  In this work we propose a new paradigm for designing efficient deep unrolling
networks using 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 the 3D cone-beam X-ray CT and 4D 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 stochastic unrolling with
subsets of operators, inspired by the success of stochastic first-order
optimization. In this work, we propose a further acceleration upon stochastic
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 sketched unrolling schemes.

Computer Vision and Pattern Recognition;Machine Learning;Image and Video Processing;Optimization and Control