A Memory-efficient Algorithm for Large-scale Sparsity Regularized Image Reconstruction

We derive a memory-efficient first-order variable splitting algorithm for convex image reconstruction problems with non-smooth regularization terms. The algorithm is based on a primal-dual approach, where one of the dual variables is updated using a step of the Frank-Wolfe algorithm, rather than the typical proximal point step used in other primal-dual algorithms. We show in certain cases this results in an algorithm with far less memory demand than other first-order methods based on proximal mappings. We demonstrate the algorithm on the problem of sparse-view X-ray computed tomography (CT) reconstruction with non-smooth edge-preserving regularization and show competitive run-time with other state-of-the-art algorithms while using much less memory.