Symmetrical Structure Based Block-iterative EM Algorithms For Image Reconstruction

The algorithm of image reconstruction by projection data can be divided into analytical algorithm and algebraic iterative algorithm. In the case of complete data, analytical algorithm is fast, and we can get the good quality of image. But in the case of high noise data, a small amount of data and missing data, algebraic iterative algorithm has more obvious advantages than analytical algorithm. With the development of computer technology, we pay more and more attention to the algebraic iterative algorithm.The EM algorithm as one of the classical algebraic iterative algorithms is a very popular method of maximum likelihood estimation. It's simple and stable. In particular, each iteration of EM algorithm can ensure that the correction value of the pixel is close to the image that is needed to be rebuilt, and at last converge to local maxima. However, EM algorithm which needs large amount of calculation has slow convergence rate.This paper rewrites the classical EM algorithm as a block format based on the symmetry structure. In the discrete image mode, there exists a eight-symmetry structure among projection lines, and also among the corresponding pixel location. And we group the projection rays by the eight-symmetry structure. That makes the data grouped combine with scanning model, and simplifies the calculation of non-zero coefficient in the projection coefficient matrix. The block EM algorithm changes the line-by-line correction which belongs to the classical EM algorithm. And it reduces the computation, also improves the speed of imaging effectively. We also study the EM and OS-EM with symmetry mesh . \Finally, this paper gives the experiments of measured and simulated data. And compare the classical EM algorithm with the block EM algorithm through the speed and accuracy of imaging. The result shows that the block EM algorithm can improve the speed of imaging.