Research Of Variation, PDE And Nonlocal Filter For Image Denoising

As the main medium of human to acquire and exchange information, image is playing an increasingly important role in people’s living. However, image is inevitably degraded in the process of acquisition, transmission, and so on, because that the existing equipments and the systems are not perfect. Noise is one of the most frequent degraded factor. Thus, it is of great significance to design high-performance denoising algorithms. This thesis mainly uses variation, partial differential equation(PDE) and nonlocal filter methods to study the problem of image denoising. The main work can be summarized as follows.1. An adaptive regularized variation model based on diffusion tensor is proposed. The model has three regularization parameters, which are respectively used to control the diffusion velocity in different directions and the overall smoothing degree. They keep the details of image in the denoising process. Coupling the shock filer in the model makes the edges sharpen. Furthermore, the adaptive diffusion coefficients are proposed, i.e. the pixel in noisy image is characterized by the eigenvectors and eigenvalues of structure tensor at this position. Simulation experiments indicate that the proposed model not only can denoise efficiently but also preserve detail information well, especially for the image with linear structures.2. In order to alleviate the staircase effects of total variation model(ROF) and decrease the computational complexity of mixed regularization variation model, we presented an adaptive image denoising algorithm coupled with the gradient. The algorithm uses second-order symmetrization derivative as the regularization term and the gradient field of image is constructed and used to guide the diffusion. The two step algorithm based on primal-dual algorithm is developed. Simulation results show the new model can get better denoised results, with low operate costs.3. A generalized metric is defined in Sobolev space, and an anisotropic diffusion PDE model is presented by minimized the energy functional in the sense of the generalized metric. Since the coefficient is a space-varying in generalized metric, the new model can control the diffusion forward and backword adaptively according to the image features, which makes the model achieve a good balance between noise removal and edge preservation. The corresponding implicit algorithm is given and discussed. Simulation results show the effectiveness of the proposed model and algorithm.4. In nonlocal means algorithm, the similarity of image patches is measured by weighted L2-norm which only considers the strength information of image patches while ignoring their structure. To improve the accuracy of similarity estimation, we propose two new metrics and construct the corresponding weight functions:kernelized nonlocal weight function and SSIM-based nonlocal weight function. The structure information of image patches are used. The experimental results show that the new nonlocal weight functions can protect image details more effectively in weighted average process.On the other hand, NLM algorithm is sensitive to noise. In order to overcome this shortcoming, we establish a coupled iterative nonlocal means model. Considering the computation complexity of the new model, we realize it by using multi-scale wavelet transform and propose an asymptotic nonlocal filtering algorithm, which switches a strong filtering into multiple weaker filterings. This asymptotic approximation approach has the advantage of the coupled iterative nonlocal filter, and its computational complexity is decreased. Simulation results indicate that the proposed algorithm not only can remove the noise but also preserve the structure of image and has good visual effect, especially for highly degenerated image.