Attenuation map estimation without transmission scanning using measured scatter data

Attenuation correction is essential for reliable interpretation of SPECT images, however the use of transmission measurements to generate attenuation maps is limited by availability of equipment and potential mismatches between the transmission and emission measurements. A method has been developed to use scatter data measured at the same time as the emission measurements to estimate an attenuation map. The algorithm iterates through a dual estimation process, fixing estimated activity and attenuation respectively. The work presented here improves the accuracy of the previously described scatter model. The possibility of using an ordered subsets technique to accelerate the reconstruction algorithm is considered and the robustness of the reconstruction algorithm to errors in the estimation of higher order scatter is investigated. The improved scatter model developed using the Klein-Nishina formula and Compton scattering angles that include solid angle effects has been found to accurately estimate single scattered photons, when compared to Monte Carlo simulation results. The use of 5 iterations or sub-iterations in each reconstruction step resulted in convergence in fewer steps. The use of 5 standard iterations in each subset took approximately 4.7 times longer than the use of a single iteration; this was reduced to be 3.9 times longer than a single iteration when using a standard ordered-subsets technique. Further acceleration can be obtained by using the same attenuation map to calculate the number of photons reaching each point for scatter for all sub-iterations; this resulted in similar reconstruction times per step regardless of the number of sub-iterations used. Both acceleration methods were able to produce convergence similar to reconstruction without the use of subsets. The algorithm has been found to be less sensitive to underestimates of higher order scatter events than to overestimates and is reasonably robust to errors in the precision of the correction - or higher order scatter events. The technique presented shows promise as a method of attenuation correction for SPECT data without the need for a separate transmission scan.