  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.
