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arXiv · 1812.06519

Alternative Fan-beam Backprojection and Adjoint Operators

Patricio Guerrero·Matheus Bernardi·Eduardo X. Miqueles
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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.

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Patricio Guerrero, Matheus Bernardi, Eduardo X. Miqueles. 2018-12-16. Alternative Fan-beam Backprojection and Adjoint Operators. https://doi.org/10.1515/jiip-2022-0029

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