-53.
|
|
Zheng Hong and Li Zhen. Survey on optimization methods for projection matrix in compress sensing theory[J]. Journal of Data Acquisition and Processing, 2014, 52(1): 43-53.
|
| [5] |
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 Qiong-hai, Fu Chang-jun, and Ji Xiang-yang. Research on compressed sensing[J]. Chinese Journal of Computers, 2011, 34(3): 425-434.
|
| [6] |
Elad M. Optimized projections for compressed sensing[J]. IEEE Transactions on Signal Processing, 2007, 55(12): 5695-5703.
|
| [7] |
Abolghasemi V, Ferdowsi S, and Sanei S. A gradient-based alternating minimization approach for optimization of the measurement matrix in compressive sensing[J]. Signal Processing, 2012, 92(3): 999-1009.
|
| [8] |
李佳, 王强, 沈毅, 等. 压缩感知中测量矩阵与重建算法的协同构造[J]. 电子学报, 2013, 41(1): 29-34.
|
|
Li Jia, Wang Qiang, Shen Yi, et al.. Collaborative construction of measurement matrix and reconstruction algorithm in compressive sensing[J]. Acta Electronica Sinica, 2013, 41(1): 29-34.
|
| [9] |
Zhang Qi-heng, Fu Yu-li, Li Hai-feng, et al.. Optimized projection matrix for compressed sensing[J]. Circuit System Signal Processing, 2014, 33(5): 1627-1636.
|
| [10] |
Xu Jian-ping, Pi Yi-ming, and Cao Zong-jie. Optimized projection matrix for compressive sensing[J]. EURASIP Journal on Advances in Signal Processing, 2010, DOI: 10.1155/2010/560349.
|
| [11] |
林波, 张增辉, 朱炬波. 基于压缩感知的DOA估计稀疏化模型与性能分析[J]. 电子与信息学报, 2014, 36(3): 589-594.
|
|
Lin Bo, Zhang Zeng-hui, and Zhu Ju-bo. Sparsity model and performance analysis of DOA estimation with compressive sensing[J]. Journal of Electronics & Information Technology, 2014, 36(3): 589-594.
|
| [12] |
Donoho D L. For most large underdetermined systems of linear equations the minimal l1-norm solution is also the sparsest solution[J]. Communications on Pure and Applied Mathematics, 2006, 59(6): 797-829.
|
| [13] |
Donoho D L and Stark P B. Uncertainty principles and signal recovery[J]. SIAM Journal on Applied Mathematics, 1989, 49(3): 906-931.
|
| [14] |
Donoho D L and Elad M. Optimally sparse representation in general (nonorthogonal) dictionaries via minimization[J]. Proceedings of the National Academy of Science, 2003, 100(5): 2197-2202.
|
| [15] |
PetersenK B and Pedersen M S. The matrix cookbook[OL]. http://www.matrixcookbook.com, 2013.10.
|
| [16] |
Barth T J, Griebel M, Keyes D E, et al.. Scientific computing with MATLAB and octave[OL]. http://www.springer.com/ series/5151, 2013.12.
|
| [17] |
Jorge N and Wright S J. Numerical Optimization Theoretical and Practical Aspects[M]. 2nd Edition, New York: Springer- Verlag Berlin and Heidelberg GmbH & Co. K, 2006: 30-60.
|
| [18] |
Stodden V and Donoho D. SparseLab21-core[OL]. http:// sparselab.stanford.edu, 2013.10.
|
|
|
|
