Sparse signal recovery in the presence of intra-vector and inter-vector correlation

This work discusses the problem of sparse signal recovery when there is correlation among the values of nonzero entries. We examine intra-vector correlation in the context of the block sparse model and inter-vector correlation in the context of the multiple measurement vector model, as well as their combination. Algorithms based on the sparse Bayesian learning are presented and the benefits of incorporating correlation at the algorithm level are discussed. The impact of correlation on the limits of support recovery is also discussed highlighting the different impact intra-vector and inter-vector correlations have on such limits.

[1]  Michael I. Jordan,et al.  Union support recovery in high-dimensional multivariate regression , 2008, 2008 46th Annual Allerton Conference on Communication, Control, and Computing.

[2]  Peng Zhao,et al.  On Model Selection Consistency of Lasso , 2006, J. Mach. Learn. Res..

[3]  Shannon L. Risacher,et al.  Sparse Bayesian multi-task learning for predicting cognitive outcomes from neuroimaging measures in Alzheimer's disease , 2012, 2012 IEEE Conference on Computer Vision and Pattern Recognition.

[4]  Bhaskar D. Rao,et al.  An Empirical Bayesian Strategy for Solving the Simultaneous Sparse Approximation Problem , 2007, IEEE Transactions on Signal Processing.

[5]  Philip Schniter,et al.  Tracking and smoothing of time-varying sparse signals via approximate belief propagation , 2010, 2010 Conference Record of the Forty Fourth Asilomar Conference on Signals, Systems and Computers.

[6]  Volkan Cevher,et al.  Sparse Signal Recovery and Acquisition with Graphical Models , 2010, IEEE Signal Processing Magazine.

[7]  Bhaskar D. Rao,et al.  Sparse solutions to linear inverse problems with multiple measurement vectors , 2005, IEEE Transactions on Signal Processing.

[8]  Bhaskar D. Rao,et al.  Limits on Support Recovery of Sparse Signals via Multiple-Access Communication Techniques , 2011, IEEE Transactions on Information Theory.

[9]  C EldarYonina,et al.  Robust recovery of signals from a structured union of subspaces , 2009 .

[10]  Martin J. Wainwright,et al.  Information-Theoretic Limits on Sparsity Recovery in the High-Dimensional and Noisy Setting , 2007, IEEE Transactions on Information Theory.

[11]  Philip Schniter,et al.  Efficient High-Dimensional Inference in the Multiple Measurement Vector Problem , 2011, IEEE Transactions on Signal Processing.

[12]  Tzyy-Ping Jung,et al.  Compressed Sensing for Energy-Efficient Wireless Telemonitoring of Noninvasive Fetal ECG Via Block Sparse Bayesian Learning , 2012, IEEE Transactions on Biomedical Engineering.

[13]  Bhaskar D. Rao,et al.  Signal processing with the sparseness constraint , 1998, Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '98 (Cat. No.98CH36181).

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

[15]  Tzyy-Ping Jung,et al.  Low Energy Wireless Body-Area Networks for Fetal ECG Telemonitoring via the Framework of Block Sparse Bayesian Learning , 2012, ArXiv.

[16]  Emmanuel J. Candès,et al.  Decoding by linear programming , 2005, IEEE Transactions on Information Theory.

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

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

[19]  George Eastman House,et al.  Sparse Bayesian Learning and the Relevance Vector Machine , 2001 .

[20]  Y. Bresler,et al.  Spectrum-blind minimum-rate sampling and reconstruction of 2-D multiband signals , 1996, Proceedings of 3rd IEEE International Conference on Image Processing.

[21]  Vahid Tarokh,et al.  Shannon-Theoretic Limits on Noisy Compressive Sampling , 2007, IEEE Transactions on Information Theory.

[22]  Namrata Vaswani,et al.  LS-CS-Residual (LS-CS): Compressive Sensing on Least Squares Residual , 2009, IEEE Transactions on Signal Processing.

[23]  Ping Feng,et al.  Spectrum-blind minimum-rate sampling and reconstruction of multiband signals , 1996, 1996 IEEE International Conference on Acoustics, Speech, and Signal Processing Conference Proceedings.

[24]  Rohit U. Nabar,et al.  Introduction to Space-Time Wireless Communications , 2003 .

[25]  Volkan Cevher,et al.  Model-Based Compressive Sensing , 2008, IEEE Transactions on Information Theory.

[26]  Yonina C. Eldar,et al.  Exploiting Statistical Dependencies in Sparse Representations for Signal Recovery , 2010, IEEE Transactions on Signal Processing.

[27]  Andrzej Cichocki,et al.  Improved M-FOCUSS Algorithm With Overlapping Blocks for Locally Smooth Sparse Signals , 2008, IEEE Transactions on Signal Processing.

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

[29]  Sundeep Rangan,et al.  Necessary and Sufficient Conditions for Sparsity Pattern Recovery , 2008, IEEE Transactions on Information Theory.

[30]  Zhilin Zhang,et al.  Exploiting Correlation in Sparse Signal Recovery Problems: Multiple Measurement Vectors, Block Sparsity, and Time-Varying Sparsity , 2011, ArXiv.

[31]  Bhaskar D. Rao,et al.  Extension of SBL Algorithms for the Recovery of Block Sparse Signals With Intra-Block Correlation , 2012, IEEE Transactions on Signal Processing.

[32]  Bhaskar D. Rao,et al.  Sparse Signal Recovery With Temporally Correlated Source Vectors Using Sparse Bayesian Learning , 2011, IEEE Journal of Selected Topics in Signal Processing.

[33]  M. Yuan,et al.  Model selection and estimation in regression with grouped variables , 2006 .

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

[35]  Bhaskar D. Rao,et al.  On the benefits of the block-sparsity structure in sparse signal recovery , 2012, 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[36]  Martin J. Wainwright,et al.  Information-theoretic limits on sparsity recovery in the high-dimensional and noisy setting , 2009, IEEE Trans. Inf. Theory.