Class conditional entropic prior for MRI enhanced SPECT reconstruction

Maximum Likelihood Estimation can provide an accurate estimate of activity distribution for Positron Emission Tomography (PET) and Single Photon Emission Computed Tomography (SPECT), however its unconstrained application suffers from dimensional instability due to approximation of activity distribution to a grid of point processes. Correlation between the activity distribution and the underlying tissue morphology enables the use of information from an intra-subject anatomical image to improve the activity estimate. Several approaches have been proposed to include anatomical information in the process of activity estimation. Methods based on information theoretic similarity functionals are particularly appealing as they abstract from any assumption about the nature of the images. However, due to multiplicity of the similarity functional, such methods tend to discard boundary information from the anatomical image. This paper presents an extension of state of the art methods by introducing a hidden variable denoting tissue composition that conditions an entropie similarity functional. This allows one to include explicit knowledge of the MRI imaging system model, effectively introducing additional information. The proposed method provides an intrinsic edge-preserving feature, it outperforms conventional methods based on Joint Entropy in terms of bias/variance characteristics, and it does not introduce additional parameters.