Gradient pursuits

Blumensath, T. and Davies, M.E. (2008) Gradient pursuits. IEEE Transactions on Signal Processing, 56, (6), 2370 -2382 . (doi:10.1109/TSP.2007.916124).


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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.

Item Type: Article
Digital Object Identifier (DOI): doi:10.1109/TSP.2007.916124
ISSNs: 1053-587X (print)
1941-0476 (electronic)
Keywords: sparse representations/approximations, matching pursuit, orthogonal matching pursuit, gradient optimisation, conjugate gradient optimisation
Subjects: Q Science > Q Science (General)
Divisions : University Structure - Pre August 2011 > Other
Faculty of Engineering and the Environment > Institute of Sound and Vibration Research > Signal Processing & Control Research Group
ePrint ID: 142525
Accepted Date and Publication Date:
June 2008Published
Date Deposited: 31 Mar 2010 15:21
Last Modified: 31 Mar 2016 13:18

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