Benjamin Stephens, University of Toronto

Title: Measuring the geodesic Radon transform with mass transport

Abstract:

In tomography one extracts averages of an input image along slices.  Given a
precision requirement on the slice average output, how precisely known must the
input data be?  We study this for probability distributions on the sphere $S^{n-1}$,
acted on by the geodesic Radon transform $R$, relative to the natural image metric
Wasserstein-$p$. Our answer is that $R$ is a contraction, with Lipschitz constant
$C(p,n)$ that is sharp, less than one, and given by a simple trigonometric formula.
One consequence is a new range criterion for $R$.