Four-Directional Total Variation With Overlapping Group Sparsity for Image Denosing

Abstract

In this paper, a new model combining four-directional total variation with overlapping group sparsity is proposed, which not only suppresses the staircase effects introduced by traditional total variation, but also fully utilizes the gradient neighborhood information on each pixel of the image. In order to decrease the computation time of image denoising, the alternating direction method of multipliers (ADMM) is adopted to divide the complex optimization problem into separate subproblems that are easy to solve. At the same time, two-dimensional Fast Fourier Transform (FFT) and majorization-minimization (MM) are used to solve the subproblems alternatively. Then, the proposed new model is compared with other state-of-the-art models. Experiments show that the new model is robust in denoising. The new model not only excavates the gradient information of the four directions on the image to remove the noise more effectively, but also better in preserving image features, further reducing staircase artifacts. INDEX TERMS Image denoising; Four-directional total variation; Overlapping group sparsity; ADMM.

A nonlinear total variation based computed tomography (CT) image reconstruction method using gradient reinforcement

“…The impact of single direction constraint over a limited angle tomographic image taken from both x and y directions also showed that the directional information plays an important role in feature preservation in the image taken from a limited view angle ( Zhang et al, 2021 ). There have been alternative modified gradient based total variation algorithms ( Zhang et al, 2021 ; Sakurai et al, 2011 ; Fan Liao & Shu, 2015 ; Huang et al, 2016 ; Huang et al, 2018 ; Hu & Jacob, 2012 ; Zhou & Fan, 2021 ). Sakurai et al proposed a faster four directional TV algorithm that brings two additional partial terms to the horizontal and vertical directional terms in classical TV ( Sakurai et al, 2011 ).…”