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.
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.
2016, Vol. 5 
