We introduce a general iterative scheme for angle-limited image reconstruction based on Landwebet＇s method. We derive a representation formula for this scheme and consequently establish its convergence conditions. Ou...We introduce a general iterative scheme for angle-limited image reconstruction based on Landwebet＇s method. We derive a representation formula for this scheme and consequently establish its convergence conditions. Our results suggest certain relaxation strategies for an accelerated convergence for angle-limited image reconstruction in L^2-norm comparing with alternative projection methods. The convolution-backprojection algorithm is given for this iterative process.展开更多
Filter back-projection （FBP） algorithms are available and extensively used methods for tomogra- phy. In this paper, we prove the convergence of FBP algorithms at any continuous point of image function, in L2-norm an...Filter back-projection （FBP） algorithms are available and extensively used methods for tomogra- phy. In this paper, we prove the convergence of FBP algorithms at any continuous point of image function, in L2-norm and L1-norm under the certain assumptions of image and window functions of FBP algorithms.展开更多
We establish an improved GP iterative algorithm for the extrapolation of band-limited function to fully 3-dimensional image reconstruction by the convolution-backprojection algorithm. Numerical experiments demonstrate...We establish an improved GP iterative algorithm for the extrapolation of band-limited function to fully 3-dimensional image reconstruction by the convolution-backprojection algorithm. Numerical experiments demonstrate that the image resolving power of IGP algorithm is better than that of the original GP algorithm for noisy data.展开更多
The Landweber scheme is a method for algebraic image reconstructions. The convergence behavior of the Landweber scheme is of both theoretical and practical importance. Using the diagonalization of matrix, we derive a ...The Landweber scheme is a method for algebraic image reconstructions. The convergence behavior of the Landweber scheme is of both theoretical and practical importance. Using the diagonalization of matrix, we derive a neat iterative representation formula for the Landweber schemes and consequently establish the convergence conditions of Landweber iteration. This work refines our previous convergence results on the Landweber scheme.展开更多
基金Supported by the National Natural Science Foundation of China(No.60772041,60325101,60272018,60628102)the National Key Basic Research Special Foundation(2003CB716101),Ministry of Education(306017)Engineering Research Institute of Peking University,and Microsoft Research Asia.
文摘We introduce a general iterative scheme for angle-limited image reconstruction based on Landwebet＇s method. We derive a representation formula for this scheme and consequently establish its convergence conditions. Our results suggest certain relaxation strategies for an accelerated convergence for angle-limited image reconstruction in L^2-norm comparing with alternative projection methods. The convolution-backprojection algorithm is given for this iterative process.
基金Supported by the National Natural Science Foundation of China(No.61271012,61671004)
文摘Filter back-projection （FBP） algorithms are available and extensively used methods for tomogra- phy. In this paper, we prove the convergence of FBP algorithms at any continuous point of image function, in L2-norm and L1-norm under the certain assumptions of image and window functions of FBP algorithms.
基金G.R. Qu is partially supported by the National Natural Science Foundation of China (No. 60372015, 60772041) the Science Foundation of Beijing Jiaotong University (2002SM54)+2 种基金M. Jiang is partially supported by the National Key Basic Research Special Foundation of China (2003CB716101) National Science Foundation of China (60325101, 60272018, 60628102) Ministry of Education (306017), Engineering Research Institute of Peking University, and Microsoft Research Asia.
文摘We establish an improved GP iterative algorithm for the extrapolation of band-limited function to fully 3-dimensional image reconstruction by the convolution-backprojection algorithm. Numerical experiments demonstrate that the image resolving power of IGP algorithm is better than that of the original GP algorithm for noisy data.
基金Supported by the National Natural Science Foundation of China(No.61071144,61271012,61121002,10990013)
文摘The Landweber scheme is a method for algebraic image reconstructions. The convergence behavior of the Landweber scheme is of both theoretical and practical importance. Using the diagonalization of matrix, we derive a neat iterative representation formula for the Landweber schemes and consequently establish the convergence conditions of Landweber iteration. This work refines our previous convergence results on the Landweber scheme.
