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