Matrices Of Three-dimensional Projection And Iterative Reconstruction To Accelerate Research

Iterative algorithms, a kind of reconstruction algorithms, have gotten more and more peoples'attention for it can reconstruct images simply and effectively and can reconstruct images under the condition that the projection data isn't complete. When we do the reconstruction with iterative algorithms, we actually solve the large scale linear equation AX = b, in which A is projection matrix. So, the precision of the projection matrix decide the quality of the reconstructed image.Based on the linear integral, the paper derives an algorithm calculating the parallel beam projection matrix and applies the algorithm to reconstruct the neutron images. The reconstructions prove that the method can calculate the matrix accurately and rapidly.The paper also derives an algorithm calculating the cone beam projection matrix based on the parallel bean algorithm with the spatial linear integral. When computing the points the radials crossing with the object, the paper utilizes the direction of the radials and the merged-sort algorithm to increase the speed. Otherwise, the paper generalizes the cone beam algorithm to compute helical cone beam project matrix. With the helical cone beam algorithm, we do the real reconstruction successfully.However, the major drawback of the iterative algorithms is the huge computation and the low speed of convergence. This is why the iterative method has never been used in clinical. To accelerate the iterative image reconstruction, the paper introduces the OSEM algorithm. By the simulated experiment the paper analyzes the convergence situation of OSEM when the subset level is different and the intensity of noise is various. Simulated results show that these methods can provide the reconstruction image with better quality after small iterations. At the same time, we also compare the results of OSEM and ART and the compare show that the OS method can enhance the convergent speed better than ART.Furthermore, we introduce the parallel method to solve the problem present above. And we rewrite the ART algorithm into parallel format and run it on the PC cluster. By parallel computing, the speedup factor is roughly equal to the number of CPUs (6) and the precision of reconstruction is the same. This technique is very suitable for real-time reconstruction with iterative methods.