PET Image Reconstruction Using Information Theoretic Anatomical Priors

We describe a nonparametric framework for incorporating information from co-registered anatomical images into positron emission tomographic (PET) image reconstruction through priors based on information theoretic similarity measures. We compare and evaluate the use of mutual information (MI) and joint entropy (JE) between feature vectors extracted from the anatomical and PET images as priors in PET reconstruction. Scale-space theory provides a framework for the analysis of images at different levels of detail, and we use this approach to define feature vectors that emphasize prominent boundaries in the anatomical and functional images, and attach less importance to detail and noise that is less likely to be correlated in the two images. Through simulations that model the best case scenario of perfect agreement between the anatomical and functional images, and a more realistic situation with a real magnetic resonance image and a PET phantom that has partial volumes and a smooth variation of intensities, we evaluate the performance of MI and JE based priors in comparison to a Gaussian quadratic prior, which does not use any anatomical information. We also apply this method to clinical brain scan data using Fallypride, a tracer that binds to dopamine receptors and therefore localizes mainly in the striatum. We present an efficient method of computing these priors and their derivatives based on fast Fourier transforms that reduce the complexity of their convolution-like expressions. Our results indicate that while sensitive to initialization and choice of hyperparameters, information theoretic priors can reconstruct images with higher contrast and superior quantitation than quadratic priors.