A very fast Implementation of 2D Iterative Reconstruction Algorithms

One of the limitations of using iterative reconstruction methods in tomography is the slow performance compared with the direct reconstruction methods, such as Filtered Backprojection. In this paper we demonstrate a very fast implementation of most types of iterative reconstruction methods. The key idea of our method is to generate the huge system matrix only once, and store it using sparse matrix techniques. From the sparse matrix we can perform the matrix vector products very fast, which implies a major acceleration of the reconstruction algorithms. In this paper we demonstrate that iterative reconstruction algorithms can be implemented and run almost as fast as direct reconstruction algorithms. The method has been implemented in a software package that is available for free, providing reconstruction algorithms using ART, EM, and the Least Squares Conjugate Gradient Method.