一种适用于TDOMP算法的测量矩阵优化方法

赵娟; 白霞

doi:10.12000/JR15131

一种适用于TDOMP算法的测量矩阵优化方法

doi: 10.12000/JR15131

赵娟^,,
白霞

(北京理工大学信息与电子学院北京 100081)

基金项目:

国家自然科学基金(61421001, 61331021),北京市高等教育青年英才资助课题(YETP1159)

详细信息

作者简介:
赵娟(1975-),女,四川人,北京理工大学信息与电子学院副教授,博士,主要研究领域为压缩感知理论及应用。E-mail:juanzhao@bit.edu.cn白霞(1978-),女,辽宁人,北京理工大学信息与电子学院讲师,博士,主要研究领域为SAR信号处理。E-mail:bai@bit.edu.cn

通讯作者:
赵娟juanzhao@bit.edu.cn

计量
- 文章访问数: 2612
- HTML全文浏览量: 480
- PDF下载量: 1114
- 被引次数: 0
出版历程
- 收稿日期: 2015-12-26
- 修回日期: 2016-01-24
- 网络出版日期: 2016-02-28

Measurement Matrix Optimization Method for TDOMP Algorithm

Zhao Juan^,,
Bai Xia

(School of Information and Electronics, Beijing Institute of Technology, Beijing 100081, China)

Funds:

The National Natural Science Foundation of China (61421001, 61331021), Beijing Higher Education Young Elite Teacher Project (YETP1159)

摘要

摘要: 测量矩阵的优化设计有利于提高压缩感知中信号的重构性能。该文研究了适用于TDOMP (TwoDictionaries OMP)重构算法的测量矩阵优化方法。TDOMP算法是一种改进的OMP算法,该算法使用与感知矩阵互相关性低的匹配矩阵来辨识正确的感知矩阵原子。所提方法利用交替投影的思想来优化测量矩阵从而得到相关性低的感知矩阵和匹配矩阵,然后用于TDOMP算法来提高信号的重建性能。仿真实验验证了所提方法的有效性。
- 压缩感知 /
- 测量矩阵 /
- Gram矩阵 /
- 互相关
Abstract: Optimizing the measurement matrix can improve reconstruction performance in compressed sensing. In this study, we study the measurement matrix optimization method regarding its application to the Two Dictionaries Orthogonal Matching Pursuit (TDOMP) algorithm. The TDOMP is a modified OMP, which uses a matching matrix with low cross-coherence to identify the correct atoms of the sensing matrix. The proposed optimization method is based on alternative projection technique to construct the measurement and matching matrices with low cross-coherence to improve the performance of the TDOMP. Experimental results verify the effectiveness of the proposed method.
- Compressed Sensing (CS) /
- Measurement matrix /
- Gram matrix /
- Mutual coherence

HTML全文

参考文献(15)

[1]	Donoho D L. Compressed sensing[J]. IEEE Transactions on Information Theory, 2006, 52(4): 1289-1306.
[2]	Candes E J, Romberg J, and Tao T. Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information[J]. IEEE Transactions on Information Theory, 2006, 52(2): 489-509.
[3]	Tsaig Y and Donoho D L. Extensions of compressed sensing[J].Signal Processing, 2006, 86(3): 549-571.
[4]	Ender J H G. On compressive sensing applied to radar[J]. Signal Processing, 2010, 90(5): 1402-1414.
[5]	Sharma S K, Patwary M and Abdel-Maguid M. Spectral efficient compressive transmission framework for wireless communication systems[J]. IET Signal Processing, 2013, 7(7): 558-564.
[6]	Majumdar A and Ward R K. On the choice of compressed sensing priors and sparsifying transforms for MR image reconstruction: an experimental study[J]. Signal Processing: Image Communication, 2012, 27(9): 1035-1048.
[7]	Kim S, Koh K, Lustig M, et al.. An interior-point method for large scale l1 regularized least squares[J]. IEEE Journal of Selected Topics in Signal Processing, 2007, 1(4): 606-617.
[8]	Tropp J A. Greed is good: algorithmic results for sparse approximation[J]. IEEE Transactions on Information Theory, 2004, 50(10): 2231-2242.
[9]	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.
[10]	Duarte J M and Sapiro G. Learning to sense sparse signals: simultaneous sensing matrix and sparsifying dictionary optimization[J]. IEEE Transactions on Image Processing, 2009, 18(7): 1395-1408.
[11]	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(4): 999-1009.
[12]	Elad M. Optimized projections for compressed sensing[J]. IEEE Transactions on Signal Processing, 2007, 55(12): 5695-5702.
[13]	Xu J, Pi Y, and Cao Z. Optimized projection matrix for compressive sensing[J]. EURASIP Journal on Advances in Signal Processing, 2010: 560349.
[14]	Schnass K and Vandergheynst P. Dictionary preconditioning for greedy algorithms[J]. IEEE Transactions on Signal Processing, 2008, 56(5): 1994-2002.
[15]	Zhao Juan, Bai Xia, Bi Shi-he, et al.. Coherence-based analysis of modified orthogonal matching pursuit using sensing dictionary[J]. IET Signal Processing, 2015, 9(3): 218-225.