Convex reconstruction of moving particles with inexact motion model

Abstract

AbstractWe propose a novel convex optimization problem for the reconstruction of temporally moving nonnegative point sources or particles. As in previously developed approaches from the literature, we base our reconstruction on a linear motion model in which particles move at constant d‐dimensional velocity. However, in contrast to existing approaches we allow a deviation from the exact linear motion, thereby accounting for the modelling error inherent in that motion model. The deviation is measured with the help of Wasserstein distances and is constrained not to exceed a freely selectable bound which represents the model inexactness. We show well‐posedness and first numerical results for the model.