Partial Differential Equation Method And Its Applications For Image Denoising

Image denoising is one of the essential topics in image processing, which can greatly improve image quality. Partial differential equation(PDE) technique can keep line-like structures such as edges and textures well while denoising, so it has been focused for recent years. P-M diffusion and coherence enhancing diffusion are two widely used PDE denoising methods. P-M diffusion can remove noise in intra-region sufficiently but cannot eliminate noise at edges successfully and line-like structures cannot be held very well, coherence enhancing diffusion can remove noise at edges and preserve edges very well but false textures arise in intra-region. So, we propose two denoising methods of jointing the two models.Firstly, we develop a jointing diffusion denoising method based on edge detection, that is using coherence enhancing diffusion at the edge of images while using P-M diffusion at the other part.Secondly, we propose a jointing diffusion method of denoising based on wavelet transform. After an image is decomposed by wavelet, denoise the low frequency sub-image by coherence enhancing diffusion and the high frequency sub-images by wavelet threshold denoising method based on edge detection, then an inverse wavelet transform is used to reconstruct the initial denoising image. Next, PDE is used to acquire the final image.Furthermore, we have analyzed how to choose the parameter in P-M diffusion theoretically and how to choose parameters in coherence enhancing diffusion in the aspect of application, then apply them in experiments. Results show that these two methods can reduce noise efficiently in intra-region and at edges, keep line-like structures such as edges and textures better, and reduce artifacts a lot in intra-region in coherence enhancing diffusion.