Image deblurring is a typical inverse problem. For the reason of ill-pose in inverse problem, it is hard to find the true solution, or the solutions that fit our perceptual, in the huge solution space of image deblurring problem. Furthermore, the observation noise enlarge the difficulty. As an inverse problem, the deblurring problem has two partitions in their optimization model. One is the prior model which reflects the knowledge about image. The progress of the prior model includes smooth, picewise smooth and sparse in gradient domain et al. These prior was used wildly in blind and nonblind deblurring. The other is the likelihood model based on the observation noise distribution. Such model include euclidian norm, ℓ1 norm et al. The properties about image, such as edge structure information and knowledge about camera, were not considered enough in the exist likelihood term. In this thesis, we start from the likelihood term to discuss the following problem in deblurring: 1)Based on analyzing ringing artifacts, we introduce the relative error in frequency domain to image deblurring. This error model reflects the ringing artifacts in deblurring result significantly, and has strong relationship to the blur kernel. Then the deblurring model was proposed by using relative error in frequency domain and can be approximated by wavelet decomposition. The approximated model can be solved by some common optimization methods. 2)When the blur image include occlude artifacts, we propose the extended convolution model to handle it. This model derives from our observation that the occlude is equivalent to the boundary condition in image. Our model is a linear system and can be solved by exist optimization methods. 3)In spacial-variant motion blur problem, the 3-D convolution model is proposed to describe rotation and zoom blur. The key idea for our method is introducing the time dimension to the model. Then, the deblurring problem forrotation/zoom blur was converted to 3-D deconvolution problem. The main problem in our deblurring method is constructing 3-D blur images, which can be constructed using blur property. And we estimate the blur parameters. 4)We analyze the main component of MSE and present a weighted likelihood form to solve the deblurring problem. The weighted likelihood term is proved to have more suitable properties, which can reduce solution error, than traditional simple likelihood term. With the use of the optimal weight parameter and the high-...
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