  This paper investigates the problem of recovering hyperspectral (HS) images
from single RGB images. To tackle such a severely ill-posed problem, we propose
a physically-interpretable, compact, efficient, and end-to-end learning-based
framework, namely AGD-Net. Precisely, by taking advantage of the imaging
process, we first formulate the problem explicitly based on the classic
gradient descent algorithm. Then, we design a lightweight neural network with a
multi-stage architecture to mimic the formed amended gradient descent process,
in which efficient convolution and novel spectral zero-mean normalization are
proposed to effectively extract spatial-spectral features for regressing an
initialization, a basic gradient, and an incremental gradient. Besides, based
on the approximate low-rank property of HS images, we propose a novel rank loss
to promote the similarity between the global structures of reconstructed and
ground-truth HS images, which is optimized with our singular value weighting
strategy during training. Moreover, AGD-Net, a single network after one-time
training, is flexible to handle the reconstruction with various spectral
response functions. Extensive experiments over three commonly-used benchmark
datasets demonstrate that AGD-Net can improve the reconstruction quality by
more than 1.0 dB on average while saving 67$\times$ parameters and 32$\times$
FLOPs, compared with state-of-the-art methods. The code will be publicly
available at https://github.com/zbzhzhy/GD-Net.
