Development of fast image reconstruction technique for CT image using active nonlinear dynamics of iterative method

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Iterative reconstruction is a well known method of reconstructing computed tomography (CT) images, and it has advantages over the filtered back-projection procedure, which is commonly used for CT reconstruction in medical practices, in reducing artifacts. Because of the high quality of these reconstructions, a lot of research has been done on improving the iterative deblurring procedures. Of the iterative reconstruction algorithms, the power multiplicative algebraic reconstruction technique (PMART) has good properties for maximizing entropy ; however, it requires a large number of iterations to obtain the final reconstructed image for large data sets.The final reconstructed image obtained by applying an iterative reconstruction algorithm for appropriate initial pixel values corresponds to a fixed or periodic point observed in the dynamical system describing the iterative reconstruction technique. Our bifurcation analysis of PMART with multiple pixels enabled us to observe various kinds … More of nonlinear phenomena such as the coexistence of a false image, the transition of stability of fixed points, and the generation of a two-periodic point, by changing one of the system parameters. The results also suggest appropriate parameter regions and phantom-image values within the PMART can operate normally.To improve the speed of convergence, we propose an extended PMART, which is a dynamical class that includes the multiplicative algebraic reconstruction technique (MART) as well as PMART. The process of convergence for iterative points in the neighborhood of a reconstructed image can be reduced to the property of the characteristic multiplier of a stable fixed point observed in the dynamical system. To investigate the behavior of convergence, we present a computational method of obtaining parameter sets in which the given real or absolute values of the characteristic multiplier are equal. The advantage of the extended PMART is verified by comparing it with the standard MART using numerical experiments. Less