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Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems (2007)
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| Venue: | IEEE JOURNAL OF SELECTED TOPICS IN SIGNAL PROCESSING |
| Citations: | 519 - 16 self |
BibTeX
@TECHREPORT{Figueiredo07gradientprojection,
author = {Mário A. T. Figueiredo and Robert D. Nowak and Stephen J. Wright},
title = {Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems},
institution = {IEEE JOURNAL OF SELECTED TOPICS IN SIGNAL PROCESSING},
year = {2007}
}
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Abstract
Many problems in signal processing and statistical inference involve finding sparse solutions to under-determined, or ill-conditioned, linear systems of equations. A standard approach consists in minimizing an objective function which includes a quadratic (squared ℓ2) error term combined with a sparseness-inducing (ℓ1) regularization term.Basis pursuit, the least absolute shrinkage and selection operator (LASSO), wavelet-based deconvolution, and compressed sensing are a few well-known examples of this approach. This paper proposes gradient projection (GP) algorithms for the bound-constrained quadratic programming (BCQP) formulation of these problems. We test variants of this approach that select the line search parameters in different ways, including techniques based on the Barzilai-Borwein method. Computational experiments show that these GP approaches perform well in a wide range of applications, often being significantly faster (in terms of computation time) than competing methods. Although the performance of GP methods tends to degrade as the regularization term is de-emphasized, we show how they can be embedded in a continuation scheme to recover their efficient practical performance.
Keyphrases
gradient projection inverse problem sparse reconstruction regularization term gp method bound-constrained quadratic programming abstract many problem wide range barzilai-borwein method signal processing linear system objective function computation time computational experiment gp approach sparse solution absolute shrinkage standard approach different way basis pursuit selection operator line search parameter statistical inference involve wellknown example continuation scheme error term waveletbased deconvolution efficient practical performance
