Submitted Paper

Inserted: 11 sep 2025
Last Updated: 26 jan 2026

Year: 2025

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: Functions of Bounded Deformation, imaging, total generalized variation, Generalized Orlicz spaces, Modular

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• BDRZ.pdf