Abstract
A new approach in single photon emission computed tomography (SPECT) is presented to reconstruct the distributions of both activity and attenuation from projection data. Poisson noise, attenuation, scatter, and collimator effects were corrected completely with a Bayesian statistical model. The attenuation distribution was modeled with deformable template since the attenuation coefficients for the (gamma) -ray used in SPECT were nearly uniform within different regions of the human body. A prior probability was constructed for the attenuation distribution with a Gibbs measure on a hierarchical deformable template while the activity distribution was modeled by a Markov random field. By maximizing the joint posterior probability, the maximum-a-posteriori (MAP) estimate of the distributions of both activity and attenuation was obtained. The implementation of MAP estimation was achieved approximately by a hybrid algorithm of iterated conditional modes and gradient descent.
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