Image restoration with shifting reflective boundary conditions  

作　　者：HUANG Jie HUANG TingZhu ZHAO XiLe XU ZongBen 

机构地区：[1]School of Mathematical Sciences,University of Electronic Science and Technology of China [2]Institute of Information and System Sciences,Xi'an Jiaotong University

出　　处：《Science China(Information Sciences)》2013年第6期41-55,共15页中国科学（信息科学）（英文版）

基　　金：supported by National Basic Research Program of China (Grant No. 2007CB311002);NSFC(Grant Nos. 61170311,60973015);Sichuan Province Sci. & Tech. Research Project (Grant No. 2011JY0002);Fundamental Research Funds for the Central Universities (Grant No. E022050205)

摘　　要：In signal and image processing,we want to recover a faithful representation of an original scene from blurred,noisy image data.This process can be transformed mathematically into solving a linear system with a blurring matrix.Particularly,the blurring matrix is determined from not only a point spread function（PSF）,which defines how each pixel is blurred,but also boundary conditions（BCs）,which specify our assumptions on the data outside the domain of consideration.In this paper,we first propose shifting reflective BCs which preserve the continuity at the boundaries and,therefore,reduce ringing effects in the restored image.A Kronecker product approximation of the corresponding blurring matrix is then provided,regardless of symmetry requirement of the PSF.Finally,we demonstrate the efficiency of our approximation in an SVD-based regularization method by several numerical examples.In signal and image processing,we want to recover a faithful representation of an original scene from blurred,noisy image data.This process can be transformed mathematically into solving a linear system with a blurring matrix.Particularly,the blurring matrix is determined from not only a point spread function（PSF）,which defines how each pixel is blurred,but also boundary conditions（BCs）,which specify our assumptions on the data outside the domain of consideration.In this paper,we first propose shifting reflective BCs which preserve the continuity at the boundaries and,therefore,reduce ringing effects in the restored image.A Kronecker product approximation of the corresponding blurring matrix is then provided,regardless of symmetry requirement of the PSF.Finally,we demonstrate the efficiency of our approximation in an SVD-based regularization method by several numerical examples.

关 键 词：Image restoration boundary conditions Kronecker product singular value decomposition 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术] O177.6[自动化与计算机技术—计算机科学与技术]