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February  2010, 4(1): 111-130. doi: 10.3934/ipi.2010.4.111

The weighted Doppler transform

Sean Holman 1, and  Plamen Stefanov 1,

1. 

Department of Mathematics, Purdue University, 150 N University Street, West Lafayette, IN 47907, United States, United States

Received  May 2009 Revised  November 2009 Published  February 2010

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.
Keywords: Integral geometry, Pseudodifferential operators., Inverse problems.
Mathematics Subject Classification: Primary: 34A55, 53C65; Secondary: 47G3.
Citation: Sean Holman, Plamen Stefanov. The weighted Doppler transform. Inverse Problems & Imaging, 2010, 4 (1) : 111-130. doi: 10.3934/ipi.2010.4.111
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