Adaptive Sensing Matrix Design for Greedy Algorithms in Mmv Compressive Sensing

Sensing matrix can be designed with low coherence with the measurement matrix to improve the sparse signal recovery performance of greedy algorithms. However, most of the sensing matrix design algorithms are computationally expensive due to large number of iterations. This paper proposes an iteration-free sensing matrix design algorithm for multiple measurement vectors (MMV) compressive sensing. Specifi-cally, sensing matrix is designed in the sense of the local cumulative cross-coherence (LCCC) of the sensing matrix with respect to the measurement matrix when the number of M-MV is sufficient and the sparse signals are of full rank. Experiment results verify the effectiveness of the proposed algorithm in terms of improving the sparse signal recovery performance of greedy algorithms.

[1]  J. Tropp.  Algorithms for simultaneous sparse approximation. Part II: Convex relaxation , 2006, Signal Process..

[2]  Michael Elad,et al.  Optimized Projections for Compressed Sensing , 2007, IEEE Transactions on Signal Processing.

[3]  Joel A. Tropp,et al.  Algorithms for simultaneous sparse approximation. Part I: Greedy pursuit , 2006, Signal Process..

[4]  Jong Chul Ye,et al.  Compressive MUSIC: Revisiting the Link Between Compressive Sensing and Array Signal Processing , 2012, IEEE Trans. Inf. Theory.

[5]  Abolfazl Mehbodniya,et al.  A re-weighted algorithm for designing data dependent sensing dictionary , 2011 .

[6]  Yi Shen,et al.  Dictionaries Construction Using Alternating Projection Method in Compressive Sensing , 2011, IEEE Signal Processing Letters.

[7]  Yonina C. Eldar,et al.  Rank Awareness in Joint Sparse Recovery , 2010, IEEE Transactions on Information Theory.

[8]  Zhihui Zhu,et al.  On Projection Matrix Optimization for Compressive Sensing Systems , 2013, IEEE Transactions on Signal Processing.

[9]  Yonina C. Eldar,et al.  Reduce and Boost: Recovering Arbitrary Sets of Jointly Sparse Vectors , 2008, IEEE Transactions on Signal Processing.

[10]  Joel A. Tropp,et al.  Greed is good: algorithmic results for sparse approximation , 2004, IEEE Transactions on Information Theory.

[11]  Jean-Jacques Fuchs.  Extension of the Pisarenko method to sparse linear arrays , 1997, IEEE Trans. Signal Process..

[12]  Jie Chen,et al.  Theoretical Results on Sparse Representations of Multiple-Measurement Vectors , 2006, IEEE Transactions on Signal Processing.

[13]  Saeid Sanei,et al.  A gradient-based alternating minimization approach for optimization of the measurement matrix in compressive sensing , 2012, Signal Process..

[14]  Pierre Vandergheynst,et al.  Dictionary Preconditioning for Greedy Algorithms , 2008, IEEE Transactions on Signal Processing.

[15]  Michael Elad,et al.  Optimally sparse representation in general (nonorthogonal) dictionaries via ℓ1 minimization , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[16]  S. Mallat,et al.  Adaptive greedy approximations , 1997 .

[17]  Zhouchen Lin,et al.  Optimized Projections for Compressed Sensing via Direct Mutual Coherence Minimization , 2015, Signal Process..

[18]  Miguel R. D. Rodrigues,et al.  Projection Design for Statistical Compressive Sensing: A Tight Frame Based Approach , 2013, IEEE Transactions on Signal Processing.