Comparison between post-smoothed maximum-likelihood and penalized-likelihood for image reconstruction with uniform spatial resolution

Abstract

Regularization is desirable for image reconstruction in emission tomography. One of the most powerful regularization techniques is the penalized-likelihood reconstruction algorithm (or equivalently, maximum-a-posteriori reconstruction), where the sum of the likelihood and a noise suppressing penalty term (or Bayesian prior) is optimized. Usually, this approach yields position dependent resolution and bias. However, for some applications in emission tomography, a shift invariant point spread function would be advantageous. Recently, a new method has been proposed, in which the penalty term is tuned in every pixel in order to impose a uniform local impulse response. In this paper, an alternative way to tune the penalty term is presented. The performance of the new method is compared to that of the post-smoothed maximum-likelihood approach, using the impulse response of the former method as the post-smoothing filter for the latter. For this experiment, the noise properties of the penalized-likelihood algorithm were not superior to those of post-smoothed maximum-likelihood reconstruction.