alexa Application of the Topological Gradient Method to Color Image Restoration
Mathematics

Mathematics

Journal of Applied & Computational Mathematics

Author(s): Didier Auroux

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The aim of this paper is to generalize to color images the topological gradient method for the restoration problem. First, we consider a simple extension from grey-level to color images, by considering a channel by channel method. Then, as there should be some coupling between the different channels, we propose considering a tensorial approach: the Di Zenzo gradient. We derive an asymptotic expansion of this gradient with respect to the insertion of a small crack in the image, and we propose a new algorithm based on the topological gradient for the color image restoration problem. Finally, we illustrate these two approaches with numerical results.

This article was published in SIAM Journal on Imaging Sciences and referenced in Journal of Applied & Computational Mathematics

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