The Identification Problem for the attenuated X-ray transform

Details The Identification Problem for the attenuated X-ray transform The Identification Problem for the attenuated X-ray transform

2011-05-08

arxiv.org/abs/1105.1489v1

Mathematics

Analysis of PDEs

Scientific paper

We study the problem of recovery both the attenuation $a$ and the source $f$ in the attenuated X-ray transform in the plane. We study the linearization as well. It turns out that there are natural Hamiltonian flow that determines which singularities we can recover. If the perturbations $\delta a$, $\delta f$ are supported in a compact set that is non-trapping for that flow, then the problem is well posed. Otherwise, it may not be, and least in the case of radial $a$, $f$, it is not. We present uniqueness and non-uniqueness results for both the linearized and the non-linear problem; as well as a H\"older stability estimate.

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