  Inspired by certain optimization solvers, the deep unfolding network (DUN)
has attracted much attention in recent years for image compressed sensing (CS).
However, there still exist the following two issues: 1) In existing DUNs, most
hyperparameters are usually content independent, which greatly limits their
adaptability for different input contents. 2) In each iteration, a plain
convolutional neural network is usually adopted, which weakens the perception
of wider context prior and therefore depresses the expressive ability. In this
paper, inspired by the traditional Proximal Gradient Descent (PGD) algorithm, a
novel DUN for image compressed sensing (dubbed DUN-CSNet) is proposed to solve
the above two issues. Specifically, for the first issue, a novel content
adaptive gradient descent network is proposed, in which a well-designed step
size generation sub-network is developed to dynamically allocate the
corresponding step sizes for different textures of input image by generating a
content-aware step size map, realizing a content-adaptive gradient updating.
For the second issue, considering the fact that many similar patches exist in
an image but have undergone a deformation, a novel deformation-invariant
non-local proximal mapping network is developed, which can adaptively build the
long-range dependencies between the nonlocal patches by deformation-invariant
non-local modeling, leading to a wider perception on context priors. Extensive
experiments manifest that the proposed DUN-CSNet outperforms existing
state-of-the-art CS methods by large margins.
