Improved penalized likelihood reconstruction of anatomically correlated emission data

This paper presents a method for incorporating anatomical NMR boundary side information into penalized maximumlikelihood (PML) emission image reconstructions. The NMR boundary is parameterized as a periodic spline curve of fixed order and number of knots that is known a priori. Maximum Likelihood (ME) estimation of the spline coefficients yields an “extracted” boundary, which is used to define a set of Gibbs weights on the emission image space. These weights, when coupled with a quadratic penalty function, create an edgepreserving penalty that incorporates our prior knowledge effectively. Qualitative analysis demonstrates that our method results in smooth images that do not suffer loss of edge contrast, while quantitative estimates of bias and variance for various values of the smoothing parameter show an improvement over standard quadratically penalized maximum likelihood.