Jin, B;
Lu, X;
Jiao, Y;
(2017)
Group Sparse Recovery via the ℓ0(ℓ2) Penalty: Theory and Algorithm.
IEEE Transactions on Signal Processing
, 65
(4)
pp. 998-1012.
10.1109/TSP.2016.2630028.
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Abstract
In this work we propose and analyze a novel approach for recovering group sparse signals, which arise naturally in a number of practical applications. It is based on regularized least squares with an ℓ0(ℓ2) penalty. One distinct feature of the new approach is that it has the built-in decorrelation mechanism within each group, and thus can handle the challenging strong inner-group correlation. We provide a complete analysis of the regularized model, e.g., the existence of global minimizers, invariance property, support recovery, and characterization and properties of block coordinatewise minimizers. Further, the regularized functional can be minimized efficiently and accurately by a primal dual active set algorithm with provable global convergence. In particular, at each iteration, it involves solving least squares problems on the active set only, and merits fast local convergence, which makes the method extremely efficient for recovering group sparse signals. Extensive numerical experiments are presented to illustrate salient features of the model and the efficiency and accuracy of the algorithm. A comparative experimental study indicates that it is competitive with existing approaches.
| Type: | Article |
|---|---|
| Title: | Group Sparse Recovery via the ℓ0(ℓ2) Penalty: Theory and Algorithm |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1109/TSP.2016.2630028 |
| Publisher version: | http://dx.doi.org/10.1109/TSP.2016.2630028 |
| Language: | English |
| Additional information: | Copyright © 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. |
| Keywords: | group sparsity, block sparsity, blockwise mutual incoherence, global minimizer, block coordinatewise minimizer, primal dual active set algorithm, ℓ0(ℓ2) penalty |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1524665 |
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