Double phase image restoration

Abstract

In this paper we explore the potential of the double phase functional in an image processing context. To this end, we study minimizers of the double phase energy for functions with bounded variation and show that this energy can be obtained by $\Gamma$-convergence or relaxation of regularized functionals. A central tool is a capped fractional maximal function of the derivative of $BV$ functions.

arXiv commentJ. Math. Anal. Appl., to appear

References in corpus (6)

• Maximal regularity for local minimizers of non-autonomous functionals
• Derivative bounds for fractional maximal functions
• Existence of renormalized solutions to elliptic equation in Musielak-Orlicz space
• Endpoint Sobolev and BV continuity for maximal operators
• Hölder continuity of $\omega$-minimizers of functionals with generalized Orlicz growth
• A borderline case of Calderón-Zygmund estimates for non-uniformly elliptic problems

Cited by in corpus (9)

• The weak Harnack inequality for unbounded supersolutions of equations with generalized Orlicz growth
• Regularity theory for non-autonomous problems with a priori assumptions
• Regularity results for a class of obstacle problems with $p,q-$growth conditions
• A fundamental condition for harmonic analysis in anisotropic generalized Orlicz spaces
• Bounded variation spaces with generalized Orlicz growth related to image denoising
• Convergence of generalized Orlicz norms with lower growth rate tending to infinity
• The double phase Dirichlet problem when the lowest exponent is equal to 1
• Bloch estimates in non-doubling generalized Orlicz spaces
• A double-phase Neumann problem with $p=1$