New statistical reconstruction method for emission tomography

The topic of the reconstruction of data acquired in emission tomography is examined in this work. A new statistical estimator of voxel activities is derived assuming Poisson statistics of the data. A Monte Carlo algorithm to calculate the estimator and its covariance is provided. The estimator is based on the calculation of expectations of random variables which differ from commonly used iterative optimization approaches based on maximum likelihood (ML) or posterior likelihood (MAP) principles. The new estimator is defined as the expectation of maximized activities in complete-data (C-D) space (EMACS). A new super-complete-data space (also refereed to as origin ensemble space) is defined. Using this discrete space the EMACS estimator and its covariance is computed using Markov Chain process. An example of the application of EMACS for 3D positron emission tomography (PET) is presented. The compute intensive projection and backprojection operations are not used in EMACS. This may constitute a major advantage in terms of computing time for systems with complex acquisition geometries (e.g. Compton Camera) and for systems with accurate modeling of the physics of the data acquisition (e.g. detector spatial and energy resolutions).