Nonlinear projection digital image inpainting and restoration methods

TL;DR

This paper introduces nonlinear projection methods combined with variational models for digital image inpainting and restoration, effectively reconstructing images from sparse, incomplete, and distorted data, demonstrated through art restoration examples.

Contribution

It presents a novel approach integrating nonlinear sampling, interpolation, and variational techniques for improved image inpainting and restoration from limited and distorted information.

Findings

Effective reconstruction from sparse data

Numerical results validate the method's accuracy

Coupled Hamilton-Jacobi equations are well-posed

Abstract

This paper concerns with nonuniform sampling and interpolation methods combined with variational models for the solution of a generalized image inpainting problem and the restoration of digital signals. In particular, we discuss the problem of reconstructing a digital signal/image from very few, sparse, and complete information and a substantial incomplete information, which will be assumed as the result of a nonlinear distortion. As a typical and inspiring example, we illustrate the concrete problem of the color restoration of a destroyed art fresco from its few known fragments and some gray picture taken prior to the damage. Numerical implementations are included together with several examples and numerical results to illustrate the proposed method. The numerical experience suggests furthermore that a particular system of coupled Hamilton-Jacobi equations is well-posed.