Gradient pursuits
Gradient pursuits
Sparse signal approximations have become a fundamental tool in signal processing with wide ranging applications from source separation to signal acquisition. The ever growing number of possible applications and in particular the ever increasing problem sizes now addressed lead to new challenges in terms of computational strategies and the development of fast and efficient algorithms has become paramount.
Recently, very fast algorithms have been developed to solve convex optimisation problems that are often used to approximate the sparse approximation problem, however, it has also been shown, that in certain circumstances, greedy strategies, such as Orthogonal Matching Pursuit, can have better performance than the convex methods.
In this paper improvements to greedy strategies are proposed and algorithms are developed that approximate Orthogonal Matching Pursuit with computational requirements more akin to Matching Pursuit. Three different directional optimisation schemes based on the gradient, the conjugate gradient and an approximation to the conjugate gradient are discussed respectively. It is shown that the conjugate gradient update leads to a novel implementation of Orthogonal Matching Pursuit, while the gradient based approach as well as the approximate conjugate gradient methods both lead to fast approximations to Orthogonal Matching Pursuit, with the approximate conjugate gradient method being superior to the gradient method.
sparse representations/approximations, matching pursuit, orthogonal matching pursuit, gradient
optimisation, conjugate gradient optimisation
2370 -2382
Blumensath, T.
470d9055-0373-457e-bf80-4389f8ec4ead
Davies, M.E.
2f97d5ab-efda-4d6f-936d-00ae95d19e65
June 2008
Blumensath, T.
470d9055-0373-457e-bf80-4389f8ec4ead
Davies, M.E.
2f97d5ab-efda-4d6f-936d-00ae95d19e65
Blumensath, T. and Davies, M.E.
(2008)
Gradient pursuits.
IEEE Transactions on Signal Processing, 56 (6), .
(doi:10.1109/TSP.2007.916124).
Abstract
Sparse signal approximations have become a fundamental tool in signal processing with wide ranging applications from source separation to signal acquisition. The ever growing number of possible applications and in particular the ever increasing problem sizes now addressed lead to new challenges in terms of computational strategies and the development of fast and efficient algorithms has become paramount.
Recently, very fast algorithms have been developed to solve convex optimisation problems that are often used to approximate the sparse approximation problem, however, it has also been shown, that in certain circumstances, greedy strategies, such as Orthogonal Matching Pursuit, can have better performance than the convex methods.
In this paper improvements to greedy strategies are proposed and algorithms are developed that approximate Orthogonal Matching Pursuit with computational requirements more akin to Matching Pursuit. Three different directional optimisation schemes based on the gradient, the conjugate gradient and an approximation to the conjugate gradient are discussed respectively. It is shown that the conjugate gradient update leads to a novel implementation of Orthogonal Matching Pursuit, while the gradient based approach as well as the approximate conjugate gradient methods both lead to fast approximations to Orthogonal Matching Pursuit, with the approximate conjugate gradient method being superior to the gradient method.
More information
Published date: June 2008
Keywords:
sparse representations/approximations, matching pursuit, orthogonal matching pursuit, gradient
optimisation, conjugate gradient optimisation
Organisations:
Other, Signal Processing & Control Grp
Identifiers
Local EPrints ID: 142525
URI: http://eprints.soton.ac.uk/id/eprint/142525
ISSN: 1053-587X
PURE UUID: 50d713b9-1e89-4070-8e68-42789e718a35
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Date deposited: 31 Mar 2010 15:21
Last modified: 14 Mar 2024 02:55
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Contributors
Author:
M.E. Davies
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