Sourceless and source-assisted reconstruction in SPECT, with application to attenuation correction using medium energy transmission scanning

This study outlines new results obtained from a family of MLEM based algorithms and a likelihood function based on knowledge of the emission data only. Algorithms are developed for SPECT and PET, but results are shown for SPECT only. Algorithm validation was based on MCAT simulations, phantom studies with low-energy emission imaging and medium energy scanning point source transmission imaging. The scanning point source provides asymmetric fan beam data, while the emission data has parallel collimation. It is shown that the sourceless algorithms will converge to the ML solution if the initial input images are within the domain of influence of the local maximum. If a successive update rule is followed, in which the emission image is updated, followed by an update of the attenuation image, the likelihood function is concave in the neighborhood of its maximum. Line-search estimates for the relaxation parameter are guaranteed to converge. In general, the sourceless likelihood function is complex and has many local maxima.