Image denoising by a novel variable‐order total fractional variation model

Abstract

The total variation model performs very well for removing noise while preserving edges. However, it gives a piecewise constant solution which often leads to the staircase effect, consequently small details such as textures are filtered out in the denoising process. Fractional‐order total variation method is one of the major approaches to overcome such drawbacks. Unlike their good quality of fractional order, all these methods use a fixed fractional order for the whole of the image. In this paper, a novel variable‐order total fractional variation model is proposed for image denoising, in which the order of fractional derivative will be allocated automatically for each pixel based on the context of the image. This kind of selection is able to capture the edges and texture of the image simultaneously. In this regard, we prove the existence and uniqueness of the presented model. The split Bregman method is adapted to solve the model. Finally, the results illustrate the efficiency of the proposed model that yielded good visual effects and a better signal‐to‐noise ratio.