Accelerated iterative image reconstruction in computed tomography using Dykstra-like splitting

Abstract Model-based iterative reconstruction methods that minimize the cost function, consisting of a sum of the data fidelity term and the total variation regularization term, are used in low-dose and sparse-view computed tomography. However, popular iterative methods like the fast iterative soft-thresholding algorithm (FISTA) that are used to minimize the cost function are slow in convergence. We propose to construct a class of row-action-type iterative methods using an optimization framework called Dykstra-like splitting, which belongs to multi-splitting. By splitting the data fidelity term as finely as possible in such a way that each subset contains only single line integral data, the resulting iterative method becomes a row-action-type method. Among the few existing frameworks of multi-splitting, we propose to use Dykstra-like splitting and its improved version, called Dykstra-like splitting with proximal minimization (DLPM). We compare the performances of row-action iterative methods constructed by the Dykstra-like splitting and DLPM methods to existing algorithms, i.e., ordered-subset simultaneous iterative reconstruction technique total variation, FISTA, and Passty’s splitting methods.