The USC Andrew and Erna Viterbi School of Engineering USC Signal and Image Processing Institute USC Ming Hsieh Department of Electrical Engineering University of Southern California

Technical Report USC-SIPI-400

“Information Theoretic Measures for PET Image Reconstruction and Non-Rigid Image Registration”

by Sangeetha Somayajula

December 2009

This dissertation explores the use of information theoretic measures for positron emission tomography (PET) image reconstruction and for multi-modality non-rigid registration.

PET is a functional imaging modality based on imaging the uptake of a radioactive tracer. It is widely used in oncology, pharmacology, and neurology to visualize function. PET images are typically of low resolution (> 3mm for clinical applications) and are accompanied by high resolution (< 1mm) anatomical images such as CT or MR for localization of activity. PET tracer uptake typically results in a spatial density that is highly correlated to the anatomical morphology. The incorporation of this correlated anatomical information can potentially improve the quality of low resolution PET images. We propose using information theoretic similarity measures to incorporate anatomical information in PET reconstruction. We use mutual information (MI) and joint entropy (JE) as similarity measures with the goal of reconstructing a PET image that fits the data and is most similar to the anatomical image in the information theoretic sense. We apply this approach to positron range correction, which is a fundamental resolution limiting problem in PET.

Non-rigid registration is the estimation of a high dimensional deformation field that defines a mapping between two images such that homologous features in the two images have the same coordinates. This high dimensional mapping is required for automated image analysis in inter-subject studies, or same subject studies performed over a period of time. Non-rigid registration of small animals is especially challenging because of the presence of a rigid skeleton within non-rigid soft tissue. We present a framework for multi-modality non-rigid registration that can be used for clinical as well as pre-clinical (small animal) images. This framework uses the log likelihood of the reference image (target) given the image to be registered (template) as a similarity metric wherein the likelihood is modeled using Gaussian mixture models (GMM). Maximizing this similarity metric is approximately equivalent to maximizing MI between the images. Using the GMM formulation reduces the density estimation step to that of estimating the GMM parameters, which are small in number for images that have few regions of distinct intensities, such as brain or microCT images. This reduces the overall dimensionality of the problem, and makes it more robust to local minima compared to the non-parametric approach that is commonly used for MI based registration. We present results for brain as well as mouse images.

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