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Recovering images from undersampled linear measurements typically leads to anill-posed linear inverse problem, that asks for proper statistical priors.Building effective priors is however challenged by the low train and testoverhead dictated by real-time tasks; and the need for retrieving visually"plausible" and physically "feasible" images with minimal hallucination. Tocope with these challenges, we design a cascaded network architecture thatunrolls the proximal gradient iterations by permeating benefits from generativeresidual networks (ResNet) to modeling the proximal operator. A mixture ofpixel-wise and perceptual costs is then deployed to train proximals. Theoverall architecture resembles back-and-forth projection onto the intersectionof feasible and plausible images. Extensive computational experiments areexamined for a global task of reconstructing MR images of pediatric patients,and a more local task of superresolving CelebA faces, that are insightful todesign efficient architectures. Our observations indicate that for MRIreconstruction, a recurrent ResNet with a single residual block effectivelylearns the proximal. This simple architecture appears to significantlyoutperform the alternative deep ResNet architecture by 2dB SNR, and theconventional compressed-sensing MRI by 4dB SNR with 100x faster inference. Forimage superresolution, our preliminary results indicate that modeling thedenoising proximal demands deep ResNets.

Recurrent Generative Adversarial Networks for Proximal Learning and Automated Compressive Image Recovery