Research On Image Inpainting Using Hybrid Regularization Method

In recent years, digital image processing technology has been developing rapidly.The difference with the traditional methods is that modern image processing method isbased on the digital imaging model. At the same time, because of the exploration of illposed problems, and the establishment of the regularization theoretical system,especially the regularization method proposed by Tikhonov, the development of imageprocessing has a solid theoretical foundation.Image restoration is an important branch of digital image processing. This problemcan be viewed as the inverse problem of imaging process, the purpose of which is tobuild the model of this process so that we can estimate the original image by solvingthis model. The basic idea is to improve the ill-pose of the original problem byconstructing regularization terms, and build a regularized model. Although people hasproposed a lot of regularization models, it is difficult to find a suitable method for anyimage, because of the diversity of image types, also the degree and types of damage.People found that, when the image has many characteristics, combining withregularization terms will lead to better results. This paper mainly research on the hybridregularization method, according to the different features of the image, combining withregularization terms, and creating a new regularization model. The main contents of thispaper are as follows:1. Summarizing image restoration from the visual aspects and mathematicalaspects. On this basis, the current image processing research status and the main idea ofregularization model was summarized. Introducing the basic concept of imagerestoration problems and regularization method, and the corresponding mathematicaltheory tools, also the split Bregman algorithm is summarized.2. To address the problems of edge blurring and detail preservation in the highdimensional filtering, a novel high-dimensional filtering using gradient minimizedMumford-Shah model is proposed, which applies the minimization of L0and L1regularization terms to achieve edge-preserving and texture-smoothing. This algorithmcan achieve both properties of edge-preserving and texture-smoothing. Thecharacteristic is helpful for obtaining the perfect structure-texture separation andoptimizing the results in some specific visual applications. 3. On the basis of MCA method, we propose GMCA algorithm, which allows themodel to includes more regularization terms, and give specific constraints according todifferent morphological components. We use the fast algorithm of optimization “SplitBregman algorithm" and fast approximation method and get a faster rate of convergenceusing GMCA compared with MCA.