Abstract: Given a Riemannian manifold, the geodesic X-ray transform of a
function or tensor field is defined by its line integrals over
geodesics, and it is a central object in geometric inverse problems. In
this talk, we will focus on the X-ray transform in the classical
geometric setting of two-dimensional hyperbolic space. This setting is
particularly interesting due to its lack of compactness and its role as
a model for more general geometries, such as asymptotically hyperbolic
spaces. We will report on recent progress in characterizing the range of
the geodesic X-ray transform in this setting, deriving singular value
decompositions, establishing sharp mapping properties, and developing
reconstruction procedures. Based on joint work with François Monard and
Yuzhou Zou.
If you are interested in participating online please contact Tobias Weich or Benjamin Delarue in order to receive the login details.