光学学报, 2013, 33 (2): 0220001, 网络出版: 2012-11-09   

基于0-1稀疏循环矩阵的测量矩阵分离研究

Separation Research of Measurement Matrices Based on 0-1 Sparse Circulant Matrix
作者单位
1 武汉大学测绘遥感信息工程国家重点实验室, 湖北 武汉 430079
2 广西工学院汽车工程系, 广西 柳州 545006
摘要
当前压缩感知中测量矩阵的优化是测量阶段和重构阶段采用同一矩阵的事前优化。采用了以行变换为主的测量矩阵优化算法和过渡矩阵将压缩感知的测量矩阵和重构矩阵相分离,在测量阶段采用单像素相机的0-1稀疏矩阵,在重构阶段采用近似矩阵,这是区别于传统思路的测量数据和测量矩阵的事后优化方法。理论分析和实验结果表明,优化矩阵的性能好于稀疏循环矩阵,近似矩阵和优化矩阵具有相近的性能。研究成果降低了测量矩阵工程设计和实现的难度。
Abstract
Current optimization of measurement matrix of compressive sensing is optimization beforehand by using the same matrix in measurement and reconstruction stages. Transition matrix and optimization algorithm mainly based on row transformation are proposed to separate the measurement matrix and reconstruction matrix of compressive sensing. 0-1 sparse matrix of single-pixel camera is adopted during measurement, while approximate matrix is adopted during reconstruction. It is a kind of afterwards optimization method of measurement data and measurement matrix, different from traditional thinking. Theory analysis and experiment results demonstrate that the characteristics of optimal matrix are better than circulant sparse matrix, and approximate matrix and optimal matrix have similar characteristics. The research results reduce the difficulty of engineering design and implementation of measurement matrix.
参考文献

[1] 吴海佳, 张雄伟, 陈卫卫. 压缩感知理论中测量矩阵的构造方法 [J]. 军事通信技术, 2012, 33(1): 90~94

    Wu Haijia, Zhang Xiongwei, Chen Weiwei. Measurement matrixes in compressed sensing theory [J]. J. Military Communications Technology, 2012, 33(1): 90~94

[2] 张成, 杨海蓉, 韦穗. 确定性相位掩膜可压缩双透镜成像 [J]. 光子学报, 2011, 40(6): 949~954

    Zhang Cheng, Yang Hairong, Wei Sui. Compressive double lens imaging using deterministic phase mask [J]. Acta Photonica Sinica, 2011, 40(6): 949~954

[3] M. F. Duarte, M. A. Davenport, D. Takhar et al.. Single-pixel imaging via compressive sampling [J]. IEEE Signal Processing Magazine, 2008, 25(2): 83~91

[4] M. Akcakaya, P. Jinsoo, V. Tarokp. A coding theory approach to noisy compressive sensing using low density frames [J]. IEEE Trans. Signal Processing, 2011, 59(11): 5369~5379

[5] 付强, 李琼. 压缩感知中构造测量矩阵研究 [J]. 电脑与电信, 2011, 47(9): 39~41

    Fu Qiang, Li Qiong. The research of constructing the measurement matrix in compressive sensing [J]. Computer & Telecommunication, 2011, 47(9): 39~41

[6] 焦李成, 杨淑媛, 刘芳 等. 压缩感知回顾与展望 [J]. 电子学报, 2011, 39(7): 1651~1662

    Jiao Licheng, Yang Shuyuan, Liu Fang et al.. Development and prospect of compressive sensing [J]. Acta Electronica Sinica, 2011, 39(7): 1651~1662

[7] 刘吉英. 压缩感知理论及在成像中的应用 [D]. 长沙: 国防科学技术大学, 2010

    Liu Jiying. Application of Compressed Sensing in Imaging [D]. Changsha: National University of Defense Technology, 2010

[8] M. Elad. Optimized projections for compressed sensing [J]. IEEE Trans. Signal Processing, 2007, 55(12): 5695~5702

[9] J. M. Duarte-Carvajalino, G. Sapiro. Learning to sense sparse signals: simultaneous sensing matrix and sparsifying dictionary optimization [J]. IEEE Trans. Image Processing, 2009, 18(7): 1395~1408

[10] 肖小潮, 郑宝玉, 王臣昊. 基于最优观测矩阵的压缩信道感知 [J]. 信号处理, 2012, 28(1): 67~72

    Xiao Xiaochao, Zheng Baoyu, Wang Chenhao. Compressed channel estimation based on optimized measurement matrix [J]. Signal Processing, 2012, 28(1): 67~72

[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, Hu Shaohai. An optimization method for measurement matrix based on eigenvalue decomposition [J]. Signal Processing, 2012, 28(5): 653~658

[12] Yu Lifeng, Li Gang, Chang Liping. Optimizing projection matrix for compressed sensing systems[C]. 2011 8th International Conference on Information, Communications and Signal Processing (ICICS), 2011

[13] D. L. Donoho, Y. Tsaig, I. Drori et al.. Sparse solution of underdetermined systems of linear equations by stagewise orthogonal matching pursuit [J]. IEEE Trans. Information Theory, 2012, 58(2): 1094~1121

[14] E. J. Candes, T. Tao. Near-optimal signal recovery from random projections: universal encoding strategies [J]. IEEE Trans. Information Theory, 2006, 52(12): 5406~5425

[15] D. L. Donoho. Compressed sensing [J]. IEEE Trans. Information Theory, 2006, 52(4): 1289~1306

[16] D. Wei, O. Milenkovic. Subspace pursuit for compressive sensing signal reconstruction [J]. IEEE Trans. Information Theory, 2009, 55(5): 2230~2249

程涛, 朱国宾, 刘玉安. 基于0-1稀疏循环矩阵的测量矩阵分离研究[J]. 光学学报, 2013, 33(2): 0220001. Cheng Tao, Zhu Guobin, Liu Yu′an. Separation Research of Measurement Matrices Based on 0-1 Sparse Circulant Matrix[J]. Acta Optica Sinica, 2013, 33(2): 0220001.

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