Cosamp and SP for the cosparse analysis model

CoSaMP and Subspace-Pursuit (SP) are two recovery algorithms that find the sparsest representation for a given signal under a given dictionary in the presence of noise. These two methods were conceived in the context of the synthesis sparse representation modeling. The cosparse analysis model is a recent construction that stands as an interesting alternative to the synthesis approach. This new model characterizes signals by the space they are orthogonal to. Despite the similarity between the two, the cosparse analysis model is markedly different from the synthesis one. In this paper we propose analysis versions of the CoSaMP and the SP algorithms, and demonstrate their performance for the compressed sensing problem.

[1]  Emmanuel J. Candès,et al.  Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies? , 2004, IEEE Transactions on Information Theory.

[2]  M. Davies,et al.  Greedy-like algorithms for the cosparse analysis model , 2012, 1207.2456.

[3]  Mike E. Davies,et al.  Iterative Hard Thresholding for Compressed Sensing , 2008, ArXiv.

[4]  Michael Elad,et al.  From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images , 2009, SIAM Rev..

[5]  Simon Foucart,et al.  Hard Thresholding Pursuit: An Algorithm for Compressive Sensing , 2011, SIAM J. Numer. Anal..

[6]  Michael Elad,et al.  Cosparse Analysis Modeling , 2011 .

[7]  S. Foucart.  Sparse Recovery Algorithms: Sufficient Conditions in Terms of RestrictedIsometry Constants , 2012 .

[8]  Rémi Gribonval,et al.  Iterative cosparse projection algorithms for the recovery of cosparse vectors , 2011, 2011 19th European Signal Processing Conference.

[9]  Michael Elad,et al.  The Cosparse Analysis Model and Algorithms , 2011, ArXiv.

[10]  Michael Elad,et al.  Analysis versus synthesis in signal priors , 2006, 2006 14th European Signal Processing Conference.

[11]  Pierre Vandergheynst,et al.  Compressed Sensing and Redundant Dictionaries , 2007, IEEE Transactions on Information Theory.

[12]  Olgica Milenkovic,et al.  Subspace Pursuit for Compressive Sensing Signal Reconstruction , 2008, IEEE Transactions on Information Theory.

[13]  Yonina C. Eldar,et al.  Compressed Sensing with Coherent and Redundant Dictionaries , 2010, ArXiv.

[14]  Deanna Needell,et al.  CoSaMP: Iterative signal recovery from incomplete and inaccurate samples , 2008, ArXiv.