Poisson image denoising based on fractional-order total variation

Abstract

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.

A fractional-order total variation-based model for image color transfer

“…where I is the identity matrix. Following the ideas in [41], we note that the matrix µ(∇ α ) T ∇ α + I can be diagonalized by a two-dimensional fast Fourier transform (FFT) under periodic boundary condition. Hence, this normal equation ( 21) can be efficiently solved by using FFT :…”

Discrete Laplacian Operator and Its Applications in Signal Processing

“…Similar to PDE(s), variational models with integer derivatives in the context of image processing date back to the 80s, but the introduction of fractional-order variational models is recent. Applications in this category include image denoising [55]- [66], in-painting [58], [67], fusion [56], [64], nonrigid registration [68], super-resolution [56] and optical flow estimation [69].…”

Adaptive Image Restoration via a Relaxed Regularization of Mean Curvature

“…Specifically, the operator ∇ 2 in (3) is changed to Δ. Furthermore, an ADMM-based algorithm same to [8] is applied to solve the proposed model (10). erefore, the rigorous convergence proof of Algorithm 1 can refer to the proof presented in [8].…”

“…To solve this inverse problem, one of the most popular research directions is applying variational regularization methods. It mainly includes total variation (TV) regularization [1][2][3], nonlocal regularization [4], sparse regularization [5], higher-order regularization based on higher-order derivatives [6][7][8][9], and fractionalorder regularization based on fractional-order derivatives [10,11].…”