An improved spatially controlled reaction–diffusion equation with a non-linear second order operator for image super-resolution. (December 2021)

• Record Type: Journal Article
• Authors: Hadri, Aissam; Khalfi, Hamza; Laghrib, Amine; Nachaoui, Mourad
• Is Part Of: Nonlinear analysis. Volume 62(2021)
• Publication Date: 2021-12
• Subjects: Multi-frame super-resolution -- Non-linear PDE -- Tensor diffusion; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2021.103352
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this work, we introduce an efficient second-order reaction–diffusion (R.D.) equation for noise removal and image super-resolution. The main idea is to decompose the image into two components: cartoon and texture parts using a new spatially controlled diffusion obtained by incorporating into R.D. equation an anti-diffusion effect modelled by a space dependent parameter γ . Hence, the proposed equation leads to a noticeable improvement in texture structure preservation. Moreover, we demonstrate an existence result of global solutions and analyse the asymptotic behaviour of the equation. Furthermore, an approximation of the sensitive parameter γ is established using a learning optimization technique. As a result, the anti-diffusion parameter γ can be efficiently computed to increase the quality of the restored image and preserve its texture. The proposed approach is tested and validated using multiple numerical experiments alongside a comparison with some competitive methods for a variety of applications including image de-noising, decomposition and super-resolution.