Epigraphical reformulation for non-proximable mixed norms

Seisuke Kyochi, Shunsuke Ono, Ivan Selesnick

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

Abstract

This paper proposes an epigraphical reformulation (ER) technique for non-proximable mixed norm regularization. Various regulariza- tion methods using mixed norms have been proposed, where their optimization relies on efficient computation of the proximity opera- tor of the mixed norms. Although the sophisticated design of mixed norms significantly improves the performance of regularization, the proximity operator of such a mixed norm is often unavailable. Our ER decouples a non-proximable mixed norm function into a prox- imable norm and epigraphical constraints. Thus, it can handle a wide range of non-proximable mixed norms as long as the proximal oper- ator of the outermost norm, and the projection onto the epigraphical constraints can be efficiently computed. Moreover, we prove that our ER does not change the minimizer of the original problem de- spite using a certain inequality approximation. We also provide a new structure-tensor-based regularization as an application of our framework, which illustrates the utility of ER.

Original languageEnglish (US)
Title of host publication2020 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2020 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages5400-5404
Number of pages5
ISBN (Electronic)9781509066315
DOIs
StatePublished - May 2020
Event2020 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2020 - Barcelona, Spain
Duration: May 4 2020May 8 2020

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Volume2020-May
ISSN (Print)1520-6149

Conference

Conference2020 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2020
CountrySpain
CityBarcelona
Period5/4/205/8/20

Keywords

  • Convex optimization
  • Epigraph
  • Epigraphical projection
  • Image recovery
  • Structure tensor total variation

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Electrical and Electronic Engineering

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  • Cite this

    Kyochi, S., Ono, S., & Selesnick, I. (2020). Epigraphical reformulation for non-proximable mixed norms. In 2020 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2020 - Proceedings (pp. 5400-5404). [9054650] (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings; Vol. 2020-May). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ICASSP40776.2020.9054650