Stagewise Weak Gradient Pursuits
Stagewise Weak Gradient Pursuits
Finding sparse solutions to underdetermined inverse problems is a fundamental challenge encountered in a wide range of signal processing applications, from signal acquisition to source separation. This paper looks at greedy algorithms that are applicable to very large problems. The main contribution is the development of a new selection strategy (called stagewise weak selection) that effectively selects several elements in each iteration. The new selection strategy is based on the realization that many classical proofs for recovery of sparse signals can be trivially extended to the new setting. What is more, simulation studies show the computational benefits and good performance of the approach. This strategy can be used in several greedy algorithms, and we argue for the use within the gradient pursuit framework in which selected coefficients are updated using a conjugate update direction. For this update, we present a fast implementation and novel convergence result
sparse representations/approximations, orthogonal
matching pursuit, weak matching pursuit, gradient
pursuit, stagewise selection, compressed sensing
4333-4346
Blumensath, T.
470d9055-0373-457e-bf80-4389f8ec4ead
Davies, M.E.
2f97d5ab-efda-4d6f-936d-00ae95d19e65
November 2009
Blumensath, T.
470d9055-0373-457e-bf80-4389f8ec4ead
Davies, M.E.
2f97d5ab-efda-4d6f-936d-00ae95d19e65
Blumensath, T. and Davies, M.E.
(2009)
Stagewise Weak Gradient Pursuits.
IEEE Transactions on Signal Processing, 57 (11), .
(doi:10.1109/TSP.2009.2025088).
Abstract
Finding sparse solutions to underdetermined inverse problems is a fundamental challenge encountered in a wide range of signal processing applications, from signal acquisition to source separation. This paper looks at greedy algorithms that are applicable to very large problems. The main contribution is the development of a new selection strategy (called stagewise weak selection) that effectively selects several elements in each iteration. The new selection strategy is based on the realization that many classical proofs for recovery of sparse signals can be trivially extended to the new setting. What is more, simulation studies show the computational benefits and good performance of the approach. This strategy can be used in several greedy algorithms, and we argue for the use within the gradient pursuit framework in which selected coefficients are updated using a conjugate update direction. For this update, we present a fast implementation and novel convergence result
More information
Published date: November 2009
Keywords:
sparse representations/approximations, orthogonal
matching pursuit, weak matching pursuit, gradient
pursuit, stagewise selection, compressed sensing
Organisations:
Signal Processing & Control Grp
Identifiers
Local EPrints ID: 142503
URI: http://eprints.soton.ac.uk/id/eprint/142503
ISSN: 1053-587X
PURE UUID: b6375ccc-ae29-47e8-aab9-dca0c88ca1bc
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Date deposited: 31 Mar 2010 15:02
Last modified: 14 Mar 2024 02:55
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Contributors
Author:
M.E. Davies
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