Maximum-likelihood transmission image reconstruction for overlapping transmission beams

In many transmission imaging geometries, the transmitted "beams" of photons overlap on the detector, such that a detector element may record photons that originated in different sources or source locations and thus traversed different paths through the object. Examples include systems based on scanning line sources or on multiple parallel rod sources. The overlap of these beams has been disregarded by both conventional analytical reconstruction methods as well as by previous statistical reconstruction methods. The authors propose a new algorithm for statistical image reconstruction of attenuation maps that explicitly accounts for overlapping beams in transmission scans. The algorithm is guaranteed to monotonically increase the objective function at each iteration. The availability of this algorithm enables the possibility of deliberately increasing the beam overlap so as to increase count rates. Simulated single photon emission tomography transmission scans based on a multiple line source array demonstrate that the proposed method yields improved resolution/noise tradeoffs relative to "conventional" reconstruction algorithms, both statistical and nonstatistical.