English

Alternative Fan-beam Backprojection and Adjoint Operators

Numerical Analysis 2023-02-07 v4 Numerical Analysis

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(N2.3729)O(N^{2.3729}) matrix multiplication. Proofs are provided together with numerical simulations compared with conventional fan-beam O(N3)O(N^{3}) backprojection representations showing more robustness when dealing with highly noisy data.

Keywords

Cite

@article{arxiv.1812.06519,
  title  = {Alternative Fan-beam Backprojection and Adjoint Operators},
  author = {Patricio Guerrero and Matheus Bernardi and Eduardo X. Miqueles},
  journal= {arXiv preprint arXiv:1812.06519},
  year   = {2023}
}
R2 v1 2026-06-23T06:43:57.594Z