Randomized simultaneous orthogonal matching pursuit

In this paper, we develop randomized simultaneous orthogonal matching pursuit (RandSOMP) algorithm which computes an approximation of the Bayesian minimum mean-squared error (MMSE) estimate of an unknown rowsparse signal matrix. The approximation is based on greedy iterations, as in SOMP, and it elegantly incorporates the prior knowledge of the probability distribution of the signal and noise matrices into the estimation process. Unlike the exact MMSE estimator which is computationally intractable to solve, the Bayesian greedy pursuit approach offers a computationally feasible way to approximate the MMSE estimate. Our simulations illustrate that the proposed RandSOMP algorithm outperforms SOMP both in terms of mean-squared error and probability of exact support recovery. The benefits of RandSOMP are further illustrated in direction-of-arrival estimation with sensor arrays and image denoising.

[1]  Yonina C. Eldar,et al.  Structured Compressed Sensing: From Theory to Applications , 2011, IEEE Transactions on Signal Processing.

[2]  Neil Robertson,et al.  21st European Signal Processing Conference , 2013 .

[3]  Michael Elad,et al.  A Plurality of Sparse Representations Is Better Than the Sparsest One Alone , 2009, IEEE Transactions on Information Theory.

[4]  Justin Ziniel,et al.  Fast bayesian matching pursuit , 2008, 2008 Information Theory and Applications Workshop.

[5]  Gaël Richard,et al.  Blind Denoising with Random Greedy Pursuits , 2014, IEEE Signal Processing Letters.

[6]  Jeffrey D. Blanchard,et al.  Greedy Algorithms for Joint Sparse Recovery , 2014, IEEE Transactions on Signal Processing.

[7]  Y. C. Pati,et al.  Orthogonal matching pursuit: recursive function approximation with applications to wavelet decomposition , 1993, Proceedings of 27th Asilomar Conference on Signals, Systems and Computers.

[8]  Dmitry M. Malioutov,et al.  A sparse signal reconstruction perspective for source localization with sensor arrays , 2005, IEEE Transactions on Signal Processing.

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

[10]  Yonina C. Eldar,et al.  Average Case Analysis of Multichannel Sparse Recovery Using Convex Relaxation , 2009, IEEE Transactions on Information Theory.

[11]  Michael Elad,et al.  Sparse and Redundant Representations - From Theory to Applications in Signal and Image Processing , 2010 .