Time-fractional diffusion equation-based image denoising model

Abstract

In the last two decades, due to the use of total variation (TV) denoising, variation models for image reconstruction have achieved great success. Compare to some known variation models which have just adopted the space-fractional diffusion equation, the time-fractional diffusion equation has another adjustable time-fractional derivative order to control the diffusion process. Therefore, in this paper, a new denoising model based on time-fractional diffusion equation is proposed, where the discretization in space is the application of classical difference scheme while the discretization in time is the approximation of the Caputo differential. Furthermore, both the explicit and implicit numerical scheme named TFEIS are built and its stability and convergence are rigorously discussed. We prove the full-discretization is stable under some conditions and the numerical solution converges to the exact one with order $$O(\tau^{2 - \alpha } + h^{2} )$$ , where τ and $$h$$ are the time and space step size, respectively. Finally, various evaluation indexes such as histogram recovery degree, signal-to-noise ratio, and edge texture retention index are applied to compare new and original models comprehensively in lots of images. Computer simulation results show our models