NONITERATIVE METHODS AND THEIR NOISE CHARACTERISTICS IN 2D SPECT IMAGE-RECONSTRUCTION

In this work, we derive explicit relationships between an ideal sinogr am in 2D SPECT and the sinogram after degradation by constant attenuat ion and by distance-dependent spatial resolution that is described by either a Cauchy or a Gaussian function. Attempts to reduce statistical variance in the reconstructed image lead to the development of infini te classes of closed-form methods for estimation of the ideal sinogram . We applied this approach to 2D SPECT in both computer-simulation and real-data studies. Extensive computer-simulation studies demonstrate that the counterparts of a ''quasi-optimal'' method, which we had prov ed to be the optimal member of its class in 2D SPECT when only attenua tion is present, provide the smallest global image variance among the methods in their classes also when Cauchy or Gaussian functions descri be the distance-dependent spatial resolution function.