PROJECT SUMMARY This grant deals with Emission Computed Tomography (ECT), defined broadly as three- dimensional imaging of molecules or cells that have been labeled so that they emit light, high- energy photons or charged particles without significant alteration of their biological function. The labeling can use radionuclides or light-emitting molecules, so the emissions can be nuclear decay products, including electrons, positrons and high-energy photons, or visible or near-infrared photons. The main application of ECT, and the focus of this grant, is molecular imaging in clinical medicine and biomedical research. The basic premise of the proposed research is that common theoretical and computational challenges recur in all forms of ECT. Five Specific Aims are proposed. Aim 1 will provide dedicated parallel computing systems and associated algorithms optimized for image science as applied to ECT. The systems will combine field-programmable gate arrays (FPGAs) with a cluster of graphics processing units (GPUs) and fast interconnects. Aim 2 is on imaging the radiance, a function that describes any radiation field in terms of six variables: 3 spatial coordinates, 2 variables specifying direction of flux and an energy or wavelength. We give particular attention to photon-processing detectors, which use advanced statistical methods to estimate as accurately as possible some subset of the six radiance variables for each detected photon or particle. Tools will be developed for analyzing all steps in the imaging chain in terms of radiance. Aim 3 deals with a critical but often neglected issue in imaging: null functions, which are components of an object that make no contribution to the image data. We will develop methods to compute these invisible components and determine how they influence the ability to extract information from ECT images. Aim 4 relates objects of interest in molecular imaging to the underlying physiology of the patient or animal subject being imaged. New mathematical tools, never before used in biology or medicine, will be applied to the analysis and optimization of ECT systems. Aim 5 will develop task-based measures of image quality, which are crucial to any rigorous science of imaging. We will develop the theory and computational tools needed to assess image quality of ECT systems in terms of therapeutic efficacy as well as diagnostic efficacy, and we will develop algorithms to search efficiently for configurations of ECT systems that are optimal in terms of task performance.