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Alternative Fan-beam Backprojection and Adjoint Operators (1812.06519v4)
Published 16 Dec 2018 in math.NA and cs.NA
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.