A recovery algorithm for multitask compressive sensing based on block sparse Bayesian learning

Wen Fang-Qing; Zhang Gong; Ben De

doi:10.7498/aps.64.070201

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:

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).

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[14]	Candes E J 2008 Comptes Rendus Mathematique 346 589
[15]	Candes E J Tao T 2005 IEEE Trans Inform Theory 51 4203
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[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

Cited By

[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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Catalog

Vol. 64, Issue 7 - 2015-04-05

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