Algorithms for joint estimation of attenuation and emission images in PET
In positron emission tomography (PET), positron emission from radiolabeled compounds yields two high energy photons emitted in opposing directions. However, often the photons are not detected due to attenuation within the patient. This attenuation is nonuniform and must be corrected to obtain quantitatively accurate emission images. To measure attenuation effects, one typically acquires a PET transmission scan before or after the injection of radiotracer. In commercially available 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 two-step reconstruction scheme does not use all the information in the transmission and emission scans. Postinjection transmission scans contain emission contamination that includes information about emission parameters. Similarly, emission scans contain information about the attenuating medium. To use all the available information, we propose a joint estimation approach that estimates the attenuation map and the emission image simultaneously from these two scans. The penalized-likelihood objective function is nonconvex for this problem. We propose an algorithm based on paraboloidal surrogates that alternates between updating emission and attenuation parameters and is guaranteed to monotonically decrease the objective function.