DocumentCode :
3540572
Title :
Beyond ℓ1-norm minimization for sparse signal recovery
Author :
Mansour, Hassan
Author_Institution :
Univ. of British Columbia, Vancouver, BC, Canada
fYear :
2012
fDate :
5-8 Aug. 2012
Firstpage :
337
Lastpage :
340
Abstract :
Sparse signal recovery has been dominated by the basis pursuit denoise (BPDN) problem formulation for over a decade. In this paper, we propose an algorithm that outperforms BPDN in finding sparse solutions to underdetermined linear systems of equations at no additional computational cost. Our algorithm, called WSPGL1, is a modification of the spectral projected gradient for ℓ1 minimization (SPGL1) algorithm in which the sequence of LASSO subproblems are replaced by a sequence of weighted LASSO subproblems with constant weights applied to a support estimate. The support estimate is derived from the data and is updated at every iteration. The algorithm also modifies the Pareto curve at every iteration to reflect the new weighted ℓ1 minimization problem that is being solved. We demonstrate through extensive simulations that the sparse recovery performance of our algorithm is superior to that of ℓ1 minimization and approaches the recovery performance of iterative re-weighted ℓ1 (IRWL1) minimization of Candès, Wakin, and Boyd, although it does not match it in general. Moreover, our algorithm has the computational cost of a single BPDN problem.
Keywords :
compressed sensing; iterative methods; minimisation; signal denoising; ℓ1-norm minimization algorithm; IRWL1 minimization; LASSO subproblems; Pareto curve; SPGL1 algorithm; basis pursuit denoise problem; compressed sensing; iterative re-weighted ℓ1 minimization; single BPDN problem; sparse signal recovery; underdetermined linear systems; Sparse recovery; compressed sensing; iterative algorithms; partial support recovery; weighted ℓ1 minimization;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Statistical Signal Processing Workshop (SSP), 2012 IEEE
Conference_Location :
Ann Arbor, MI
ISSN :
pending
Print_ISBN :
978-1-4673-0182-4
Electronic_ISBN :
pending
Type :
conf
DOI :
10.1109/SSP.2012.6319697
Filename :
6319697
Link To Document :
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