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Application Research Of Alternating Direction Method And TGV Regularization For Image Processing

Posted on:2014-01-11Degree:DoctorType:Dissertation
Country:ChinaCandidate:J L XuFull Text:PDF
GTID:1228330398498898Subject:Applied Mathematics
Abstract/Summary:PDF Full Text Request
In recent years, variational method and partial differential equation play activeroles in many image processing fields. They have become two basic tools for imageprocessing and computer vision. This dissertation mainly uses alternating directionmethod and total generalized variation (TGV) regularization to study somemathematical models and algorithms in image processing. The main work can besummarized as follows:1. As the ROF model for additive noise removal tends to produce the staircaseeffect, two novel variational denoising models are proposed. The first is the variationaldenoising model based on alternate iteration. The model can be turned into two simplesubmodels by using the alternative minimization method, one is used to construct thevector field, and the other is used to reconstruct the image. In the numericalcomputation, the dual method and the split Bregman method are used to solve the twosubmodels alternately. The experimental results show that the new algorithm not onlyhas faster convergence rate, but also can alleviate the staircase effect. The second is theadaptive denoising model with the second order TGV. In the new model, an edgeindicator function is introduced in the regularization term of second order TGV toinduct diffusion, which makes the new model can adaptively preserve the edgeinformation while removing noise and avoid the staircase effect.2. Two image inpainting models are proposed. One is the improved TV-Stokesinpainting model. There are two variables in the new model, so it is firstly turned intotwo simple submodels by using alternating iteration method, and then the twosubproblems are solved by dual formulation and split Bregman method respectively.The new model has improved the TV-Stokes model from the way of its formation andcalculation, so the proposed algorithm can not only get the better inpainting effect, butalso get the faster inpainting speed than the TV-Stokes algorithm. The other is thevariational inpainting model based on the second order TGV. In the model, the secondorder TGV is taken as the regularization term, so the new model can not only repair theimage effectively while removing the noise, but also avoid the staircase effect, thesimulative experiments show that the proposed model is better than the classical totalvariation (TV) model in terms of both peak signal to noise ratio and visual effect.3. Aiming at the shortages of current image decomposition models, two adaptive image decomposition models are presented by using the method of variationalregularization. In the two new models, the regularization terms can automaticallycombine TV and Tikhnov quadratic TV by an adaptive function, so the proposedmodels can both possess the advantages of filter and the variational method. Thesolutions of the new models can be obtained by using the alternating direction method.Experimental results show that the proposed models can not only well preserve theedge in the cartoon part, but also extract more textures or noises from the originalimage.4. In order to overcome the drawback that TV tends to produce the staircase effect,two novel image decomposition models are proposed under the variational frameworkbased on the TGV introduced recently, TGV has many advantages, which make thenew models to be more effective for image decomposition while avoiding the staircaseeffect. In the numerical computation, the first-order primal-dual algorithm, the dualmethod and the split Bregman method are respectively used to solve the proposedmodels. The experimental results show that the proposed algorithms can get the betterresults from the visual effect and the peak signal to noise ratio.
Keywords/Search Tags:Alternating direction method, Total variation, TGV regularization, Image denoising, Image inpainting, Image decomposition
PDF Full Text Request
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