Inversion of generalized V-line transforms of vector fields in R2

Abstract

This article studies the inverse problem of recovering a vector field supported in DR, the disk of radius R centered at the origin, through a set of generalized broken ray/V-line transforms, namely longitudinal and transverse V-line transforms. Geometrically, we work with broken lines that start from the boundary of a disk and break at a fixed angle after traveling a distance along the diameter. We derive two inversion algorithms to recover a vector field in R2 from the knowledge of its longitudinal and transverse V-line transforms over two different subsets of aforementioned broken lines in R2.