Poisson image denoising based on fractional-order total variation

Poisson noise is an important type of electronic noise that is present in a variety of photon-limited imaging systems. Different from the Gaussian noise, Poisson noise depends on the image intensity, which makes image restoration very challenging. Moreover, complex geometry of images desires a regularization that is capable of preserving piecewise smoothness. In this paper, we propose a Poisson denoising model based on the fractional-order total variation (FOTV). The existence and uniqueness of a solution to the model are established. To solve the problem efficiently, we propose three numerical algorithms based on the Chambolle-Pock primal-dual method, a forward-backward splitting scheme, and the alternating direction method of multipliers (ADMM), each with guaranteed convergence. Various experimental results are provided to demonstrate the effectiveness and efficiency of our proposed methods over the state-of-the-art in Poisson denoising.