Alternating minimization algorithms for X-ray computed tomography: Multigrid acceleration and dual energy application

We consider the problem of image reconstruction for X-ray computed tomography (CT) formulated as maximization of the data loglikelihood.; We take an information-theoretic approach to the problem and propose a family of alternating minimization algorithms that give a closed-form expression for image updates. The algorithms rely on the equivalence of the 1-divergence and the loglikelihood for Poisson statistics and share convergence properties of the more general family of alternating minimization algorithms.; Although significant improvements in image quality are achieved with our algorithm, its disadvantage is a slow convergence rate which results in high computational cost. Slow convergence is a property shared by many iterative image reconstruction methods. In this work, we propose a version of our algorithm that uses ideas from multigrid methods to increase convergence rate while maintaining the monotonicity property. The multigrid version of the algorithm employs reconstruction on coarsely sampled image grids that demand fewer computations per iteration. We ensure that the resolution is not sacrificed by suggesting a way of incorporating the high-resolution grids cost effectively. We also combine multigrid implementation with ordered subsets, a known acceleration technique.; In addition, we present a version of our algorithm suitable for dual-energy CT in which the data are collected in two consecutive scans with different X-ray source energy spectra. We address the quantitative accuracy achievable with our method compared to a post-processing technique.