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arXiv · 2509.09237

Functions of bounded Musielak-Orlicz-type deformation and anisotropic Total Generalized Variation for image-denoising problems

Giacomo Bertazzoni·Elisa Davoli·Samuele Riccò·Elvira Zappale
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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.

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Giacomo Bertazzoni, Elisa Davoli, Samuele Riccò, Elvira Zappale. 2025-09-11. Functions of bounded Musielak-Orlicz-type deformation and anisotropic Total Generalized Variation for image-denoising problems. https://arxiv.org/abs/2509.09237

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