Computing the proximity operator of the lp norm with 0 <p <1

Feishe Chen, Lixin Shen, Bruce W. Suter

Research output: Contribution to journalArticle

6 Scopus citations

Abstract

Sparse modelling with the lp norm of 0 ≤ p ≤ 1 requires the availability of the proximity operator of the lp norm. The proximity operators of the l0 and l1 norms are the well-known hard- and soft-thresholding estimators, respectively. In this study, the authors give a complete study on the properties of the proximity operator of the lp norm. Based on these properties, explicit formulas of the proximity operators of the l1/2 norm and l2/3 norm are derived with simple proofs; for other values of p, an iterative Newton's method is developed to compute the proximity operator of the lp norm by fully exploring the available proximity operators of the l0, l1/2, l2/3, and l1 norms. As applications, the proximity operator of the lp norm with 0 ≤ p ≤ 1 is applied to the lp-regularisation for compressive sensing and image restoration.

Original languageEnglish (US)
Pages (from-to)557-565
Number of pages9
JournalIET Signal Processing
Volume10
Issue number5
DOIs
StatePublished - Jul 1 2016

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering

Fingerprint Dive into the research topics of 'Computing the proximity operator of the l<sub>p</sub> norm with 0 <p <1'. Together they form a unique fingerprint.

  • Cite this