Image Inpainting Based On Partial Differential Equations And Its Fast Algorithm

Digital image processing has a wide range of applications in real life. Image inpainting is one of the important parts in image processing. With the development of relevant methods and techniques, the research of image inpainting methods has got great progress.The purpose of image inpainting is to repair the damaged part automatically by using the effective information surrounded by the damaged part, until the final visual effect shows that it is close to or reaches the original image. The current methods of image inpainting are divided into two kinds: one is based on the structure; the other is the method of texture synthesis. Generally, the traditional inpainting algorithms can’t give consideration to both inpainting effect and computing time. In this paper, the inpainting methods based on total variation(TV) model are considered. Also, some fast numerical algorithms to the two inpainting models are given by incorporating the alternating direction multiplier method(ADMM). The main content and innovation points in this paper are presented as follows:(1)The three classic models based on the partial differential equation are introduced, and the mathematical mechanism of both their advantages and disadvantages are discussed.(2)By combing the TV image inpainting model and the ADMM algorithm together, a new fast numerical algorithm to the TV image inpainting model is given.(3)According to the shortcomings of the TV model in texture details, this paper proposes a new inpainting model which is called ?-TV inpainting model and also gives a fast algorithm which is cal ed ?-ADMM algorithm to this model.At last, some experimental results show that the research results of this paper have made progress in both inpainting effects and computing time.