  In this work we propose a new paradigm for designing efficient deep unrolling
networks using dimensionality reduction schemes, including minibatch gradient
approximation and operator sketching. The deep unrolling networks are currently
the state-of-the-art solutions for imaging inverse problems. However, for
high-dimensional imaging tasks, especially X-ray CT and MRI imaging, the deep
unrolling schemes typically become inefficient both in terms of memory and
computation, due to the need of computing multiple times the high-dimensional
forward and adjoint operators. Recently researchers have found that such
limitations can be partially addressed by unrolling the stochastic gradient
descent (SGD), inspired by the success of stochastic first-order optimization.
In this work, we explore further this direction and propose first a more
expressive and practical stochastic primal-dual unrolling, based on the
state-of-the-art Learned Primal-Dual (LPD) network, and also a further
acceleration upon stochastic primal-dual unrolling, using sketching techniques
to approximate products in the high-dimensional image space. The operator
sketching can be jointly applied with stochastic unrolling for the best
acceleration and compression performance. Our numerical experiments on X-ray CT
image reconstruction demonstrate the remarkable effectiveness of our
accelerated unrolling schemes.
