On the Reconstruction of Planar Vector Fields From Its Longitudinal and Transverse Ray Transform

ABSTRACT We consider a planar vector tomography problem of reconstructing a complex‐valued vector field from the (complete and partial) information of its longitudinal and transverse ray transforms, as well as from one of those transforms and its first moment. The method is based on solving an inverse boundary value problem for a system of inhomogeneous Beltrami‐like equations associated with ‐analytic and ‐anti‐analytic maps. In the partial data setting, the available data are only provided on a subset of lines, specifically those intersecting a prescribed arc. We present reconstruction methods for recovering the vector field within the convex hull of the given arc.