In this work, we consider the problem of reconstructing a planar vector field from partial knowledge of its zeroth ray transform (Doppler transform) and its first moment ray transform. Different from existing works the data is known on a subset of lines, namely the ones intersecting a given arc. We present a reconstruction method which recovers the vector field in the convex hull of the arc, and it is joint work with A. Tamasan (UCF) and H. Fujiwara (Kyoto U).