Thesis (M. Phil.)--University of Hong Kong, 2002. / Includes bibliographical references (leaves 56-60).

Thesis (M.Phil.)--Hong Kong University of Science and Technology, 2006. / Includes bibliographical references (leaves 57-58). Also available in electronic version.

Variational methods, which have proven to be very useful to solve the ill-posed inverse problems, have been generating a lot of research interest in the image restoration problem. It transforms the restoration problem into the optimization of a well-designed variational model. While the designed model is convex, the recovered image is the global solution found by an appropriate numerical algorithm and the quality of the restored image depends on the accuracy of the designed model. Thus, a lot of efforts have been put to propose a more precise model that can produce a result with more pleasing visual quality. Besides, due to the high- dimension and the nonsmoothness of the imaging model, an efficient algorithm to find the exact solution of the variational model, is also of the research interest, since it influences the efficiency of the restoration techniques in the practical applications. In this thesis, we are interested in the designing of both the variational models for image restoration problems and the numerical algorithms to solve these models. The first objective of this thesis is to make improvements on two models for image denoising. For the multiplicative noise removal, we designed a regularizer based on the statistical property of the speckle noise, which can transform the traditional model (named by AA) into a convex one. Therefore, a global solution can be found independent of the initialization of the numerical algorithm. Moreover, the regularization term added on the AA model can help produce a sharper result. The second model is improved on the traditional ROF model by adding an edge regularization which incorporates an edge prior obtained from the observed image. Extensive experiments show that designed edge regularization has superiority to increase the texture of the recovered result and remove the staircase artifacts in the meanwhile. It is also presented that the edge regularization designed can be easily adapted into other restoration task, such as image deblurring. The second objective of this thesis is to study the numerical algorithms for a general nonsmooth imaging restoration model. As the imaging models are usually high-dimensional, the existing algorithms usually only use the first-order information of the image. Differently, a novel numerical algorithm based on the inexact Lagrangian function is proposed in this thesis, which exploits the second-order information to reach a superlinear convergence rate. Experiments show that the proposed algorithm is able to efficiently reach the solution with higher accuracy compared to the state-of-the-art algorithm

Variational methods, which have proven to be very useful to solve the ill-posed inverse problems, have been generating a lot of research interest in the image restoration problem. It transforms the restoration problem into the optimization of a well-designed variational model. While the designed model is convex, the recovered image is the global solution found by an appropriate numerical algorithm and the quality of the restored image depends on the accuracy of the designed model. Thus, a lot of efforts have been put to propose a more precise model that can produce a result with more pleasing visual quality. Besides, due to the high- dimension and the nonsmoothness of the imaging model, an efficient algorithm to find the exact solution of the variational model, is also of the research interest, since it influences the efficiency of the restoration techniques in the practical applications. In this thesis, we are interested in the designing of both the variational models for image restoration problems and the numerical algorithms to solve these models. The first objective of this thesis is to make improvements on two models for image denoising. For the multiplicative noise removal, we designed a regularizer based on the statistical property of the speckle noise, which can transform the traditional model (named by AA) into a convex one. Therefore, a global solution can be found independent of the initialization of the numerical algorithm. Moreover, the regularization term added on the AA model can help produce a sharper result. The second model is improved on the traditional ROF model by adding an edge regularization which incorporates an edge prior obtained from the observed image. Extensive experiments show that designed edge regularization has superiority to increase the texture of the recovered result and remove the staircase artifacts in the meanwhile. It is also presented that the edge regularization designed can be easily adapted into other restoration task, such as image deblurring. The second objective of this thesis is to study the numerical algorithms for a general nonsmooth imaging restoration model. As the imaging models are usually high-dimensional, the existing algorithms usually only use the first-order information of the image. Differently, a novel numerical algorithm based on the inexact Lagrangian function is proposed in this thesis, which exploits the second-order information to reach a superlinear convergence rate. Experiments show that the proposed algorithm is able to efficiently reach the solution with higher accuracy compared to the state-of-the-art algorithm

Thesis (Ph. D.)--University of Hong Kong, 2006. / Title proper from title frame. Also available in printed format.

Thesis (Ph. D.)--University of Hong Kong, 2006. / Title proper from title frame. Also available in printed format.

Thesis (Ph. D.)--University of Washington, 2003. / Vita. Includes bibliographical references (leaves 113-124).

Thesis (Ph.D.)--Hong Kong University of Science and Technology, 2006. / Vita. Includes bibliographical references (leaves 119-133). Also available in electronic version.

Thesis (Ph. D.)--University of Washington, 1999. / Vita. Includes bibliographical references (p. 162-168).

Resolution is the most important criterion for the clarity of details on an image. Therefore, high resolution images are required in numerous areas. However, obtaining high resolution images has an evident technological cost and the value of these costs change with the quality of used optical systems. Image processing methods are used to obtain high resolution images with low costs. This kind of image improvement is named as superresolution image reconstruction. This thesis focuses on two main titles, one of which is the identification methods of blur parameters, one of the degradation operators, and the stochastic SR image reconstruction methods. The performances of different stochastic SR image reconstruction methods and blur identification methods are shown and compared. Then the identified blur parameters are used in superresolution algorithms and the results are shown.