Fan-beam reconstruction algorithm for a spatially varying focal length collimator

Fan-beam collimators are used in single-photon-emission computed tomography (SPECT) to improve the sensitivity for imaging of small organs. The disadvantage of fan-beam collimation is the truncation of projection data surrounding the organ of interest or, in those cases of imaging large patients, of the organ itself, producing reconstruction artifacts. A spatially varying focal length fan-beam collimator has been proposed to eliminate the truncation problem and to maintain good sensitivity for the organ of interest. The collimator is constructed so that the shortest focal lengths are located at the center of the collimator and the longest focal length is located at the periphery. The focal length is assumed to increase monotonically toward the edge of the collimator. A reconstruction algorithm for this type of fan-beam collimation, expressed as an infinite series of convolutions followed by one backprojection, is presented. Simulations show that only a small number of N terms in the series is needed to obtain high-quality reconstructions. Computer simulations showed that if the focal length function is smooth, the reconstructions are free of artifacts.