Image denoising based on a variable spatially exponent PDE

Image denoising is always considered an important area of image processing. In this work, we address a new PDE-based model for image denoising that have been contaminated by multiplicative noise, specially the Speckle one. We propose a new class of PDEs whose nonlinear structure depends on a spatially tensor depending quantity attached to the desired solution, which takes into account the gray level information by introducing a gray level indicator function in the diffusion coefficient. We give some theoretical results, discretization and also stability condition for the suggested model. Finally, we carry out some numerical results to approve the effectiveness of our model by comparing the results obtained with some competitive models.