A Fast Iterative Method with Algebraic CT Image Reconstruction Technique Based on Dynamical System Theory

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The simultaneous iterative reconstruction technique (SIRT) is known as a method to reconstruct images of X-ray computerized tomography (CT). Iterative deblurring methods using the algebraic reconstruction technique (ART) and the expectation maximization (EM) formulation have advantages for reducing artifacts against the filtered backprojection procedure, which is commonly used for CT reconstruction in practice. Because of the high-quality reconstructions, there has been a lot of research improving the SIRT procedures. However, each type of SIRT requires a large number of iterations to obtain the final reconstruction image.On the other hand, the iterative formulae of SIRT can be considered as a dynamical system of reconstruction grid elements in the N-dimensional state space, where N is the number of pixels. Then a stable fixed point of the system corresponds to the image to be reconstructed. Moreover the dynamics in the neighborhood of the fixed point govern the convergence speed of the SIRT procedure. In this study, we investigate properties of the system from the viewpoint of dynamical system theory, and examine a numerical method for solving a fixed point of the system, using a shooting method such as Newton's method. In the study period, we found that the proposed method gives rise to the very fast convergence for the reconstruction. The efficiency was illustrated using experiments with synthetic additive noise projection data from a phantom including a metal part.