Nonconvex fractional order total variation based image denoising model under mixed stripe and Gaussian noise

Abstract

In this paper, we propose a minimization-based image denoising model for the removal of mixed stripe and Gaussian noise. The objective function includes the prior information from both the stripe noise and image. Specifically, we adopted a unidirectional regularization term and a nonconvex group sparsity term for the stripe noise component, while we utilized a nonconvex fractional order total variation (FTV) regularization for the image component. The priors for stripes enable adequate extraction of periodic or non-periodic stripes from an image in the presence of high levels of Gaussian noise. Moreover, the nonconvex FTV facilitates image restoration with less staircase artifacts and well-preserved edges and textures. To solve the nonconvex problem, we employed an iteratively reweighted $ \ell_1 $ algorithm, and then the alternating direction method of multipliers was adopted for solving subproblems. This led to an efficient iterative algorithm, and its global convergence was proven. Numerical results show that the proposed model provides better denoising performance than existing models with respect to visual features and image quality evaluations.