A forward-backward algorithm for reweighted procedures: Application to radio-astronomical imaging

Research output: Contribution to conferencePaper

Abstract

During the last decades, reweighted procedures have shown high efficiency in computational imaging. They aim to handle non-convex composite penalization functions by iteratively solving multiple approximated sub-problems. Although the asymptotic behaviour of these methods has recently been investigated in several works, they all necessitate the sub-problems to be solved accurately, which can be sub-optimal in practice. In this work we present a reweighted forward-backward algorithm designed to handle non-convex composite functions. Unlike existing convergence studies in the literature, the weighting procedure is directly included within the iterations, avoiding the need for solving any sub-problem. We show that the obtained reweighted forward-backward algorithm converges to a critical point of the initial objective function. We illustrate the good behaviour of the proposed approach on a Fourier imaging example borrowed to radio-astronomical imaging.
Original languageEnglish
Number of pages5
Publication statusSubmitted - 18 Oct 2019
EventICASSP 2020 - Barcelona, Spain
Duration: 4 May 20208 May 2020
https://2020.ieeeicassp.org

Conference

ConferenceICASSP 2020
CountrySpain
CityBarcelona
Period4/05/208/05/20
Internet address

Fingerprint

composite functions
iteration
critical point

Cite this

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title = "A forward-backward algorithm for reweighted procedures: Application to radio-astronomical imaging",
abstract = "During the last decades, reweighted procedures have shown high efficiency in computational imaging. They aim to handle non-convex composite penalization functions by iteratively solving multiple approximated sub-problems. Although the asymptotic behaviour of these methods has recently been investigated in several works, they all necessitate the sub-problems to be solved accurately, which can be sub-optimal in practice. In this work we present a reweighted forward-backward algorithm designed to handle non-convex composite functions. Unlike existing convergence studies in the literature, the weighting procedure is directly included within the iterations, avoiding the need for solving any sub-problem. We show that the obtained reweighted forward-backward algorithm converges to a critical point of the initial objective function. We illustrate the good behaviour of the proposed approach on a Fourier imaging example borrowed to radio-astronomical imaging.",
author = "Audrey Repetti and Yves Wiaux",
year = "2019",
month = "10",
day = "18",
language = "English",
note = "ICASSP 2020 ; Conference date: 04-05-2020 Through 08-05-2020",
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Repetti, A & Wiaux, Y 2019, 'A forward-backward algorithm for reweighted procedures: Application to radio-astronomical imaging' Paper presented at ICASSP 2020, Barcelona, Spain, 4/05/20 - 8/05/20, .

A forward-backward algorithm for reweighted procedures: Application to radio-astronomical imaging. / Repetti, Audrey; Wiaux, Yves.

2019. Paper presented at ICASSP 2020, Barcelona, Spain.

Research output: Contribution to conferencePaper

TY - CONF

T1 - A forward-backward algorithm for reweighted procedures: Application to radio-astronomical imaging

AU - Repetti, Audrey

AU - Wiaux, Yves

PY - 2019/10/18

Y1 - 2019/10/18

N2 - During the last decades, reweighted procedures have shown high efficiency in computational imaging. They aim to handle non-convex composite penalization functions by iteratively solving multiple approximated sub-problems. Although the asymptotic behaviour of these methods has recently been investigated in several works, they all necessitate the sub-problems to be solved accurately, which can be sub-optimal in practice. In this work we present a reweighted forward-backward algorithm designed to handle non-convex composite functions. Unlike existing convergence studies in the literature, the weighting procedure is directly included within the iterations, avoiding the need for solving any sub-problem. We show that the obtained reweighted forward-backward algorithm converges to a critical point of the initial objective function. We illustrate the good behaviour of the proposed approach on a Fourier imaging example borrowed to radio-astronomical imaging.

AB - During the last decades, reweighted procedures have shown high efficiency in computational imaging. They aim to handle non-convex composite penalization functions by iteratively solving multiple approximated sub-problems. Although the asymptotic behaviour of these methods has recently been investigated in several works, they all necessitate the sub-problems to be solved accurately, which can be sub-optimal in practice. In this work we present a reweighted forward-backward algorithm designed to handle non-convex composite functions. Unlike existing convergence studies in the literature, the weighting procedure is directly included within the iterations, avoiding the need for solving any sub-problem. We show that the obtained reweighted forward-backward algorithm converges to a critical point of the initial objective function. We illustrate the good behaviour of the proposed approach on a Fourier imaging example borrowed to radio-astronomical imaging.

M3 - Paper

ER -