The Image Inpainting Algorithm Research Based On Wavelet Transform

In recent years, with the development of science and technology, digital image technology has been widely used in digital products such as scanner, digital camera, digital TV and so on, it is one of the hot topics in computer vision field in recent years. However, in the process of image acquisition and transmission, there are many factors which can cause the defect of the image information. In order to ensure the integrity of the image and obtain the true and clear image, it is necessary to use an image inpainting technology to repair the damaged information. Because of this background, the image restoration technology has been developed rapidly, which has been widely used in the fields of image compression, cultural relic protection, removal of redundant objects and so on. The thesis mainly works and achievements are as shown below:First of all, the background and research status of digital image restoration technology are introduced, the mathematical model of image restoration and the related mathematical knowledge are presented. Meanwhile, the basic theory of wavelet transform is introduced, including the definition of wavelet, wavelet transform, multi-resolution analysis and well-known Mallat algorithm.Secondly, three classical models based on partial differential equations of the inpainting algorithm are summed up, including BSCB model, TV model, CDD model. We analyze the main ideas and numerical calculation method of the three models as well as advantages and disadvantages of three kinds of algorithms. According to the deficiencies of the classical algorithm, a model is presented in this paper which is based on curvature driven of p-harmonic model for image inpainting algorithm. In this model, the curvature is introduced in the energy functional model, and corresponding diffusion equation is established, this model combines the advantages of the p-harmonic model and the curvature, its diffusion coefficient is controlled by two variables: gradient and curvature, meeting the connectivity principle, and the model numerical solution and steps of the algorithm are given. The numerical experiments show that the method is superior to the traditional method.Finally, the image restoration is performed in the wavelet domain. Combined with the advantages of the wavelet transform, according to the presence of noise, two new image inpainting algorithms are proposed in this paper by adding curvature driven into the p-harmonic model. According to the established model, the Euler-Lagrange equation of the new model is derived by variational method, and corresponding diffusion equation is established, then finite difference method is adopted for the established diffusion equation, the discrete format of the inpainting model and the algorithm of specific steps are given to obtain the restored image.Experiment results show that the proposed algorithm in this paper is superior to the traditional algorithm in both quality and efficiency. It has achieved better inpainting effect and visual effect with less iteration steps in wavelet domain, especially with large number of lost wavelet coefficients. From the objective evaluation criteria, the restored images have a higher PSNR.