Bounded variation spaces with generalized Orlicz growth related to image denoising - UTU Research Portal

A1 Refereed original research article in a scientific journal

Bounded variation spaces with generalized Orlicz growth related to image denoising

Authors: Eleuteri, Michela; Harjulehto, Petteri; Hästö, Peter

Publisher: Springer Science and Business Media LLC

Publishing place: HEIDELBERG

Publication year: 2025

Journal: Mathematische Zeitschrift

Journal name in source: Mathematische Zeitschrift

Journal acronym: MATH Z

Article number: 26

Volume: 310

Issue: 2

Number of pages: 28

ISSN: 0025-5874

eISSN: 1432-1823

DOI: https://doi.org/10.1007/s00209-025-03731-9

Web address : https://doi.org/10.1007/s00209-025-03731-9

Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/491742249

Abstract

Motivated by the image denoising problem and the undesirable stair-casing effect of the total variation method, we introduce bounded variation spaces with generalized Orlicz growth. Our setup covers earlier variable exponent and double phase models. We study the norm and modular of the new space and derive a formula for the modular in terms of the Lebesgue decomposition of the derivative measure and a location dependent recession function. We also show that the modular can be obtained as the Γ-limit of uniformly convex approximating energies.

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Funding information in the publication:
Open Access funding provided by University of Helsinki (including Helsinki University Central
Hospital).