Research On Multiplicative Noise Removal Models Based On Doubly Anisotropic Degenerate Diffusion Equations

Image denoising is a meaningful and challenging task in image processing. Forthe past decades, noise-removal methods based on partial differential equations(PDEs) have become a powerful and well-founded tool in image analysis. Amongnumerous PDE-based approaches, the filters formulated by nonlinear partialdifferential equations have tremendous and impressive results. For addictive noiseremoval, a flood of papers have demonstrated that the nonlinear diffusion methodscan remove noise and simultaneously preserve or even enhance semanticallyimportant information. However, nonlinear diffusion equations have not yet beenstudied thoroughly in the area of multiplicative noise removal.Inspired by the impressive performance of nonlinear diffusion models inaddictive noise removal, we address this problem in the view of nonlinear diffusionequation theories rather than the traditional variation methods. We develop anonlinear diffusion filter denoising framework which takes into account not onlythe information of the gradient of the image, but also the information of gray levelsof the image.Furthermore, under such framework, we propose a double degenerate diffusionmodel for multiplicative noise removal. The diffusion coefficient is controlled bythe gradient and gray values of the image, leading the model to remove noise andpreserve important information Inspired by the idea of the Gamma correction, weintroduce the exponential parameter to release the information compressed by themultiplicative noise. We also sketch the main mechanism that used for steering thenoise removal. For the analytical details of our PDE model, we prove the existenceof the weak solution and some properties. First, we introduce the Sobolev-Orliczspace to define the weak solution. And then we prove the existence by theregularization of the original equation and some priori estimates.In numerical aspects, we introduce an efficient scheme which uses stabilizationby fast explicit diffusion (FED) for the implementation of the multiplicative noiseremoval model. We also utilize a numerical approximation to solve the problemcaused by the singularity of the original equation.Finally, we evaluate our model on different images contaminated bymultiplicative noise, and compare the results with those obtained by somestate-of-art algorithms from the literature such as AA algorithm and SO algorithm.