  This paper focuses on hyperspectral image (HSI) super-resolution that aims to
fuse a low-spatial-resolution HSI and a high-spatial-resolution multispectral
image to form a high-spatial-resolution HSI (HR-HSI). Existing deep
learning-based approaches are mostly supervised that rely on a large number of
labeled training samples, which is unrealistic. The commonly used model-based
approaches are unsupervised and flexible but rely on hand-craft priors.
Inspired by the specific properties of model, we make the first attempt to
design a model inspired deep network for HSI super-resolution in an
unsupervised manner. This approach consists of an implicit autoencoder network
built on the target HR-HSI that treats each pixel as an individual sample. The
nonnegative matrix factorization (NMF) of the target HR-HSI is integrated into
the autoencoder network, where the two NMF parts, spectral and spatial
matrices, are treated as decoder parameters and hidden outputs respectively. In
the encoding stage, we present a pixel-wise fusion model to estimate hidden
outputs directly, and then reformulate and unfold the model's algorithm to form
the encoder network. With the specific architecture, the proposed network is
similar to a manifold prior-based model, and can be trained patch by patch
rather than the entire image. Moreover, we propose an additional unsupervised
network to estimate the point spread function and spectral response function.
Experimental results conducted on both synthetic and real datasets demonstrate
the effectiveness of the proposed approach.
