(untitled) (Journal of Computational Mathematics, 2020)
A novel nonlinear anisotropic diffusion model is proposed for image denoising which can be viewed as a novel regularized model that preserves the cherished features of Perona-Malik to some extent. It is characterized by a local dependence in the diffusivity which manifests itself through the presence of p(x)-Laplacian and time-delay regularization. The proposed model offers a new nonlinear anisotropic diffusion which makes it possible to effectively enhance the denoising capability and preserve the details while avoiding artifacts. Accordingly, the restored image is very clear and becomes more distinguishable. By Galerkin's method, we establish the well-posedness in the weak setting. Numerical experiments illustrate that the proposed model appears to be overwhelmingly competitive in restoring the images corrupted by Gaussian noise.