基于块稀疏贝叶斯学习的多任务压缩感知重构算法

文方青; 张弓; 贲德

doi:10.7498/aps.64.070201

摘要

本文提出一种基于块稀疏贝叶斯学习的多任务压缩感知重构算法, 利用块稀疏的单测量矢量模型求解多任务重构问题. 通过对信号统的计特性和稀疏块内的结构特性进行联合数学建模, 将稀疏重构问题转贝叶斯框架下的特征参数的迭代更新问题. 本文算法不需要信号稀疏度和噪声强度的先验信息, 是一种高效的盲重构算法. 仿真实验表明, 本文算法能有效利用信号的统计特性和结构信息, 在重构精度和收敛速率方面能够很好地折衷.

关键词:

Abstract

As a widely applied model for compressive sensing, the multitask compressive sensing can improve the performance of the inversion by appropriately exploiting the interrelationships of the tasks. The existing multitask compressive sensing recovery algorithms only utilize the statistical characteristics of a sparse signal, the structural characteristics of the sparse signal have not been taken into consideration. A multitask compressive sensing recovery algorithm is proposed in this paper based on the block sparse Bayesian learning. The block sparse single measurement vector model is applied to the multi-task problem. Both statistical and block structural characteristics of the sparse signal are used to build a mathematical model, and the sparse inverse problem is linked to the parameter iteration problems in the Bayesian framework. The proposed algorithm does not require the sparseness information and noise beforehand, which turns out to be an effective blind recovery algorithm. Extensive numerical experiments show that the proposed algorithm can exploit both statistical and structural characteristics of the signal, therefore it may reach a good trade-off between the recovery accuracy and the convergence rate.

Keywords:

作者及机构信息

1.
南京航空航天大学, 电子信息工程学院, 南京 210016;

2.
雷达成像与微波光子技术教育部重点实验室, 南京航空航天大学, 南京 210016;

3.
南京电子技术研究所, 南京 210039

基金项目: 国家自然科学基金(批准号: 61201367, 61271327, 61471191)、南京航空航天大学博士学位论文创新与创优基金(批准号: BCXJ14-08)、江苏省研究生培养创新工程(批准号: KYLX_0277)、中央高校基本科研业务费专项资金和江苏高校优势学科建设工程(PADA)资助的课题.

Authors and contacts

1.
College of Electronic and Information Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China;

2.
Key Laboratory of Radar Imaging and Microwave Photonics, Ministry of Education, Nanjing 210016, China;

3.
Nanjing Research Institute of Electronics Technology, Nanjing 210039, China

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61201367, 61271327, 61471191), the Funding for Outstanding Doctoral Dissertation in NUAA of China (Grant No. BCXJ14-08), the Funding of Innovation Program for Graduate Education, Jiangsu Province of China (Grant Nos. KYLX_0277), and the Fundamental Research Funds for the Central Universities, and Partly Funded by the Priority Academic Program Development of Higher Education Institutions of Jiangsu Province, China (PADA).

参考文献

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施引文献

[1]	Donoho D L 2006 IEEE Trans Inform Theory 52 1289
[2]	Zhang J D, Zhu D Y Zhang G 2012 IEEE Trans. SP 60 1718
[3]	Wang L Y, Li L, Yan B, Jiang C S, Wang H Y, Bao S L 2010 Chin. Phys. B 19 088106
[4]	Zhao S M, Zhuang P 2014 Chin. Phys. B 23 054203
[5]	Sun Y L, Tao J X 2014 Chin. Phys. B 23 078703
[6]	Zhang J C, Fu N Qiao L Y 2014 Acta Phys. Sin. 63 030701 (in Chinese) [张京超, 付宁, 乔立岩 2014 63 030701]
[7]	Ji S, Dunson D, Carin L 2009 IEEE Trans. SP 57 92
[8]	Qi Y, Liu D, Dunson D 2008 Proceedings of the 25th international conference on Machine learning, Helsinki, Finland, July 5-9 2008
[9]	Wang Y G, Yang L, Tang L 2013 EURASIP Journal on Advances in Signal Processing 2013 1
[10]	Li R P, Zhao Z F, Palicot J, Zhang H G 2014 IET Commun 8 1736
[11]	Wu Q S, Yimin D, Amin M G, Himed B 2014 Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing Florence, Italy May 4-9 2014
[12]	Ji S H, Xue Y, Carin L 2008 IEEE Trans. SP 56 2346
[13]	Hao C Q, Wang J, Deng B 2012 Acta Phys. Sin 61 148901 (in Chinese) [郝崇清, 王江, 邓斌 2012 61 148901]
[14]	Candes E J 2008 Comptes Rendus Mathematique 346 589
[15]	Candes E J Tao T 2005 IEEE Trans Inform Theory 51 4203
[16]	Tropp J A, Gilbert A C 2007 IEEE Trans Inform Theory 53 4655
[17]	Ning F L, He B J, Wei J 2013 Acta Phys. Sin 62 174214 (in Chinese) [宁方立, 何碧静, 韦娟 2013 62 174214]
[18]	Huang S X Zhao X F Sheng Z 2009 Chin. Phys. B 18 5084
[19]	Sheng Z 2013 Chin. Phys. B 22 029302
[20]	Zhang Z, Rao B D 2011 IEEE Journal of Selected Topics in Signal Processing 5 912
[21]	Wipf D P, Rao D B 2007 IEEE Trans. SP 55 3704

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