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2015

Efficient tensor tomography in fan-beam coordinates

Monard, Francois

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We propose a thorough analysis of the tensor tomography problem on the Euclidean unit disk parameterized in fan-beam coordinates.

This includes, for the inversion of the Radon transform over functions, using another range characterization first appearing in [Pestov-Uhlmann, IMRN 2004] to enforce in a fast way classical moment conditions at all orders.
When considering direction-dependent integrands (e.g., tensors), a problem where injectivity no longer holds, we propose a suitable representative (other than the traditionally sought-after solenoidal candidate) to be reconstructed, as well as an efficient procedure to do so.
Numerical examples illustrating the method are provided at the end.

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