Use of measured scatter data for the attenuation correction of single photon emission tomography without transmission scanning
Purpose: Attenuation correction is essential for reliable interpretation of emission tomography, 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. The authors present a first step toward a method of estimating an attenuation map from measured scatter data without a transmission scan. Methods: A scatter model has been developed that accurately predicts the distribution of photons which have been scattered once. The scatter model has been used as the basis of a maximum likelihood gradient ascent method to estimate an attenuation map from measured scatter data. In order to estimate both the attenuation map and activity distribution, iterations of the derived scatter based algorithm have been alternated with the maximum likelihood expectation maximization algorithm in a joint estimation process. For each iteration of the attenuation map estimation, the activity distribution is fixed at the values estimated during the previous activity iteration, and in each iteration of the activity distribution estimation the attenuation map is fixed at the values estimated during the previous attenuation iteration. The use of photopeak data to enhance the estimation of the attenuation map compared to the use of scatter data alone has also been considered. The algorithm derived has been used to reconstruct data simulated for an idealized two-dimensional situation and using a physical phantom. Results: The reconstruction of idealized data demonstrated good reconstruction of both the activity distribution and attenuation map. The inclusion of information recorded in the photopeak energy window in the attenuation map estimation step demonstrated an improvement in the accuracy of the reconstruction, enabling an accurate attenuation map to be recovered. Validation of the results with physical phantom data demonstrated that different regions of attenuation could be distinguished in a real situation and produces results that represent a promising first step toward the use of scatter data to estimate the activity distribution and attenuation map from single photon emission tomography (SPECT) data without a transmission scan. Conclusions: The technique presented shows promise as a method of attenuation correction for SPECT data without the need for a separate transmission scan. Further work is required to further improve the method and to compensate for the assumptions used in the scatter model.