Analysis of lesion detectability in Bayesian emission reconstruction with nonstationary object variability

Bayesian methods based on the maximum a posteriori principle (also called penalized maximum-likelihood methods) have been developed to improve image quality in emission tomography. To explore the full potential of Bayesian reconstruction for lesion detection, we derive simplified theoretical expressions that allow fast evaluation of the detectability of a lesion in Bayesian reconstruction. This work is built on the recent progress on the theoretical analysis of image properties of statistical reconstructions and the development of numerical observers. We explicitly model the nonstationary variation of the lesion and background without assuming that they are locally stationary. The results can be used to choose the optimum prior parameters for the maximum lesion detectability. The theoretical results are validated using Monte Carlo simulations. The comparisons show good agreement between the theoretical predictions and the Monte Carlo results. We also demonstrate that the lesion detectability can be reliably estimated using one noisy data set.