Penalized Likelihood Ect Reconstruction with Uncertain Mri Side Information via Asymptotic Marginalization Draft

In a methodology for incorporating extracted MRI anatomical boundary information into penalized likeli hood PL ECT image reconstructions and tracer up take estimation was proposed This methodology used quadratic penalty based on Gibbs weights which en forced smoothness constraints everywhere in the image except across the MRI extracted boundary of the ROI When high quality estimates of the anatomical bound ary are available and MRI and ECT images are per fectly 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 signi cant this penalty function method performs poorly We give a modi ed Gibbs penalty function implemented with a set of averaged Gibbs weights where the averaging is performed with respect to a limiting form of the pos terior distribution of the MRI boundary parameters