A class of analytical methods that compensate for attenuation and spatially-variant resolution in 2D SPECT

An infinite class of closed-form methods was developed by the authors in 1994 for image reconstruction in 2D SPECT with uniform attenuation. In the work reported here, the authors extended their approach to develop a class of closed-form methods that compensate for the effects of both photon attenuation and distance-dependent spatial resolution in 2D SPECT. These methods, which are characterized by an index n that can be assigned any real number, are exact in the absence of noise but propagate noise differently. The authors implemented this class of methods for SPECT image reconstruction in both computer-simulation and real-data studies. The results demonstrate that this class of methods corrects effectively for the aforementioned effects. Extensive computer simulation studies indicate that the method obtained with n=2, which the authors had proved to be the optimal choice of n in 2D SPECT when only attenuation is present, also provides the smallest global image variance among the methods in the class when compensation for both uniform attenuation and distance-dependent spatial resolution is performed.