Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 111-130 |
| Number of pages | 19 |
| Journal | Inverse Problems and Imaging |
| Volume | 4 |
| Issue number | 1 |
| Publication status | Published - Feb 2010 |
Keywords
- Integral geometry
- Inverse problems
- Pseudodifferential operators