NDLI: Block sparsity and sampling over a union of subspaces

Content Provider	IEEE Xplore Digital Library
Author	Eldar, Y.C. Mishali, M.
Copyright Year	2009
Description	Author affiliation: Technion-Israel Institute of Technology, Haifa, Israel (Eldar, Y.C.; Mishali, M.)
Abstract	Sparse signal representations have gained wide popularity in recent years. In many applications the data can be expressed using only a few nonzero elements in an appropriate expansion. In this paper, we study a block-sparse model, in which the nonzero coefficients are arranged in blocks. To exploit this structure, we redefine the standard (NP-hard) sparse recovery problem, based on which we propose a convex relaxation in the form of a mixed ℓ program. Isometry-based analysis is used to prove equivalence of the solution to that of the optimal program, under certain mild conditions. We further establish the robustness of our algorithm to mismodeling and bounded noise. We then present theoretical arguments and numerical experiments demonstrating the improved recovery performance of our method in comparison with sparse reconstruction that does not incorporate a block structure. The results are then applied to two related problems. The first is that of simultaneous sparse approximation. Our results can be used to prove isometry-based equivalence properties for this setting. In addition, we propose an alternative approach to acquire the measurements, that leads to performance improvement over standard methods. Finally, we show how our results can be used to sample signals in a finite structured union of subspaces, leading to robust and efficient recovery algorithms.
Starting Page	1
Ending Page	8
File Size	1136298
Page Count	8
File Format	PDF
ISBN	9781424432974
DOI	10.1109/ICDSP.2009.5201211
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2009-07-05
Publisher Place	Greece
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Sampling methods Noise robustness Compressed sensing Coherence Matching pursuit algorithms Signal representations Measurement standards Sparse matrices Particle measurements Minimization methods union of subspaces Block sparsity compressed sensing multiple measurement vectors (MMV) restricted isometry property sparse approximation
Content Type	Text
Resource Type	Article

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