A Hybrid Model Combining Anisotropic Diffusion and Variable-Order Total Variation for Poisson Denoising

Variable-order TV and anisotropic diffusion for Poisson denoising

Résumé

In this paper, we present and analyze a new model for Poisson denoising, integrating variable-order fractional derivatives with anisotropic diffusion. The unique challenge of Poisson image denoising lies in its dependence on image intensity, which introduces significant complexities in the restoration process. The intricate geometry of natural images demands robust regularization techniques that can preserve fine details and maintain piecewise smooth regions. To achieve this, we employ a variable-order approach that adapts to image features and an anisotropic diffusion term that accommodates directional variations within the image. For the numerical solution, we implement the Alternating Direction Method of Multipliers (ADMM) algorithm, a powerful tool for handling complex optimization problems. Extensive experimental results highlight the effectiveness of our method, demonstrating marked improvements over existing state-of-the-art techniques for denoising images corrupted by Poisson noise.