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Image reconstruction in X-ray transmission tomography has been an importantresearch field for decades. In light of data volume increasing faster thanprocessor speeds, one needs accelerated iterative algorithms to solve theoptimization problem in the X-ray CT application. Incremental methods, in whicha subset of data is being used at each iteration to accelerate thecomputations, have been getting more popular lately in the machine learning andmathematical optimization fields. The most popular member of this family ofalgorithms in the X-ray CT field is ordered-subsets. Even though it performswell in earlier iterations, the lack of convergence in later iterations is aknown phenomenon. In this paper, we propose two incremental methods that useJensen surrogates for the X-ray CT application, one stochastic and oneordered-subsets type. Using measured data, we show that the stochastic variantwe propose outperforms other algorithms, including the gradient descentcounterparts.

Stochastic First-Order Minimization Techniques Using Jensen Surrogates for X-Ray Transmission Tomography