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1 June 1991 MAP image reconstruction using intensity and line processes for emission tomography data
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Abstract
A Bayesian approach to image reconstruction from emission tomography image is presented in which the image is modeled using a joint Gibbs distribution of emission intensities and line processes. The line process represents the presence or absence of discontinuities between each neighboring pair of pixels. It is introduced to avoid the smoothing across discontinuities, which commonly occurs in Bayesian image estimation when a line process is not included. Two algorithms for MAP estimation over both intensity and line processes are presented. Both methods employ the generalized EM (GEM) algorithm to avoid direct optimization over the posterior distribution which does not share the Markovian property of the prior. The M-step of the GEM algorithm of the MAP estimation problem requires optimization over a function which has the appealing property that the neighborhood is identical to that of the prior. During the M-step both the intensity and line processes are updated. This is achieved in two stages. In the M1-step the intensities are updated, while holding the line process constant, using a gradient descent method. In the M2-step the line process is updated, with the intensity process held constant. Two alternative M2-steps are described in the paper. The use of a line process in the image model also provides a natural framework for the incorporation of a priori information from other modalities. In this case, boundaries may be found from MR or CT images and used as known line processes in the image estimation procedure.
© (1991) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Xiao-Hong Yan and Richard M. Leahy "MAP image reconstruction using intensity and line processes for emission tomography data", Proc. SPIE 1452, Image Processing Algorithms and Techniques II, (1 June 1991); https://doi.org/10.1117/12.45380
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