Noise and Resolution Properties of Gamma-Penalized Likelihood Reconstruction

In this paper, we (re)introduce the independent gamma prior for penalized likelihood reconstruction for both emission and transmission tomography. We give the expressions for bias and variance, and validate the expressions using Monte Carlo simulations. We also test a plug-in approach to get an approximate estimate of the variance image. We list the fixed point local point-spread function expressions, investigate how the FWHM and volume of this local point-spread function vary with its smoothing hyperparameter in both low and high intensity regions, and illustrate the noise-resolution tradeoffs.