Publication result detail

Approximal operator with application to audio inpainting

MOKRÝ, O.; RAJMIC, P.

Original Title

Approximal operator with application to audio inpainting

English Title

Approximal operator with application to audio inpainting

Type

WoS Article

Original Abstract

In their recent evaluation of time-frequency representations and structured sparsity approaches to audio inpainting, Lieb and Stark (2018) have used a particular mapping as a proximal operator. This operator serves as the fundamental part of an iterative numerical solver. However, their mapping is improperly justified. The present article proves that their mapping is indeed a proximal operator, and also derives its proper counterpart. Furthermore, it is rationalized that Lieb and Stark's operator can be understood as an approximation of the proper mapping. Surprisingly, in most cases, such an approximation (referred to as the approximal operator) is shown to provide even better numerical results in audio inpainting compared to its proper counterpart, while being computationally much more effective.

English abstract

In their recent evaluation of time-frequency representations and structured sparsity approaches to audio inpainting, Lieb and Stark (2018) have used a particular mapping as a proximal operator. This operator serves as the fundamental part of an iterative numerical solver. However, their mapping is improperly justified. The present article proves that their mapping is indeed a proximal operator, and also derives its proper counterpart. Furthermore, it is rationalized that Lieb and Stark's operator can be understood as an approximation of the proper mapping. Surprisingly, in most cases, such an approximation (referred to as the approximal operator) is shown to provide even better numerical results in audio inpainting compared to its proper counterpart, while being computationally much more effective.

Keywords

proximal operator; proximal algorithms; approximation; sparsity; audio inpainting

Key words in English

proximal operator; proximal algorithms; approximation; sparsity; audio inpainting

Authors

MOKRÝ, O.; RAJMIC, P.

RIV year

2021

Released

09.09.2020

Publisher

Elsevier

ISBN

0165-1684

Periodical

SIGNAL PROCESSING

Volume

179

Number

1

State

Kingdom of the Netherlands

Pages from

1

Pages to

8

Pages count

8

URL

https://www.sciencedirect.com/science/article/pii/S0165168420303510

Full text in the Digital Library

http://hdl.handle.net/11012/195252

BibTex

@article{BUT164795,
  author="Ondřej {Mokrý} and Pavel {Rajmic}",
  title="Approximal operator with application to audio inpainting",
  journal="SIGNAL PROCESSING",
  year="2020",
  volume="179",
  number="1",
  pages="1--8",
  doi="10.1016/j.sigpro.2020.107807",
  issn="0165-1684",
  url="https://www.sciencedirect.com/science/article/pii/S0165168420303510"
}

Documents

1-s2.0-S0165168420303510-main