Bayesian image reconstruction for transmission tomography using deterministic annealing

We previously introduced a new, effective Bayesian re- construction method for transmission tomographic reconstruction that is useful in attenuation correction in single-photon-emission computed tomography (SPECT) and positron-emission tomography (PET). The Bayesian reconstruction method uses a novel object model (prior) in the form of a mixture of gamma distributions. The prior models the object as comprising voxels whose values (attenu- ation coefficients) cluster into a few classes. This model is particu- larly applicable to transmission tomography since the attenuation map is usually well-clustered and the approximate values of attenu- ation coefficients in each anatomical region are known. The recon- struction is implemented as a maximum a posteriori (MAP) estimate obtained by iterative maximization of an associated objective func- tion. As with many complex model-based estimations, the objective is nonconcave, and different initial conditions lead to different recon- structions corresponding to different local maxima. To make it more practical, it is important to avoid such dependence on initial condi- tions. We propose and test a deterministic annealing (DA) proce- dure for the optimization. Deterministic annealing is designed to seek approximate global maxima to the objective, and thus robustify the problem to initial conditions. We present the Bayesian recon- structions with and without DA and demonstrate the independence of initial conditions when using DA. In addition, we empirically show that DA reconstructions are stable with respect to small measure- ment changes. © 2003 SPIE and IS&T. (DOI: 10.1117/1.1526103)

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