English

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}
}