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The authors present a method for nondifferentiable optimization in maximum a posteriori estimation of computed transmission tomograms. This problem arises in the application of a Markov random field image model with absolute value potential functions. Even though the required optimization is on a convex function, local optimization methods, which iteratively update pixel values, become trapped on the nondifferentiable edges of the function. An algorithm which circumvents this problem by updating connected groups of pixels formed in an intermediate segmentation step is proposed. Experimental results showed that this approach substantially increased the rate of convergence and the quality of the reconstruction.>
Sauer et al. (Sat,) studied this question.