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In greedy pursuit of new directions: (nearly) orthogonal matching pursuit by directional optimisation

In greedy pursuit of new directions: (nearly) orthogonal matching pursuit by directional optimisation
In greedy pursuit of new directions: (nearly) orthogonal matching pursuit by directional optimisation
Matching Pursuit and orthogonal Matching Pursuit are greedy algorithms used to obtain sparse signal approximations. Orthogonal Matching Pursuit is known to offer better performance, but Matching Pursuit allows more efficient implementations. In this paper we propose novel greedy Pursuit algorithms based on directional updates. Using a conjugate direction, the algorithm becomes a novel implementation
of orthogonal Matching Pursuit, with computational requirements similar to current implementations based on QR factorisation. A significant reduction in memory requirements and computational complexity can be achieved by approximating the conjugate direction. Further computational savings can be made by using a steepest descent direction.
The two resulting algorithms are then comparable to Matching Pursuit in their computational requirements, their performance is however shown to be closer to that of orthogonal Matching Pursuit with the (slightly slower) approximate conjugate direction based approach outperforming the gradient
descent method .
Blumensath, Thomas
470d9055-0373-457e-bf80-4389f8ec4ead
Davies, Mike E.
9ca3625e-5b14-4f1f-90ac-1af468f521ae
Blumensath, Thomas
470d9055-0373-457e-bf80-4389f8ec4ead
Davies, Mike E.
9ca3625e-5b14-4f1f-90ac-1af468f521ae

Blumensath, Thomas and Davies, Mike E. (2007) In greedy pursuit of new directions: (nearly) orthogonal matching pursuit by directional optimisation. European Signal Processing Conference (EUSIPCO), Poland.

Record type: Conference or Workshop Item (Other)

Abstract

Matching Pursuit and orthogonal Matching Pursuit are greedy algorithms used to obtain sparse signal approximations. Orthogonal Matching Pursuit is known to offer better performance, but Matching Pursuit allows more efficient implementations. In this paper we propose novel greedy Pursuit algorithms based on directional updates. Using a conjugate direction, the algorithm becomes a novel implementation
of orthogonal Matching Pursuit, with computational requirements similar to current implementations based on QR factorisation. A significant reduction in memory requirements and computational complexity can be achieved by approximating the conjugate direction. Further computational savings can be made by using a steepest descent direction.
The two resulting algorithms are then comparable to Matching Pursuit in their computational requirements, their performance is however shown to be closer to that of orthogonal Matching Pursuit with the (slightly slower) approximate conjugate direction based approach outperforming the gradient
descent method .

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More information

Published date: September 2007
Venue - Dates: European Signal Processing Conference (EUSIPCO), Poland, 2007-09-01
Organisations: Signal Processing & Control Grp

Identifiers

Local EPrints ID: 151921
URI: https://eprints.soton.ac.uk/id/eprint/151921
PURE UUID: 2f9bd7b6-bf6e-49ea-8bab-183edfa518a1

Catalogue record

Date deposited: 15 Jun 2010 09:01
Last modified: 17 Jul 2019 00:00

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