Nonlinear model order reduction of continuous-time image reconstruction systems

Abstract

As an image reconstruction method for computed tomography, continuous-time nonlinear dynamical systems were proposed. However, as the nonlinear dynamical systems are very large-scale, the numerical analysis is costly and the reconstructed images are not easily obtained. Thus, we apply nonlinear model order reduction algorithm to the nonlinear dynamical systems, based on proper orthogonal decomposition. For the continuous-time image reconstruction systems, stability analysis of the equilibria is extremely important, because the reconstructed images are obtained by the equilibria. Hence, stability analysis of the reduced-order systems is presented, in which the equilibria are proved to be asymptotically stable. In the numerical examples, robustness and efficacy of the proposed reduced-order systems will be demonstrated.