Research On Image Denoising Based On Gradient Operator

With the enhancement of the computer processing capacity, people’s demand for medium information is on the increase. Images have become very important medium information. But the unavoidable noises will influence the exact obtaining of the image information. So image denoising is to improve the quality of those images so that they are more suitable for the practical using. As a result, the study for image denoising has become an very important processing field. This paper mainly does some research works of image denoising based on the total variational (TV) model which is the most classical method of partial differential equations, and the theory of non-local differential operator framework. The main body of this paper can be divided into the following parts:1. As the ROF model uses L1norm of gradient length as its regularization term, it is much better to protect the edge of images or the region where the gradient information varies a lot. However, in the smoothing region of images or the place where gradient information changes little, staircase effect often occurs; on the other hand, the ROF model uses L2norm as its fidelity term, but a large number of experiments show that using weak fidelity term can improve the effectiveness of image denoising. Based on the analysis of these two aspects, this paper tries to improve it in the following perspectives:(1) Using L1norm of gradient length as the regularization term can protect the edge information of the image better while using L2norm as the regularization term can make the smoothing areas more natural. Therefore, we can combine these two methods. The new model uses an adaptive variable exponent regularization according to the gradient of the image as ROF regularization term. At the edges of the image the exponent is close to1, and the exponent is close to2at the smoothing region of the image. The proposed method can not only protect the edge information of the image, but also solve staircase effect better.(2) A great deal of experiments have shown that using L1norm as the fidelity term of the ROF model would process noisy image better than the ROF model which uses L2norm as the fidelity term. And this change of the ROF model can especially resolve high frequency-segment well. The new model also has the obvious geometry features. And the TV-L1model shows the certain robustness, it is convenient for us to choose the parameter of the regularization. So we learn from their experience that using the L1fidelity in the new model.2. The ROF model is mainly based on the local information of images when denoising. In order to take full advantages of the redundant information and the self-similarity of the image, we will introduce non-local gradient operator in our new method by using non-local information. The main idea of non-local method can be concluded in this way:firstly, we should create a similar function about the patch that we need denoise and the patch that we need search. Then we should calculate the similarity weights of these two patches. Finally, we put average weight in the gradient operator. In this way, we can restore the pixel with noise.Due to the variable exponent TV model has local self-adaptive when denoising, we combine this method under the non-local framework. And in this way, not only can the local properties of images be made good use of, but the nonlocal information of images can be fully considered. As a result, high effectiveness of image denoising can be got on the contrary.