Nonlocal Speckle Denoising Model Based on Non-linear Partial Differential Equations

Abstract

Image denoising is among the most fundamental problems in image processing. A large range of methods covering various fields of mathematics are available for denoising an image. The initial denoising models are derived from energy minimization using nonlinear partial differential equations (PDEs). The filtering based models have also been used for quite a long time where the denoising is done by smoothing operators. The most successful among them was the very recently developed nonlocal means method proposed by Buades, Coll and Morel in 2005. Though the method is very accurate in removing noise, it is very slow and hence quite impractical. In 2008, Gilboa and Osher extended some known PDE and variational techniques in image processing to the nonlocal framework. The motivation behind this was to make any point interact with any other point in the image. Using nonlocal PDE operators, they proposed the nonlocal total variation method for Gaussian noise. In this paper, we develop a nonlinear PDE based accelerated diffusion speckle denoising model. For faster convergence, we use the Split Bregman scheme to find the solution to this new model. The new model shows more accurate results than the existing speckle denoising model. It is also faster than the original nonlocal means method.