Hyperspectral Super-Resolution: A Coupled Tensor Factorization Approach

Hyperspectral super-resolution refers to the problem of fusing a hyperspectral image (HSI) and a multispectral image (MSI) to produce a super-resolution image (SRI) that admits fine spatial and spectral resolutions. State-of-the-art methods approach the problem via low-rank matrix approximations to the matricized HSI and MSI. These methods are effective to some extent, but a number of challenges remain. First, HSIs and MSIs are naturally third-order tensors (data "cubes") and thus matricization is prone to a loss of structural information, which could degrade performance. Second, it is unclear whether these low-rank matrix-based fusion strategies can guarantee the identifiability of the SRI under realistic assumptions. However, identifiability plays a pivotal role in estimation problems and usually has a significant impact on practical performance. Third, a majority of the existing methods assume known (or easily estimated) degradation operators from the SRI to the corresponding HSI and MSI, which is hardly the case in practice. In this paper, we propose to tackle the super-resolution problem from a tensor perspective. Specifically, we utilize the multidimensional structure of the HSI and MSI to propose a coupled tensor factorization framework that can effectively overcome the aforementioned issues. The proposed approach guarantees the identifiability of the SRI under mild and realistic conditions. Furthermore, it works with little knowledge about the degradation operators, which is clearly a favorable feature in practice. Semi-real scenarios are simulated to showcase the effectiveness of the proposed approach.