  We present a reconstruction method that stably recovers the real valued,
symmetric tensors compactly supported in the Euclidean plane, from knowledge of
their attenuated momenta ray transform. The problem is recast as an inverse
boundary value problem for a system of transport equations, which we solve by
an extension of Bukhgeim's $A$-analytic theory. The method of proof is
constructive. To illustrate the reconstruction method, we present results
obtained in the numerical implementation for the non-attenuated case of
1-tensors. This new version now includes the results of the preprint arXiv:
2307.10758.
