Abstract
This paper presents analytical fan‐beam and cone‐beam reconstruction algorithms that compensate for uniform attenuation in single photon emission computed tomography. First, a fan‐beam algorithm is developed by obtaining a relationship between the two‐dimensional (2D) Fourier transform of parallel‐beam projections and fan‐beam projections. Using this relationship, 2D Fourier transforms of equivalent parallel‐beam projection data are obtained from the fan‐beam projection data. Then a quasioptimal analytical reconstruction algorithm for uniformly attenuated Radon data, developed by Metz and Pan, is used to reconstruct the image. A cone‐beam algorithm is developed by extending the fan‐beam algorithm to solid angle geometry. The cone‐beam algorithm is also an exact algorithm.
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