  In this paper, we propose the generative patch prior (GPP) that defines a
generative prior for compressive image recovery, based on patch-manifold
models. Unlike learned, image-level priors that are restricted to the range
space of a pre-trained generator, GPP can recover a wide variety of natural
images using a pre-trained patch generator. Additionally, GPP retains the
benefits of generative priors like high reconstruction quality at extremely low
sensing rates, while also being much more generally applicable. We show that
GPP outperforms several unsupervised and supervised techniques on three
different sensing models -- linear compressive sensing with known, and unknown
calibration settings, and the non-linear phase retrieval problem. Finally, we
propose an alternating optimization strategy using GPP for joint
calibration-and-reconstruction which performs favorably against several
baselines on a real world, un-calibrated compressive sensing dataset.
