Efficient tensor tomography in fan-beam coordinates

François  Monard

doi:10.3934/ipi.2016007

Article Contents

2016, Volume 10, Issue 2: 433-459. Doi: 10.3934/ipi.2016007

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Efficient tensor tomography in fan-beam coordinates

François Monard^1,

1.
Department of Mathematics, University of Michigan, 2074 East Hall, 530 Church Street, Ann Arbor, MI 48109-1043

Received: September 30, 2015

Revised: January 31, 2016

Published: April 2016

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Abstract

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 [32] 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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Mathematics Subject Classification: Primary: 35R30, 44A12; Secondary: 30E20, 92C55.

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