  Recovering images from undersampled linear measurements typically leads to an
ill-posed linear inverse problem, that asks for proper statistical priors.
Building effective priors is however challenged by the low train and test
overhead dictated by real-time tasks; and the need for retrieving visually
"plausible" and physically "feasible" images with minimal hallucination. To
cope with these challenges, we design a cascaded network architecture that
unrolls the proximal gradient iterations by permeating benefits from generative
residual networks (ResNet) to modeling the proximal operator. A mixture of
pixel-wise and perceptual costs is then deployed to train proximals. The
overall architecture resembles back-and-forth projection onto the intersection
of feasible and plausible images. Extensive computational experiments are
examined for a global task of reconstructing MR images of pediatric patients,
and a more local task of superresolving CelebA faces, that are insightful to
design efficient architectures. Our observations indicate that for MRI
reconstruction, a recurrent ResNet with a single residual block effectively
learns the proximal. This simple architecture appears to significantly
outperform the alternative deep ResNet architecture by 2dB SNR, and the
conventional compressed-sensing MRI by 4dB SNR with 100x faster inference. For
image superresolution, our preliminary results indicate that modeling the
denoising proximal demands deep ResNets.
