Well-posedness and simulation results of a coupled denoising PDE. (June 2022) - El Hakoume, A.; Afraites, L.; Laghrib, A.
Abstract: In this paper, we are interested in the mathematical and numerical study of a new non variational model based on a high order non-linear PDE system for image denoising. The proposed model generalizes and improves the nonvariational model of Halim and Kumar (2020). Our model is based on a diffusion tensor that improves the behavior of the Perona–Malik diffusion directions in homogeneous regions and the Weickert model near tiny edges with a high diffusion order. The proposed approach takes into consideration the best of regularized Perona–Malik process in flat regions, and the benefit of the Weickert filter effect near sharp edges. To overcome the difficulty of the 4th order in the proposed equation, we involve the decomposition approach of H − 1 norm suggested by Guo et al. (2011) [20, 21] to transform it into coupled second order equations which is more appropriate to represent the small details in the textured image. By the Schauder method, we establish the existence and uniqueness of the weak solution of the proposed reaction–diffusion System. In the end, some experiment results illustrate the effectiveness of the proposed model compared with the results of some existing models.