The weighted doppler transform

@article{Holman2009TheWD,
  title={The weighted doppler transform},
  author={Sean F. Holman and P. Stefanov},
  journal={Inverse Problems and Imaging},
  year={2009},
  volume={4},
  pages={111-130}
}
We consider the tomography problem of recovering a covector field on a simple Riemannian manifold based on its weighted Doppler transformation over a family of curves $\Gamma$. This is a generalization of the attenuated Doppler transform. Uniqueness is proven for a generic set of weights and families of curves under a condition on the weight function. This condition is satisfied in particular if the weight function is never zero, and its derivatives along the curves in $\Gamma$ are never zero. 
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