Optimization-based image reconstruction in computed tomography by alternating direction method with ordered subsets

Nowadays, diversities of task-specific applications for computed tomography (CT) have already proposed multiple challenges for algorithm design of image reconstructions. Consequently, efficient algorithm design tool is necessary to be established. A fast and efficient algorithm design framework for CT image reconstruction, which is based on alternating direction method (ADM) with ordered subsets (OS), is proposed, termed as OS-ADM. The general ideas of ADM and OS have been abstractly introduced and then they are combined for solving convex optimizations in CT image reconstruction. Standard procedures are concluded for algorithm design which contain 1) model mapping, 2) sub-problem dividing and 3) solving, 4) OS level setting and 5) algorithm evaluation. Typical reconstruction problems are modeled as convex optimizations, including (non-negative) least-square, constrained L1 minimization, constrained total variation (TV) minimization and TV minimizations with different data fidelity terms. Efficient working algorithms for these problems are derived with detailed derivations by the proposed framework. In addition, both simulations and real CT projections are tested to verify the performances of two TV-based algorithms. Experimental investigations indicate that these algorithms are of the state-of-the-art performances. The algorithm instances show that the proposed OS-ADM framework is promising for practical applications.