An efficient ordered subsets CT image reconstruction algorithm for sparse-view, noisy data

We investigate an ordered subsets algorithm that solves an optimization problem that minimizes a data fidelity term, motivated by maximum likelihood (ML) for Poisson distributed noise in the transmission data, while enforcing a constraint on the image total variation (TV). We refer to this optimization problem as TV-constrained, transmission PML. Due to recent progress in first-order solvers such non-smooth convex optimization problems can be solved accurately for large-scale systems such as what occurs in CT image reconstruction. The primal-dual algorithm developed by Chambolle and Pock (CP), for example, can be employed to solve TV-constrained, transmission PML. While sufficient for research purposes, more efficient algorithms are needed for clinical use. A convergent ordered subsets algorithm for TV-constrained, transmission PML is developed from the incremental framework of Bertsekas. The proposed ordered subsets algorithm is demonstrated on simulated breast CT data, modeling a noise level comparable to two mammographic projection images.