Hyperspectral Image Fusion via Logarithmic Low-rank Tensor Ring
  Decomposition
Jun Zhang Lipeng Zhu Chao Wang Shutao Li
Integrating a low-spatial-resolution hyperspectral image (LR-HSI) with a
high-spatial-resolution multispectral image (HR-MSI) is recognized as a valid
method for acquiring HR-HSI. Among the current fusion approaches, the tensor
ring (TR) decomposition-based method has received growing attention owing to
its superior performance on preserving the spatial-spectral correlation.
Furthermore, the low-rank property in some TR factors has been exploited via
the matrix nuclear norm regularization along mode-2. On the other hand, the
tensor nuclear norm (TNN)-based approaches have recently demonstrated to be
more efficient on keeping high-dimensional low-rank structures in tensor
recovery. Here, we study the low-rankness of TR factors from the TNN
perspective and consider the mode-2 logarithmic TNN (LTNN) on each TR factor. A
novel fusion model is proposed by incorporating this LTNN regularization and
the weighted total variation which is to promote the continuity of HR-HSI in
the spatial-spectral domain. Meanwhile, we have devised a highly efficient
proximal alternating minimization algorithm to solve the proposed model. The
experimental results indicate that our method improves the visual quality and
exceeds the existing state-of-the-art fusion approaches with respect to various
quantitative metrics.