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 γ. 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 γ are never zero. © 2010 American Institute of Mathematical Sciences.
|Number of pages||19|
|Journal||Inverse Problems and Imaging|
|Publication status||Published - Feb 2010|
- Integral geometry
- Inverse problems
- Pseudodifferential operators