In  a methodology for incorporating extracted MRI anatomical boundary information into penalized likelihood (PL) ECT image reconstructions and tracer uptake estimation was proposed. This methodology used quadratic penalty based on Gibbs weights which enforced smoothness constraints everywhere in the 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 method was shown to be very close to that attainable using ideal side information, i.e. noiseless anatomical boundary estimates.
However when the variance of the MRI-extracted boundary estimates becomes significant this penalty function method performs poorly. We give a modified Gibbs penalty function implemented with a set of averaged Gibbs weights, where the averaging is performed with respect to a limiting form of the posterior distribution of the MRI boundary parameters.