Exponential total variation model for noise removal, its numerical algorithms and applications

The total variation model has been considered to be one of the most successful and representative denoising models that can preserve edges well. However, its main shortage is that it frequently causes the undesirable “block” effect. To solve this problem, high-order TV models have been proposed. Yet, they tend to damp the high frequency components in an image, often resulting in over smoothing or blurring of main features in an image. Besides, the optimization solutions underlying high-order TV models can only be obtained through numerically solving the associated high-order PDEs derived from the Euler–Lagrange equation, which is quite time-consuming. In this paper, we propose a novel total variation model based on exponential function (ETV). Furthermore, a fast numerical algorithm is designed for ETV based on Split Bregman algorithm. We test our ETV on a broad range of standard images, synthetic aperture radar (SAR) image and medical magnetic resonance images (MRI), and compared with the related TV, and high-order TV models. The experimental results have demonstrated that our ETV offers much better trade-off between noise removal and edge preservation as compared with TV and high-order TV models. In addition, ETV also shows a high computational efficiency when boosted by split Bregman algorithm.