Block-sparse compressed sensing with partially known signal support via non-convex minimisation

The mixed l 2 / l p (0 <; p ≤ 1) norm minimisation method with partially known support for recovering block-sparse signals is studied. The authors mainly extend this work on block-sparse compressed sensing by incorporating some known part of the block support information as a priori and establish sufficient restricted p -isometry property ( p -RIP) conditions for exact and robust recovery. The authors' theoretical results show it is possible to recover the block-sparse signals via l 2 / l p minimisation from reduced number of measurements by applying the partially known support. The authors also derive a lower bound on necessary random Gaussian measurements for the p -RIP conditions to hold with high possibility. Finally, a series of numerical experiments are carried out to illustrate that fewer measurements with smaller p are needed to reconstruct the signal.

[1]  Joel A. Tropp,et al.  Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit , 2007, IEEE Transactions on Information Theory.

[2]  S. Foucart,et al.  Sparsest solutions of underdetermined linear systems via ℓq-minimization for 0 , 2009 .

[3]  Zongben Xu,et al.  Restricted p-isometry properties of nonconvex block-sparse compressed sensing , 2014, Signal Process..

[4]  Yonina C. Eldar,et al.  Robust Recovery of Signals From a Structured Union of Subspaces , 2008, IEEE Transactions on Information Theory.

[5]  Rick Chartrand,et al.  Exact Reconstruction of Sparse Signals via Nonconvex Minimization , 2007, IEEE Signal Processing Letters.

[6]  Rabab K. Ward,et al.  Compressed sensing of color images , 2010, Signal Process..

[7]  R. von Borries,et al.  Compressed Sensing Using Prior Information , 2007, 2007 2nd IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing.

[8]  I. Daubechies,et al.  Iteratively reweighted least squares minimization for sparse recovery , 2008, 0807.0575.

[9]  Song Li,et al.  Restricted p–isometry property and its application for nonconvex compressive sensing , 2012, Adv. Comput. Math..

[10]  Wei Lu,et al.  Modified-CS: Modifying compressive sensing for problems with partially known support , 2009, 2009 IEEE International Symposium on Information Theory.

[11]  Wang Yao,et al.  L 1/2 regularization , 2010 .

[12]  Babak Hassibi,et al.  On the Reconstruction of Block-Sparse Signals With an Optimal Number of Measurements , 2008, IEEE Transactions on Signal Processing.

[13]  S. Horvath,et al.  Statistical Applications in Genetics and Molecular Biology , 2011 .

[14]  Yonina C. Eldar,et al.  Block-Sparse Signals: Uncertainty Relations and Efficient Recovery , 2009, IEEE Transactions on Signal Processing.

[15]  S. Frick,et al.  Compressed Sensing , 2014, Computer Vision, A Reference Guide.

[16]  Namrata Vaswani,et al.  Exact reconstruction conditions and error bounds for regularized Modified Basis Pursuit (Reg-modified-BP) , 2010, 2010 Conference Record of the Forty Fourth Asilomar Conference on Signals, Systems and Computers.

[17]  Zongben Xu,et al.  On recovery of block-sparse signals via mixed l 2 / l q ( 0 < q ≤ 1 ) normminimization , 2013 .

[18]  E. Candès,et al.  Stable signal recovery from incomplete and inaccurate measurements , 2005, math/0503066.

[19]  Weiyu Xu,et al.  Weighted ℓ1 minimization for sparse recovery with prior information , 2009, 2009 IEEE International Symposium on Information Theory.

[20]  Emmanuel J. Candès,et al.  Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information , 2004, IEEE Transactions on Information Theory.

[21]  Hassan Mansour,et al.  Recovering Compressively Sampled Signals Using Partial Support Information , 2010, IEEE Transactions on Information Theory.

[22]  R. Chartrand,et al.  Restricted isometry properties and nonconvex compressive sensing , 2007 .

[23]  Laurent Jacques,et al.  A short note on compressed sensing with partially known signal support , 2009, Signal Process..

[24]  Yonina C. Eldar,et al.  Blind Multiband Signal Reconstruction: Compressed Sensing for Analog Signals , 2007, IEEE Transactions on Signal Processing.

[25]  Chiara Sabatti,et al.  Empirical Bayes Estimation of a Sparse Vector of Gene Expression Changes , 2005, Statistical applications in genetics and molecular biology.