Motion Tomography via Occupation Kernels

TL;DR

This paper introduces a novel predictor-corrector algorithm using occupation kernels to improve the recovery of vector flow fields from trajectory data, demonstrating superior performance on simulated data and comparable results on real-world data.

Contribution

The paper develops an iterative method utilizing occupation kernels as an adaptive basis for motion tomography, with proven convergence under mild conditions.

Findings

Significant improvement over existing methods on simulated data

Comparable results to established methods on real-world data

Convergence proven using the Contraction Mapping Theorem

Abstract

The goal of motion tomography is to recover a description of a vector flow field using information on the trajectory of a sensing unit. In this paper, we develop a predictor corrector algorithm designed to recover vector flow fields from trajectory data with the use of occupation kernels developed by Rosenfeld et al.. Specifically, we use the occupation kernels as an adaptive basis; that is, the trajectories defining our occupation kernels are iteratively updated to improve the estimation on the next stage. Initial estimates are established, then under mild assumptions, such as relatively straight trajectories, convergence is proven using the Contraction Mapping Theorem. We then compare to the established method by Chang et al. by defining a set of error metrics. We found that for simulated data, which provides a ground truth, our method offers a marked improvement and that for a real-world example we have similar results to the established method.