A fourth-order Partial Differential Equation model for multiplicative noise removal in images

In coherent imaging, the sensed images are usually corrupted with multiplicative data dependent noise. Unlike additive noise, the presence of multiplicative noise destroys the information content in the original image to a great extent. In this paper, we propose a new fourth-order Partial Differential Equation (PDE) model with a noise adaptive fidelity term for multiplicative Gamma noise removal under the variational Regularization framework. Variational approaches for multiplicative noise removal generally consist of a maximum a posteriori (MAP) based fidelity term and a Total-Variation (TV) regularization term. However, the second-order TV diffusion approximates the observed images with piecewise constant images, leading to the so-called block effect. The proposed model removes the multiplicative noise effectively and approximates observed images with planar ones making the restored images more natural compared to the second-order diffusion models. The proposed method is compared with the recent state-of-the art methods and the effective restoration capability of the filter is demonstrated experimentally.