  Recent works that utilized deep models have achieved superior results in
various image restoration applications. Such approach is typically supervised
which requires a corpus of training images with distribution similar to the
images to be recovered. On the other hand, the shallow methods which are
usually unsupervised remain promising performance in many inverse problems,
\eg, image compressive sensing (CS), as they can effectively leverage non-local
self-similarity priors of natural images. However, most of such methods are
patch-based leading to the restored images with various ringing artifacts due
to naive patch aggregation. Using either approach alone usually limits
performance and generalizability in image restoration tasks. In this paper, we
propose a joint low-rank and deep (LRD) image model, which contains a pair of
triply complementary priors, namely \textit{external} and \textit{internal},
\textit{deep} and \textit{shallow}, and \textit{local} and \textit{non-local}
priors. We then propose a novel hybrid plug-and-play (H-PnP) framework based on
the LRD model for image CS. To make the optimization tractable, a simple yet
effective algorithm is proposed to solve the proposed H-PnP based image CS
problem. Extensive experimental results demonstrate that the proposed H-PnP
algorithm significantly outperforms the state-of-the-art techniques for image
CS recovery such as SCSNet and WNNM.
