# Modeling variational inpainting methods with splines

## TL;DR

This paper introduces a novel approach to image inpainting by modeling variational methods, especially total variation, using finite-dimensional spline spaces, providing an alternative to traditional discretization techniques.

## Contribution

The paper develops a spline-based variational inpainting model and analyzes its properties, offering a new discretization method that improves upon classical pointwise approaches.

## Key findings

- Spline-based inpainting yields comparable or better results than classical TV inpainting.
- The proposed method effectively handles image inpainting tasks with smooth and textured regions.
- Numerical experiments demonstrate the advantages of the spline approach over traditional discretization.

## Abstract

Mathematical methods of image inpainting involve the discretization of given continuous models. We present a method that avoids the standard pointwise discretization by modeling known variational approaches, in particular total variation (TV), using a finite dimensional spline space. Besides the analysis of the resulting model, we present a numerical implementation based on the alternating method of multipliers. We compare the results numerically with classical TV inpainting and give examples of applications.