Tomographic reconstruction of vector fields in variable background media

This paper considers the problem of determination of a planar vector field when its Doppler data are modified by the presence of an unknown scalar field. Such a problem occurs in the investigation of velocity distribution in a flow through media of variable sound speed. We show that the curl of the vector field can be stably recovered. In absorbing media the integrals are weighted to account for the attenuation along the path. When the boundary values of the vector field are known, its solenoidal part is determined from its curl. We use Bukhgeim's approach to the problem of tomography.