Hybrid Euler Method for Discretizing Continuous-Time Tomographic Dynamical System

Abstract

To discretize a nonlinear differential equation, we have previously proposed a hybrid method constructed as a combination of the additive and multiplicative Euler methods. In this study, we formulate the vector field for which the hybrid Euler method is effective. Then, we evaluate the method through numerical and physical experiments for a tomographic dynamical system using, respectively, a sinogram synthesized by a digital phantom and a measured projection acquired from an X-ray computed tomography scanner. We found that the hybrid Euler method has an advantage over both the additive and multiplicative Euler methods.