  Deep unfolding networks (DUNs) have proven to be a viable approach to
compressive sensing (CS). In this work, we propose a DUN called low-rank CS
network (LR-CSNet) for natural image CS. Real-world image patches are often
well-represented by low-rank approximations. LR-CSNet exploits this property by
adding a low-rank prior to the CS optimization task. We derive a corresponding
iterative optimization procedure using variable splitting, which is then
translated to a new DUN architecture. The architecture uses low-rank generation
modules (LRGMs), which learn low-rank matrix factorizations, as well as
gradient descent and proximal mappings (GDPMs), which are proposed to extract
high-frequency features to refine image details. In addition, the deep features
generated at each reconstruction stage in the DUN are transferred between
stages to boost the performance. Our extensive experiments on three widely
considered datasets demonstrate the promising performance of LR-CSNet compared
to state-of-the-art methods in natural image CS.
