  We propose a new type of efficient deep-unrolling networks for solving
imaging inverse problems. Conventional deep-unrolling methods require full
forward operator and its adjoint across each layer, and hence can be
significantly more expensive computationally as compared with other end-to-end
methods that are based on post-processing of model-based reconstructions,
especially for 3D image reconstruction tasks. We develop a stochastic
(ordered-subsets) variant of the classical learned primal-dual (LPD), which is
a state-of-the-art unrolling network for tomographic image reconstruction. The
proposed learned stochastic primal-dual (LSPD) network only uses subsets of the
forward and adjoint operators and offers considerable computational efficiency.
We provide theoretical analysis of a special case of our LSPD framework,
suggesting that it has the potential to achieve image reconstruction quality
competitive with the full-batch LPD while requiring only a fraction of the
computation. The numerical results for two different X-ray computed tomography
(CT) imaging tasks (namely, low-dose and sparse-view CT) corroborate this
theoretical finding, demonstrating the promise of LSPD networks for large-scale
imaging problems.
