Extended Ordered-subsets Expectation-maximization Algorithm with Power Exponent for Noise-robust Image Reconstruction in Computed Tomography

Abstract

The maximum-likelihood expectation-maximization (ML-EM) algorithm is the most popular iterative reconstruction method in emission-computed tomography with a noise model based on the Poisson distribution. The ordered-subsets EM (OS-EM) algorithm is known owing to accelerating the convergence of the ML-EM algorithm with the drawback of slow convergence. In this paper, we propose an extended OS-EM algorithm with a power exponent. We theoretically prove the asymptotic stability of an equilibrium corresponding to the solution of the nonlinear hybrid dynamical system whose numerical discretization based on multiplicative calculus coincides with the extended OS-EM algorithm. We provide a numerical experiment to demonstrate the effectiveness of the proposed system and confirm the acceleration of the proposed method and the robustness against noise. The reconstruction of high-quality images made by the method even when the projection data is noisy allows patient dose reduction in clinical practice.