Correction for photon attenuation in SPECT: analytical framework, average attenuation factors, and a new hybrid...

We provide a unified framework for the investigation of convergence properties of the iterative algorithms for photon attenuation correction in SPECT, including the iterative Chang method--a commonly used approach in which an average attenuation factor calculated over all projection angles is employed in a pointwise correction scheme. A new average attenuation factor calculated along the projection line is introduced, which can compensate exactly for the attenuation effect in the case of a uniform activity distribution. We propose a new hybrid approach in which we use this new average attenuation factor initially and then shift to the iterative Chang method in later iterations. This hybrid approach was evaluated in a simulation study by use of a computer-generated phantom with both non-uniform activity and non-uniform attenuation distributions. The results demonstrate that this hybrid approach improves the convergence speed of the iterative Chang method and produces reconstructed images of high quality.