| Digital image processing is of using the computer technique to process the imageinformation in order to meet the application demand of people. Digital image processingincludes the related felds, such as image enhancement, image restoration, image segmen-tation, image decomposition and image compression, etc. Image inpainting, which is ahot issue in the feld of image processing, is mainly used to inpaint damaged images orremove of objects in images to achieve special goals. Image decomposition is also animportant task in image processing, it consists of removing image noise, decomposing theimage edge or texture, etc. In this thesis, based on total variation type functional, weresearch on the image inpainting and decomposition problems.First, we introduce the background and development of the digital image processing,image inpainting and image decomposition. Then we briefy review some preliminaries,which consists of the ROF model(total variation model), the variational method, thegradient descent method and the gradient projection algorithm.In chapter3, we mainly discuss the variational image inpainting model based onthe ROF model. In order to overcome the nondiferential of|u|in the total variationterm, we introduce the Huber function to approximate it and therefore the model has alocal suitable self-adaption. Then the modifed model is solved by the steepest descentmethod, and experiments show that the model could get better efect than the ROFmodel. Therefore, our proposed modifed model is practicable.In chapter4, for the image decomposition problem, based on the mixed model whichcombines the ROF model with the LLT model, we propose a new image decompositionmodel by introducing an edge detection function. The corresponding algorithm is givenfor the proposed model by using the alternative semi-implicit gradient descent method.Some numerical examples show that our proposed model has better results than the ROFmodel, LLT model, and the mixed model. |
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