Joint estimation of attenuation and emission images from PET scans

In modern PET scanners, image reconstruction is performed sequentially in two steps regardless of the reconstruction method: 1. Attenuation correction factor computation (ACF) from transmission scans, 2. Emission image reconstruction using the computed ACFs. This reconstruction scheme does not use all the information in the transmission and emission scans. Post-injection transmission scans contain emission contamination which includes information about emission parameters. Conversely emission scans contain information about the attenuating medium. To use all the available information, the authors propose a joint estimation approach that estimates the attenuation map and the emission image from these two scans. The penalized-likelihood objective function is nonconvex for this problem. The authors propose an algorithm based on paraboloidal surrogates that alternates between emission and attenuation parameters and is guaranteed to monotonically decrease the objective function.