A fast method for simultaneous reconstruction and segmentation in X-ray CT application

In this paper, we propose a fast method for simultaneous reconstruction and segmentation (SRS) in X-ray computed tomography (CT). Our work is based on the SRS model where Bayes' rule and the maximum a posteriori (MAP) are used on hidden Markov measure field model (HMMFM). The original method leads to a logarithmic-summation (log-sum) term, which is non-separable to the classification index. The minimization problem in the model was solved by using constrained gradient descend method, Frank-Wolfe algorithm, which is very time-consuming especially when dealing with large-scale CT problems. The starting point of this paper is the commutativity of log-sum operations, where the log-sum problem could be transformed into a sum-log problem by introducing an auxiliary variable. The corresponding sum-log problem for the SRS model is separable. After applying alternating minimization method, this problem turns into several easy-to-solve convex sub-problems. In the paper, we also study an improved model by adding Tikhonov regularization, and give some convergence results. Experimental results demonstrate that the proposed algorithms could produce comparable results with the original SRS method with much less CPU time.