Bayesian image reconstruction for transmission tomography using mixture model priors and deterministic annealing algorithms

We previously introduced a new Bayesian reconstruction method for transmission tomographic reconstruction that is useful in attenuation correction in SPECT and PET. To make it practical, we apply a deterministic annealing algorithm to the method in order to avoid the dependence of the MAP estimate on the initial conditions. The Bayesian reconstruction method used a novel pointwise prior in the form of a mixture of gamma distributions. The prior models the object as comprising voxels whose values (attenuation coefficients) cluster into a few classes (e.g. soft tissue, lung, bone). This model is particularly applicable to transmission tomography since the attenuation map is usually well-clustered and the approximate values of attenuation coefficients in each region are known. The algorithm is implemented as two alternating procedures, a regularized likelihood reconstruction and a mixture parameter estimation. The Bayesian reconstruction algorithm can be effective, but has the problem of sensitivity to initial conditions since the overall objective is non-convex. To make it more practical, it is important to avoid such dependence on initial conditions. Here, we implement a deterministic annealing (DA) procedure on the alternating algorithm. We present the Bayesian reconstructions with/out DA and show the independence of initial conditions with DA.