Inexact Proximal Operators for Lp-Quasinorm Minimization (bibtex)

by Cian O'Brien, Mark D. Plumbley

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 forp≤ 1 the algorithm is effective in the high-noise scenario, outperforming the Lasso despite the inexactness of the proximal step.

Reference:

Cian O'Brien, Mark D. Plumbley, "Inexact Proximal Operators for Lp-Quasinorm Minimization", In 2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), vol. , no. , pp. 4724-4728, 2018.

Bibtex Entry:

@inproceedings{DBLP:conf/icassp/OBrienP18, author = {Cian O'Brien and Mark D. Plumbley}, booktitle={2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)}, title={Inexact Proximal Operators for Lp-Quasinorm Minimization}, year={2018}, volume={}, number={}, pages={4724-4728}, 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 forp≤ 1 the algorithm is effective in the high-noise scenario, outperforming the Lasso despite the inexactness of the proximal step.}, keywords={convex programming;iterative methods;minimisation;signal processing;proximal operator;ℓp-quasinorm Minimization;classic ℓ1-Lasso;high-noise scenario;smooth fitting term;signal processing applications;proximal methods;Majorization-Minimization procedure;iterative algorithm;convex regularization term;Signal processing algorithms;Minimization;Machine learning;Signal processing;Image denoising;Optimization;Approximation algorithms;Proximal Methods;Compressed Sensing;Sparse Recovery;Majorization-Minimization}, doi={10.1109/ICASSP.2018.8462524}, ISSN={2379-190X}, month={April}, url = {http://epubs.surrey.ac.uk/846268/} }