A spatially variant finite mixture model is proposed for pixel labeling and image segmentation. For the case of spatially varying mixtures of Gaussian density functions with unknown means and variances, an expectation-maximization (EM) algorithm is derived for maximum likelihood estimation of the pixel labels and the parameters of the mixture densities, An a priori density function is formulated for the spatially variant mixture weights. A generalized EM algorithm for maximum a posteriori estimation of the pixel labels based upon these prior densities is derived. This algorithm incorporates a variation of gradient projection in the maximization step and the resulting algorithm takes the form of grouped coordinate ascent. Gaussian densities have been used for simplicity, but the algorithm can easily be modified to incorporate other appropriate models for the mixture model component densities. The accuracy of the algorithm is quantitatively evaluated through Monte Carlo simulation, and its performance is qualitatively assessed via experimental images from computerized tomography (CT) and magnetic resonance imaging (MRI).

The class of noninverse problems versus inverse problems is discussed. A general optimization approach to solving certain constrained noninverse problems is presented. This approach is applied in the area of single photon emission computed tomography to estimate the patient outer contour directly from the photo-peak projection data. The resulting algorithm is fully automated, fast, and the determined 3-D patient contour satisfies smoothness constraints. The accuracy and reliability of the algorithm is evaluated through Monte Carlo simulations, patient studies, and an experimental validation study.

In single photon emission computed tomography (SPECT), every reconstruction algorithm must use some model for the response of the gamma camera to emitted gamma-rays. The true camera response is both spatially variant and object dependent. These two properties result from the effects of scatter, septal penetration, and attenuation, and they forestall determination of the true response with any precision. This motivates the investigation of the performance of reconstruction algorithms when there are errors between the camera response used in the reconstruction algorithm and the true response of the gamma camera. In this regard, the authors compare the filtered backprojection algorithm, the expectation-maximization maximum likelihood algorithm, and the generalized expectation maximization (GEM) maximum a posteriori (MAP) algorithm, a Bayesian algorithm which uses a Markov random field prior.