Hyperspectral Super-Resolution: A Coupled Nonnegative Block-Term Tensor Decomposition Approach

Hyperspectral super-resolution (HSR) aims at fusing a hyperspectral image (HSI) and a multispectral image (MSI) to produce a super-resolution image (SRI) that has high spatial and spectral resolution. Many popular methods exploit the linear mixture model (LMM) of spectral images and tackle the HSR problem from a coupled matrix decomposition viewpoint. Recently, a coupled tensor factorization approach was proposed to handle this challenging problem, which admits a series of advantages over the matrix-based methods. In particular, modeling the HSI and MSI as low-rank tensors, and leveraging the powerful model uniqueness properties of the canonical polyadic decomposition (CPD), the approach was shown to be able to provably identify the SRI, under some mild conditions. However, the latent factors in the CPD model have no physical meaning, which makes utilizing prior information as constraints or regularizations difficult-but using prior information is important in practice, especially when the data is noisy. In this work, we propose an alternative coupled tensor decomposition approach, where the HSI and MSI are assumed to follow the block-term decomposition (BTD) model. Notably, the new method also admits identifiability of the SRI under realistic conditions. More importantly, when modeling a spectral image as a BTD tensor, the latent factors have clear physical meaning, and thus prior information on the key constituents of spectral images, namely, endmembers and abundance maps (which are nonnegative, and smooth in spectrum and space, respectively), can be naturally incorporated. Simulations using real hyperspectral images are employed to showcase the effectiveness of the proposed approach with nonnegativity constraints.