LI Zhetao, XIE Jingxiong, ZHU Gengming, PENG Xin, XIE Yanrong, CHOI Youngjune. Block-Based Projection Matrix Design for Compressed Sensing[J]. Chinese Journal of Electronics, 2016, 25(3): 551-555. doi: 10.1049/cje.2016.05.022
 Citation: LI Zhetao, XIE Jingxiong, ZHU Gengming, PENG Xin, XIE Yanrong, CHOI Youngjune. Block-Based Projection Matrix Design for Compressed Sensing[J]. Chinese Journal of Electronics, 2016, 25(3): 551-555.

# Block-Based Projection Matrix Design for Compressed Sensing

##### doi: 10.1049/cje.2016.05.022
Funds:  This work is supported by the National Natural Science Foundation of China (No.61100215, No.61311140261, No.61379115, No.61372049, No.61300039), Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (No.2012R1A1A1017284), Ministry of Science, ICT and Future Planning of Korea under the Global IT Talent Support Program (No.NIPA-2014-H0904-14-1004) supervised by the National IT Industry Promotion Agency, Hunan Provincial Natural Science Foundation of China (No.13JJ8006, No.12JJ9021, No.14JJ3130) and the Construct Program of the Key Discipline in Hunan Province and College Students Innovation Project (No.2013XTUXJ47).
• Corresponding author: ZHU Gengming is a professor in Hunan University of Science and Technology. His research interests include wireless sensor network and compressive sensing. (Email: gengmingzhu@gmail.com)
• Rev Recd Date: 2014-09-24
• Publish Date: 2016-05-10
• The objective of optimizing a projection matrix is to decrease the mutual coherence between a projection matrix and a basis matrix. In this paper, a novel block-based method is proposed to design a projection matrix in compressed sensing. Here, the projection matrix is divided into two blocks. The relationship between the two blocks was obtained by reasoning and proving. Theoretical analysis demonstrates that the mutual coherence between the whole projection matrix and the whole basis matrix keeps as good as the mutual coherence between the block matrix and blocked basis matrix. Experimental results show that the proposed method obtains better performance compared to existing methods.
•  E.J. Candes and M.B. Wakin, "An introduction to compressive sampling", IEEE Signal Process Magazine, Vol.25, No.2, pp.21-30, 2008. Z.T. Li, J.X. Xie, D.B. Tu, et al., "Sparse signal recovery by stepwise subspace pursuit in compressed sensing", International Journal of Distributed Sensor Networks. Vol.2013, Article ID 798537, 5 pages, 2013. L.C. Jiao, S. Yang, F. Liu, et al., "Development and prospect of compressive sensing", Acta Electronica Sinica, Vol.39, No.1, pp.18-22, 2011. (in Chinese) E.J. Candes, "The restricted isometry property and its implications for compressed sensing", Comptes Rendus Mathematique, Vol.346, No.9, pp.589-592, 2008. G.M. Shi, D.H. Liu and D.H. Gao, "Advances in theory and application of compressed sensing", Acta Electronica Sinica, Vol.37, No.5, pp.1070-1081, 2009. (in Chinese) Y.H. Rong, Zh. Cheng, D.D. Wei, et al., "The theory of compressed sensing and reconstruction algorithm", Acta Electronica Sinica, Vol.39, No.1, pp.142-148, 2011. (in Chinese) Z.T. Li, T. Pan, G.M. Zhu, et al., "A construction algorithm of measurement matrix with low power average column coherence", Chinese Journal of Electronics, Vol.42, No.7, pp.1360- 1364, 2014. (in Chinese) V. Abolghasemi, S. Ferdowsi and S. Sanei, "A gradient-based alternating minimization approach for optimization of the measurement matrix in compressive sensing", Signal Processing, Vol.92, No.4, pp.999-1009, 2012. M. Elad, "Optimized projections for compressed sensing", IEEE Transactions on Signal Processing, Vol.55, No.12, pp.5695- 5702, 2007. J.M. Duarte-Carvajalino and G Sapiro, "Learning to sense sparse signals: Simultaneous sensing matrix and sparsifying dictionary optimization", IEEE Transactions on Image Processing, Vol.18, No.7, pp.1395-1408, 2009. G. Li, Z.H. Zhu, D.H. Yang, et al., "On projection matrix optimization for compressive sensing systems", IEEE Transactions on Signal Processing, Vol.61, No.11, pp.2887-2898, 2013. J.P. Xu, Y.M. Pi and Z.J. Cao, "Optimized projection matrix for compressive sensing", EURASIP Journal of Advance Signal Process, Vol.2010, No.43, pp.1-8, 2010. Q.H. Zhang, Y.L. Fu, H.F. Li, et al., "Optimized projection matrix for compressed sensing", Circuits, Systems, and Signal Processing, Vol.33, No.5, pp.1627-1636, 2014. Z.W. Wen and W.T. Yin, "A feasible method for optimization with orthogonality constraints", Mathematical Programming, Vol.142, No.1-2, pp.397-434, 2013. N. Cleju, "Optimized projections for compressed sensing via rank-constrained nearest correlation matrix", Applied and Computational Harmonic Analysis, Vol.36, No.3, pp.495-507, 2014. J.A. Tropp and A.C. Gilbert, "Signal recovery from random measurements via orthogonal matching pursuit", IEEE Transactions on Infomation Theory, Vol.53, No.12, pp.4655-4666. 2007. S.S. Chen, D.L. Donoho and M.A. Saunders, "Atomic decomposition by basis pursuit", SIAM Journal on Scientific Computing, Vol.20, No.1, pp.33-61, 1998.

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