High order partial differential equations for images restoration

Abstract

In the present work, a thorough mathematical investigation is presented of a nonlinear anisotropic diffusion-based model that can be utilized for image restoration purposes. The model is designed to address common image corruption factors such as noise and blurring. The mathematical analysis of the model has demonstrated its well-posedness, stability, and convergence properties. Furthermore, numerical experiments have been conducted to show the model's effectiveness in restoring degraded images. These investigations have yielded valu- able insights into both the theoretical and practical aspects of the model's image restoration capabilities. As such, this research significantly contributes to the development of mathe- matical models for image processing and provides a solid foundation for future research in this field. Keywords: Image restoration, edge-preserving image denoising, nonlinear anisotropic