The fusion of a low-resolution hyperspectral image (LR-HSI) with a
high-resolution multispectral image (HR-MSI) has emerged as an effective
technique for achieving HSI super-resolution (SR). Previous studies have mainly
concentrated on estimating the posterior distribution of the latent
high-resolution hyperspectral image (HR-HSI), leveraging an appropriate image
prior and likelihood computed from the discrepancy between the latent HSI and
observed images. Low rankness stands out for preserving latent HSI
characteristics through matrix factorization among the various priors. However,
this method only enhances resolution within the dimensions of the two
modalities. To overcome this limitation, we propose a novel continuous low-rank
factorization (CLoRF) by integrating two neural representations into the matrix
factorization, capturing spatial and spectral information, respectively. This
approach enables us to harness both the low rankness from the matrix
factorization and the continuity from neural representation in a
self-supervised manner. Theoretically, we prove the low-rank property and
Lipschitz continuity in the proposed continuous low-rank factorization.
Experimentally, our method significantly surpasses existing techniques and
achieves user-desired resolutions without the need for neural network
retraining.

通过融合低分辨率高光谱图像（LR-HSI）与高分辨率多光谱图像（HR-MSI），提出了一种连续低秩分解（CLoRF）方法，通过将两种神经表示集成到矩阵分解中，分别捕捉空间和光谱信息，实现了低秩和连续性的自监督学习，在实验中显著超过现有技术，并实现了用户期望的分辨率提升，无需神经网络重新训练。