Fisher information analysis of list-mode SPECT emission data for joint estimation of activity and attenuation distribution

The potential to perform attenuation and scatter compensation (ASC) in single-photon emission computed tomography (SPECT) without a separate transmission scan is highly significant. In this context, attenuation in SPECT is primarily due to Compton scattering, where the probability of Compton scatter is proportional to the attenuation coefficient of the tissue and the energy of the scattered photon and the scattering angle are related. Based on this premise, we investigated whether the SPECT emission data, including the scatter-window data, acquired in list-mode (LM) format and including the energy information, can be used to estimate the attenuation map. For this purpose, we propose a Fisher-information-based method that yields the Cramér-Rao bound (CRB) for the task of jointly estimating the activity and attenuation distribution using only the SPECT emission data. In the process, a path-based formalism to process the LM SPECT emission data, including the scattered-photon data, is proposed. The Fisher information method was implemented on NVIDIA graphics processing units (GPUs) for acceleration. The method was applied to quantify the information content of SPECT LM emission data, which contains up to first-order scattered events, in a simulated SPECT system with parameters modeling a clinical system using realistic computational studies with 2D digital synthetic and anthropomorphic phantoms. Experiments with anthropomorphic phantoms simulated myocardial perfusion and dopamine transporter (DaT)-Scan SPECT studies. The method was also applied to LM data containing up to second-order scatter for a synthetic phantom. The results show that the CRB obtained for the attenuation and activity coefficients was typically much lower than the true value of these coefficients. An increase in the number of detected photons yielded lower CRB for both the attenuation and activity coefficients. Further, we observed that systems with better energy resolution yielded a lower CRB for the attenuation coefficient. Overall, the results provide evidence that LM SPECT emission data, including the scatter-window data, contains information to jointly estimate the activity and attenuation coefficients.