A Research Of Total Variation And Block-wise Low Rank Cartoon-texture Regularized Image Decomposition And Restoration

Image decomposition and restoration are important research field in image processing. Usually, an image is composed of cartoon and texture components. The large scale and smooth outline of the image is called cartoon, while the highly frequently oscillated component with repeated pattern is called texture. The aim of image decomposition is to decompose the image into two parts: cartoon and texture, according to the prior information of the cartoon and texture of the image. Based on large scale smooth prior information of cartoon and high frequently oscillation with repeated structure prior information of texture, the aim of image restoration is to reconstruct images from the noise and blur corrupted or pixel missed observed images. In addition, it is crucial to design fast and efficient numerical schemes in the research of image processing. The contribution of this thesis is the following three aspects:1. We extend the accelerated alternative direction method of multiplier with restart algorithm to solve the total variation cartoon and low rank texture regularized image decomposition and restoration(LPR) model proposed in paper[1]. Meanwhile, we compare our algorithm with the general alternative direction method of multiplier based algorithm in term of convergence rate. Numerical experiments demonstrate that this algorithm is faster.2. We extend the accelerated alternative direction method of multiplier with restart algorithm to solve the total variation cartoon and block-wise low rank texture regularized image decomposition and restoration(TV+BNN) model proposed in paper[2]. Meanwhile, we compare our algorithm with the general alternative direction of multiplier based algorithm in term of convergence rate. Numerical experiments demonstrate that this new algorithm is faster. In addition, we compare the image decomposition and restoration results of the TV+BNN model and LPR model. Experiments show that the results of the TV+BNN model are better.3. To overcome the staircase effects of smooth image region produced by the TV+BNN model in the image restoration case, we propose a new total general variation cartoon and block-wise low rank texture regularized(TGV+BNN) model, and use the accelerated alternative direction method of multiplier with restart to solve this model. Experiment results show that the TGV+BNN model can effectively reduce the stair-case effect. Lastly, we demonstrate that the accelerated alternative direction method of multiplier with restart is faster than the general alternative direction method of multiplier in term of convergence speed when solving the TGV+BNN model.