Bounded variation spaces with generalized Orlicz growth related to image denoising

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 $\Gamma$-limit of uniformly convex approximating energies.

References in corpus (5)

• Maximal regularity for local minimizers of non-autonomous functionals
• Double phase image restoration
• Regularity theory for non-autonomous partial differential equations without Uhlenbeck structure
• A fundamental condition for harmonic analysis in anisotropic generalized Orlicz spaces
• Bilevel training schemes in imaging for total-variation-type functionals with convex integrands

Cited by in corpus (1)

• A double-phase Neumann problem with $p=1$