A Time-Fractional Approach to High-Order PDE Systems in Image Denoising
摘要
This paper introduces a novel time-fractional PDE model for image denoising, which leverages the Caputo fractional derivative to provide enhanced accuracy in preserving fine details during denoising. Our model combines the strengths of Perona-Malik anisotropic diffusion and Weickert’s structure tensor, with a time-fractional evolution equation to account for non-local temporal effects. The model is formulated as a reaction-diffusion system, and we establish the existence and uniqueness of solutions using the Schauder fixed point theorem. Numerical results show that our method improves texture preservation while effectively removing noise, outperforming existing methods in both visual quality and computational efficiency.