一种用于压缩感知理论的投影矩阵优化算法

吴光文; 张爱军; 王昌明

doi:10.11999/JEIT141450

一种用于压缩感知理论的投影矩阵优化算法

doi: 10.11999/JEIT141450

2.
(南京理工大学机械工程学院南京 210094) ②(东华理工大学电子与机械工程学院抚州 344000)

基金项目:

国家自然科学基金(61161010, 11265001)和高等学校博士学科点专项科研基金(20133219110027)

计量
- 文章访问数: 1532
- HTML全文浏览量: 124
- PDF下载量: 700
- 被引次数: 0
出版历程
- 收稿日期: 2014-11-20
- 修回日期: 2015-02-11
- 刊出日期: 2015-07-19

Novel Optimization Method for ProjectionMatrix in Compress Sensing Theory

2.
(School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China)

摘要

摘要: 考虑到投影矩阵对压缩感知(CS)算法性能的影响，该文提出一种优化投影矩阵的算法。该方法提出可导的阈值函数，通过收缩Gram矩阵非对角元的方法压缩投影矩阵和稀疏字典的相关系数，引入基于沃尔夫条件(Wolfes conditions)的梯度下降法求解最佳投影矩阵，达到提高投影矩阵优化算法稳定度和重构信号精度的目的。通过基追踪(BP)算法和正交匹配追踪(OMP)算法求解l0优化问题，用压缩感知方法实现随机稀疏向量、小波测试信号和图像信号的感知和重构。仿真实验表明，该文提出的投影矩阵优化算法能较大地提高重构信号的精度。
- 压缩感知 /
- 相干性 /
- 基追踪算法 /
- 正交匹配追踪算法
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 signals 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 Wolfs-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 minimuml0-norm optimization issue and the compressed sensing are utilized to sense and reconstruct the random vectors, wavelets 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.
- Compressed Sensing (CS) /
- Mutual coherence /
- Basis-Pursuit (BP) algorithm /
- Orthogonal Matching- Pursuit (OMP) algorithm

HTML全文

参考文献(19)

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.

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

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.

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.

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.

Elad M. Optimized projections for compressed sensing[J]. IEEE Transactions on Signal Processing, 2007, 55(12): 5695-5703.

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.

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.

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.

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.

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.

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.

Donoho D L and Stark P B. Uncertainty principles and signal recovery[J]. SIAM Journal on Applied Mathematics, 1989, 49(3): 906-931.

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.

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.

施引文献

资源附件(0)

访问统计