Functions of bounded Musielak-Orlicz-type deformation and anisotropic Total Generalized Variation for image-denoising problems
Analysis of PDEs
2026-01-27 v4
Abstract
In the first part of this paper we introduce the space of bounded deformation fields with generalized Orlicz growth. We establish their main properties, provide a modular representation, and characterize a decomposition of the modular into an absolutely continuous part and a singular part weighted via a recession function. A further analysis in the variable exponent case is also provided. The second part of the paper contains a notion of Musielak-Orlicz anisotropic Total Generalized Variation. We establish a duality representation, and show well-posedness of the corresponding image reconstruction problem.
Keywords
Cite
@article{arxiv.2509.09237,
title = {Functions of bounded Musielak-Orlicz-type deformation and anisotropic Total Generalized Variation for image-denoising problems},
author = {Giacomo Bertazzoni and Elisa Davoli and Samuele Riccò and Elvira Zappale},
journal= {arXiv preprint arXiv:2509.09237},
year = {2026}
}