An improved ROF denoising model based on time-fractional derivative

Abstract

In this study, we discuss mainly the image denoising and texture retention issues. Usually, the time-fractional derivative has an adjustable fractional order to control the diffusion process, and its memory effect can nicely retain the image texture when it is applied to image denoising. Therefore, we design a new Rudin-Osher-Fatemi model with a time-fractional derivative based on a classical one, where the discretization in space is based on the integer-order difference scheme and the discretization in time is the approximation of the Caputo derivative (i.e., Caputo-like difference is applied to discretize the Caputo derivative). Stability and convergence of such an explicit scheme are analyzed in detail. We prove that the numerical solution to the new model converges to the exact solution with the order of O(τ^2−α+h²), where τ, α, and h are the time step size, fractional order, and space step size, respectively. Finally, various evaluation criteria including the signal-to-noise ratio, feature similarity, and histogram recovery degree are used to evaluate the performance of our new model. Numerical test results show that our improved model has more powerful denoising and texture retention ability than existing ones.