English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the zaia usage as premium feature

ZAIA

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the access of premium content as premium feature

Premium Content

Zendy Tools

Zendy Open

The Cahn--Hilliard equation provides a simple and fast tool for binary image inpainting. By now, two generalizations to gray value images exist: bitwise binary inpainting and TV-H$^{-1}$ inpainting. This paper outlines a model based on the vector-valued Cahn--Hilliard equation. Additionally, we generalize our approach to a fractional-in-space version. Fourier spectral methods provide efficient solvers since they yield a fully diagonal scheme. Furthermore, their application to three spatial dimensions is straightforward. Numerical examples show the superiority of the proposed fractional Cahn--Hilliard inpainting approach over its nonfractional version. It improves the peak signal-to-noise ratio and structural similarity index. Likewise, the experiments confirm that the proposed model competes with previous inpainting methods, such as the total variation inpainting approach and its fourth-order variant.

A Fractional Inpainting Model Based on the Vector-Valued Cahn--Hilliard Equation