Sharpening Sparse Regularizers

Abdullah Al-Shabili, Ivan Selesnick

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Non-convex penalties outperform the convex ℓ-norm, but generally sacrifice the cost function convexity. As a middle ground, we propose a framework to design non-convex penalties that induce sparsity more effectively than the ℓ-norm, but without sacrificing the cost function convexity. The non-smooth non-convex regularizers are constructed by subtracting from the non-smooth convex penalty its smoothed version. We propose a generalized infimal convolution smoothing smoothing technique to obtain the smoothed version. We call the proposed framework sharpening sparse regularizers (SSR) to imply its advantages compared to convex and non-convex regularizers. The SSR framework is applicable to any sparsity regularized ill-posed linear inverse problem. Furthermore, it recovers and generalizes several non-convex penalties in the literature as special cases. The SSR-RLS problem can be formulated as a saddle point problem, and solved by a scalable generalized primal-dual algorithm. The effectiveness of the SSR framework is demonstrated by numerical experiments.

Original languageEnglish (US)
Title of host publication2019 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages4908-4912
Number of pages5
ISBN (Electronic)9781479981311
DOIs
StatePublished - May 2019
Event44th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Brighton, United Kingdom
Duration: May 12 2019May 17 2019

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Volume2019-May
ISSN (Print)1520-6149

Conference

Conference44th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019
CountryUnited Kingdom
CityBrighton
Period5/12/195/17/19

Keywords

  • Sparsity
  • convex analysis
  • convex optimization
  • non-convexity
  • smoothing

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Electrical and Electronic Engineering

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