Non-iterative methods and their noise characteristics in 2D SPECT image reconstruction

The authors derive explicit relationships between an ideal sinogram in 2D SPECT and the sinogram after degradation by constant attenuation 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 infinite classes of closed-form methods for estimation of the ideal sinogram. The authors 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 the authors had proved to be the optimal member of its class in 2D SPECT when only attenuation is present, provide the smallest global image variance among the methods in their classes also when Cauchy or Gaussian functions describe the distance-dependent spatial resolution function.