  In this paper, we investigate the problem of hyperspectral (HS) image spatial
super-resolution via deep learning. Particularly, we focus on how to embed the
high-dimensional spatial-spectral information of HS images efficiently and
effectively. Specifically, in contrast to existing methods adopting
empirically-designed network modules, we formulate HS embedding as an
approximation of the posterior distribution of a set of carefully-defined HS
embedding events, including layer-wise spatial-spectral feature extraction and
network-level feature aggregation. Then, we incorporate the proposed feature
embedding scheme into a source-consistent super-resolution framework that is
physically-interpretable, producing lightweight PDE-Net, in which
high-resolution (HR) HS images are iteratively refined from the residuals
between input low-resolution (LR) HS images and pseudo-LR-HS images degenerated
from reconstructed HR-HS images via probability-inspired HS embedding.
Extensive experiments over three common benchmark datasets demonstrate that
PDE-Net achieves superior performance over state-of-the-art methods. Besides,
the probabilistic characteristic of this kind of networks can provide the
epistemic uncertainty of the network outputs, which may bring additional
benefits when used for other HS image-based applications. The code will be
publicly available at https://github.com/jinnh/PDE-Net.
