Compressed sensing for block-sparse smooth signals

We present reconstruction algorithms for smooth signals with block sparsity from their compressed measurements. We tackle the issue of varying group size via the group-sparse least absolute shrinkage selection operator (LASSO) as well as via latent group LASSO regularizations. We achieve smoothness in the signal via fusion. We develop low-complexity solvers for our proposed formulations through the alternating direction method of multipliers.

[1]  John N. Tsitsiklis,et al.  Parallel and distributed computation , 1989 .

[2]  Michael A. Saunders,et al.  Atomic Decomposition by Basis Pursuit , 1998, SIAM J. Sci. Comput..

[3]  R. Tibshirani,et al.  A note on the group lasso and a sparse group lasso , 2010, 1001.0736.

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

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

[6]  David L Donoho,et al.  Compressed sensing , 2006, IEEE Transactions on Information Theory.

[7]  Jean-Philippe Vert,et al.  Group Lasso with Overlaps: the Latent Group Lasso approach , 2011, ArXiv.

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

[9]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[10]  Ivan W. Selesnick,et al.  Total variation denoising with overlapping group sparsity , 2013, 2013 IEEE International Conference on Acoustics, Speech and Signal Processing.

[11]  R. Tibshirani,et al.  Sparsity and smoothness via the fused lasso , 2005 .

[12]  R. Tibshirani.  Regression Shrinkage and Selection via the Lasso , 1996 .