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《Journal of Data Acquisition and Processing》 2011-01
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Image Restoration Iterative Method Based on Convolution Kernel Matrix Reconstructed by Kronecker Product

Zhang Yuye1,Jiang Bin2,Wang Chunxin3(1.Qingdao Branch,Navy Aeronautical and Astronautical University,Qingdao,266041,China;2.College of Information Engineering,Qingdao University,Qingdao,266001,China;3.North Sea Fleet,Qingdao,266001,China)  
The image restoration is a deconvolution problem and the convolution integral matrix in the restoration equation is a large size Toeplitz matrix. To reduce the computational complexity of the iterative restoration,the ill-posed character of Toeplitz system and the common solving approaches are analyzed,and a iterative method based on convolution kernel matrix reconstructed by Kronceker product is proposed.Firstly,according to the character,i.e.Toeplitz matrix can be reconstructed by Kronecker product,pointed spread function is decomposed by SVD,and the left and the right vectors corresponded to larger singular values are used to construct sub-matrixes.Then,the decomposition form of convolution kernel matrix's is obtained.Finally,the form is used to construct the precondition operator in iterative restoration algorithm and the process of pre-conditional conjugate gradient method in solving iteration equation is explained.The computational complexity analysis and the experiment prove that the method can accelerate the convergence and obtain the stable result.
【Fund】: 国家高技术研究发展计划(“八六三”计划)(2006AA0619)资助项目
【CateGory Index】: TP391.41
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