# Double phase image restoration

## TL;DR

This paper investigates the use of double phase functionals for image restoration, focusing on mathematical properties and convergence of energy minimizers in the context of bounded variation functions.

## Contribution

It introduces a novel analysis of double phase energy minimizers for BV functions and establishes their connection via $Gamma$-convergence and relaxation techniques.

## Key findings

- Double phase energy minimizers are characterized for BV functions.
- The energy can be obtained through $Gamma$-convergence of regularized functionals.
- A capped fractional maximal function is used as a key analytical tool.

## 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.