The weighted doppler transform

Details The weighted doppler transform The weighted doppler transform

2009-05-14

arxiv.org/abs/0905.2375v1

Mathematics

Differential Geometry

Scientific paper

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 $\Gamma$ is never zero.

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