  This article extends the author's past work [Inv. Probl. Imaging, 10:2
(2016), 433--459] to attenuated X-ray transforms, where the attenuation is
complex-valued and only depends on position. We give a positive and
constructive answer to the attenuated tensor tomography problem on the
Euclidean unit disc in fan-beam coordinates. For a tensor of arbitrary order,
we propose an equivalent tensor of the same order which can be uniquely and
stably reconstructed from its attenuated transform, as well as an explicit and
efficient procedure to do so.
