Cross-diffusion systems for image processing: II. The nonlinear case

TL;DR

This paper explores nonlinear cross-diffusion systems for image restoration, analyzing their mathematical properties and demonstrating their effectiveness through numerical experiments, extending previous linear models.

Contribution

It introduces and studies nonlinear cross-diffusion models for image processing, providing theoretical analysis and numerical validation of their performance.

Findings

Models are well-posed and exhibit desirable scale-space properties.

Numerical results show diverse capabilities in image filtering.

Potential for improved image restoration techniques.

Abstract

In this paper the use of nonlinear cross-diffu\-sion systems to model image restoration is investigated, theoretically and numerically. In the first case, well-posedness, scale-space properties and long time behaviour are analyzed. From a numerical point of view, a computational study of the performance of the models is carried out, suggesting their diversity and potentialities to treat image filtering problems. The present paper is a continuation of a previous work of the same authors, devoted to linear cross-diffusion models. \keywords{Cross-diffusion \and Complex diffusion \and Image restoration}