  By absorbing the merits of both the model- and data-driven methods, deep
physics-engaged learning scheme achieves high-accuracy and interpretable image
reconstruction. It has attracted growing attention and become the mainstream
for inverse imaging tasks. Focusing on the image compressed sensing (CS)
problem, we find the intrinsic defect of this emerging paradigm, widely
implemented by deep algorithm-unrolled networks, in which more plain iterations
involving real physics will bring enormous computation cost and long inference
time, hindering their practical application. A novel deep
$\textbf{P}$hysics-guided un$\textbf{R}$olled recovery $\textbf{L}$earning
($\textbf{PRL}$) framework is proposed by generalizing the traditional
iterative recovery model from image domain (ID) to the high-dimensional feature
domain (FD). A compact multiscale unrolling architecture is then developed to
enhance the network capacity and keep real-time inference speeds. Taking two
different perspectives of optimization and range-nullspace decomposition,
instead of building an algorithm-specific unrolled network, we provide two
implementations: $\textbf{PRL-PGD}$ and $\textbf{PRL-RND}$. Experiments exhibit
the significant performance and efficiency leading of PRL networks over other
state-of-the-art methods with a large potential for further improvement and
real application to other inverse imaging problems or optimization models.
