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Alternative fan-beam backprojection and adjoint operators

  • Patricio Guerrero ORCID logo EMAIL logo , Matheus Bernardi and Eduardo Miqueles ORCID logo
Published/Copyright: January 31, 2023

Abstract

We present in this work alternative analytic formulations for the fan-beam tomographic backprojection operation and its associated adjoint transform in standard (equiangular) and linear (equidistant) detector geometries. The proposed formulations are obtained from a recent backprojection theorem in parallel tomography. Such formulations are written as a Bessel–Neumann series in the frequency domain that can be implemented as an O ( N 2.3729 ) matrix multiplication. Proofs are provided together with numerical simulations compared with conventional fan-beam O ( N 3 ) backprojection representations showing more robustness when dealing with highly noisy data.

MSC 2010: 44A12; 41A58

Award Identifier / Grant number: S004217N

Funding statement: PG was supported by the FWO-SBO MetroFleX project (grant agreement S004217N).

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Received: 2022-04-15
Accepted: 2022-11-13
Published Online: 2023-01-31
Published in Print: 2023-12-01

© 2023 Walter de Gruyter GmbH, Berlin/Boston

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