Motion tomography via occupation kernels

Abstract

<p style='text-indent:20px;'>The goal of motion tomography is to recover a description of a vector flow field using measurements along 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. [<xref ref-type="bibr" rid="b9">9</xref>,<xref ref-type="bibr" rid="b10">10</xref>]. 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 in 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 the developed method with the established method by Chang et al. [<xref ref-type="bibr" rid="b5">5</xref>] by defining a set of error metrics. We found that for simulated data, where a ground truth is available, our method offers a marked improvement over [<xref ref-type="bibr" rid="b5">5</xref>]. For a real-world example, where ground truth is not available, our results are similar results to the established method.</p>