Application Of Four Directional Total Variation In Image Denoising Problem

For human being, the majority of the information is acquired by images, which are often polluted by noise during the acquisition and transmission. The existence of noise not only seriously degrades the quality of images, but also directly affects the performance of subsequent processing. Therefore, the image denosing has been one of the most basic and significant research topics in the field of image processing.As one of the most widely used image denosing models, the total variation (TV) model has been received much attention. To begin with, this thesis systematically investigates and analysis the traditional TV image denoising model, then improvements and perfections are conducted to solve the drawbacks of the existing models. Most importantly, several new image denoising methods are proposed. The research works and innovations of this paper are mainly outlined as follows.(1) Image denosing problems based on the four directional total variation (4-TV) modelBecause the traditional TV image denoising model only takes the vertical and horizontal directions into account, the information in space domain is not fully utilized. For this reason, we proposed in this thesis a 4-TV image denoising model, which uses the information in the vertical, horizontal and two orthogonal diagonal directions. Then, the gradient projection (GP) and the fast gradient projection (FGP) methods were applied to the 4-TV image denoising model. Experimental results have demonstrated that the GP and the FGP methods based on the 4-TV image denoising model have a better image denosing ability than the GP and FGP methods based on the TV image denoising model in most cases.(2) Image denosing problems based on the four directional weighted total variation (4-WTV) modelMost of natural images have completely different information in different directions, but both the TV and the 4-TV image denoising models use the same weight parameters in different directions, this may lead to unsatisfactory results. In order to overcome this shortcoming, in this thesis, we respectively proposed the weighted total variation (WTV) and the 4-WTV image denoising models on the basis of the TV and the 4-TV image denoising models, and applied the GP and FGP methods to the new models. The new models can choose different weight parameters in different directions for different images, which can enhance the ability of image denoising. Experimental results have shown that the GP and the FGP methods based on the 4-WTV image denoising model have a better performance than the GP and the FGP methods based on the 4-TV and the WTV image denoising models in image denosing.(3) Image denosing problems based on the four directional weighted total variation with sparsity (4-WTV-S) modelThe natural images have their own unique structural characteristics, and the information associated with the structural characteristics needs to be expressed by sparsity. To do that, we first use the discrete cosine transform to get the sparse representation of images, then we add the sparse term into the WTV and the 4-WTV image denoising models to obtain the weighted total variation with sparsity (WTV-S) and the 4-WTV-S image denoising models. Although the sparse term can effectively recover the local structure information of images themselves, it also results in the nonseparable problem of variables simultaneously. To surmount it, the new models use the Split Bregman method to divide the problem into two sub-problems which are easy to solve, then applies the GP method to the new models. Experimental results indicate that the GP method based on the 4-WTV-S image denoising model has a better image denosing ability than the GP method based on the 4-WTV and the WTV-S image denoising models.The experimental results also showed that all the methods proposed in this thesis are stable enough. The FGP method based on the WTV, the 4-TV and the 4-WTV image denoising models can accelerate the convergence speed from O(1/k) to O(1/k2).