Image Denoising via Time-Delay Regularization Coupled Nonlinear Diffusion Equations (Journal of Computational Mathematics, 2020)
A novel nonlinear anisotropic diffusion model is proposed for image denoising whichcan 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 whichmanifests itself through the presence of $p(x)$-Laplacian and time-delay regularization. Theproposed model offers a new nonlinear anisotropic diffusion which makes it possible toeffectively 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. Numericalexperiments illustrate that the proposed model appears to be overwhelmingly competitivein restoring the images corrupted by Gaussian noise.
Keywords: Image denoising; Galerkin's method; Existence; Uniqueness.