Benefits of angular expression to reconstruction algorithms for collimators with spatially varying focal lengths

Fan-beam collimators with spatially varying focal lengths are used in single photon emission computed tomography (SPECT) to improve the imaging sensitivity and to reduce the reconstruction artifacts resulting from the truncation of projection data. An angular representation of the detector coordinates for the projection data is adopted to investigate several aspects of the reconstruction problem for this type of collimation. A rebinning reconstruction algorithm is derived. We prove a conjecture posed by Zeng and Gullberg and obtain a simplified form of their backprojection filtering algorithm. Some computer simulations are presented to investigate the performance of the rebinning algorithm.