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Inexact proximal operators for ℓp-quasinorm minimization

O’Brien, Cian and Plumbley, Mark (2018) Inexact proximal operators for ℓp-quasinorm minimization In: 2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 15–20 Apr 2018, Calgary, Alberta, Canada.

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Abstract

Proximal methods are an important tool in signal processing applications, where many problems can be characterized by the minimization of an expression involving a smooth fitting term and a convex regularization term – for example the classic ℓ1-Lasso. Such problems can be solved using the relevant proximal operator. Here we consider the use of proximal operators for the ℓp-quasinorm where 0 ≤ p ≤ 1. Rather than seek a closed form solution, we develop an iterative algorithm using a Majorization-Minimization procedure which results in an inexact operator. Experiments on image denoising show that for p ≤ 1 the algorithm is effective in the high-noise scenario, outperforming the Lasso despite the inexactness of the proximal step.

Item Type: Conference or Workshop Item (Conference Poster)
Divisions : Faculty of Engineering and Physical Sciences > Electronic Engineering
Authors :
NameEmailORCID
O’Brien, Cian
Plumbley, Markm.plumbley@surrey.ac.uk
Date : 13 September 2018
Funders : European Union’s Seventh Framework Programme
DOI : 10.1109/ICASSP.2018.8462524
Copyright Disclaimer : © 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works
Uncontrolled Keywords : Proximal Methods; Compressed Sensing; Sparse Recovery; Majorization-Minimization
Related URLs :
Depositing User : Clive Harris
Date Deposited : 19 Apr 2018 12:51
Last Modified : 11 Dec 2018 11:24
URI: http://epubs.surrey.ac.uk/id/eprint/846268

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