The authors previously presented a methodology for incorporating perfect extracted MRI anatomical boundary estimates to improve the performance of penalized likelihood (PL) emission computed tomography (ECT) image reconstruction and ECT tracer uptake estimation. This technique used a spatially variant quadratic Gibbs penalty which enforced smoothness everywhere in the ECT image except across the MRI-extracted boundary of the ROI.
When high quality estimates of the anatomical boundary are available and MRI and ECT images are perfectly registered, the performance of this Gibbs penalty method is very close to that attainable using perfect side information, i.e., an errorless anatomical boundary estimate. However when the variance of the MRI-extracted boundary estimate becomes significant this method performs poorly. Here we present a modified Gibbs penalty function which accounts for errors in side information based on an asymptotic min-max robustness approach.
The resulting penalty is implemented with a set of averaged Gibbs weights where the averaging is performed with respect to a limiting form of the min-max induced posterior distribution of the MRI boundary parameters. Examples are presented for tracer uptake estimation using the SAGE version of the EM algorithm and various parameterizations of the anatomical boundaries.