An improved spatially controlled reaction–diffusion equation with a non-linear second order operator for image super-resolution. (December 2021) - Hadri, Aissam; Khalfi, Hamza; Laghrib, Amine; Nachaoui, Mourad
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.