Investigation of lesion detection in MAP reconstruction with non-Gaussian priors

Statistical image reconstruction methods based on maximum a posteriori (MAP) principle have been developed for emission tomography. The prior distribution of the unknown image plays an important role in MAP reconstruction. The most commonly used prior is the Gaussian prior, whose logarithm has a quadratic form. Gaussian priors are relatively easy to analyze. It has been shown that the effect of a Gaussian prior can be approximated by linear-filtering a maximum likelihood (ML) reconstruction. As a result, sharp edges in reconstructed images are not preserved. To preserve sharp transitions, non-Gaussian priors have been proposed. In this paper, we study the effect of non-Gaussian priors on lesion detection and region of interest quantification in MAP reconstructions using computer simulation. We compare three representative priors - Gaussian prior, Huber prior, and Geman-McClure prior. The results show that for detection and quantification of small lesions, using non-Gaussian priors is not beneficial.