  Hyperspectral super-resolution (HSR) fuses a low-resolution hyperspectral
image (HSI) and a high-resolution multispectral image (MSI) to obtain a
high-resolution HSI (HR-HSI). In this paper, we propose a new model, named
coupled tensor ring factorization (CTRF), for HSR. The proposed CTRF approach
simultaneously learns high spectral resolution core tensor from the HSI and
high spatial resolution core tensors from the MSI, and reconstructs the HR-HSI
via tensor ring (TR) representation (Figure~\ref{fig:framework}). The CTRF
model can separately exploit the low-rank property of each class (Section
\ref{sec:analysis}), which has been never explored in the previous coupled
tensor model. Meanwhile, it inherits the simple representation of coupled
matrix/CP factorization and flexible low-rank exploration of coupled Tucker
factorization.
  Guided by Theorem~\ref{th:1}, we further propose a spectral nuclear norm
regularization to explore the global spectral low-rank property.
  The experiments have demonstrated the advantage of the proposed nuclear norm
regularized CTRF (NCTRF) as compared to previous matrix/tensor and deep
learning methods.
