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BIFURCATION ANALYSIS OF ITERATIVE IMAGE RECONSTRUCTION METHOD FOR COMPUTED TOMOGRAPHY

Department of Radiologic Science and Engineering, Faculty of Medicine, The University of Tokushima, Tokushima 770-8509, Japan

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YOSHIHIRO IMAKURA

Graduate School of Engineering, The University of Tokushima, Tokushima 770-8506, Japan

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KEN'ICHI FUJIMOTO

Department of Radiologic Science and Engineering, Faculty of Medicine, The University of Tokushima, Tokushima 770-8509, Japan

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TETSUSHI UETA

Graduate School of Engineering, The University of Tokushima, Tokushima 770-8506, Japan

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https://doi.org/10.1142/S021812740802094XCited by:1 (Source: Crossref)

Abstract

Of the iterative image reconstruction algorithms for computed tomography (CT), the power multiplicative algebraic reconstruction technique (PMART) is known to have good properties for speeding convergence and maximizing entropy. We analyze here bifurcations of fixed and periodic points that correspond to reconstructed images observed using PMART with an image made of multiple pixels and we investigate an extended PMART, which is a dynamical class for accelerating convergence. The convergence process for the state in the neighborhood of the true reconstructed image can be reduced to the property of a fixed point observed in the dynamical system. To investigate the speed 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 multiplicative algebraic reconstruction technique (MART) using numerical experiments.

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