Image Denoising Based On High-order Model And Its Fast Algorithm

Pictures in reality inevitably contain a variety of noise which brings a lot of difficulties for people to make the accurate judgment. In order to get more reliable and robust image processing results, image denoising is in great need. Now there are many ways to denoise an image. The main property of a good image denoising model is that it will remove all the noise while preserving important features. However, different variational models have different kinds of regularisers and different denoising results depend on different kinds of regularisers.This thesis focuses on ten representative variational models containing one first order model and nine high order models which have different regularisers. High order variational models are powerful methods for image processing and analysis, but they can lead to complicated high-order nonlinear partial differential equations which are difficult to discretise to solve computationally. Thus, this thesis provides detailed descretisation of these models and numerical implementation of the split Bregman algorithm for solving these models using the fast Fourier transform to improve the computational speed. Numerical experiments are presented to validate superiority of the split Bregman algorithm based on fast fourier transform and the advantages and disadvantages of these regularisers in the context of image denoising. Then according to the conclusion that total generalized variation(TGV) regulariser is more suitable for piecewise smooth images and real images, TGV regulariser is applied to vectorial image denoising to remedy the side effect of the current denoising model. We propose robust denoising model for vectorial image denoising and validate the efficiency and effectiveness of the proposed model.