Hyperspectral Super-Resolution via Interpretable Block-Term Tensor Modeling

Hyperspectral super-resolution (HSR) aims at fusing a pair of hyperspectral and multispectral images to recover a super-resolution image (SRI). This work revisits coupled tensor decomposition (CTD)-based HSR. The vast majority of the HSR approaches take a low-rank matrix recovery perspective. The challenge is that theoretical guarantees for recovering the SRI using low-rank matrix models are either elusive or derived under stringent conditions. A couple of recent CTD-based methods ensure recoverability for the SRI under relatively mild conditions, leveraging algebraic properties of the <italic>canonical polyadic decomposition</italic> (CPD) and the <italic>Tucker</italic> decomposition models, respectively. However, the latent factors of both the CPD and Tucker models have no physical interpretations in the context of spectral image analysis, which makes incorporating prior information challenging—but using priors is often essential for enhancing performance in noisy environments. This work employs an idea that models spectral images as tensors following the block-term decomposition model with multilinear rank-<inline-formula><tex-math notation="LaTeX">$(L_r,L_r,1)$</tex-math></inline-formula> terms (i.e., the <inline-formula><tex-math notation="LaTeX">${\mathsf {LL1}}$</tex-math></inline-formula> model) and formulates the HSR problem as a coupled <inline-formula><tex-math notation="LaTeX">${\mathsf {LL1}}$</tex-math></inline-formula> tensor decomposition problem. Similar to the existing CTD approaches, recoverability of the SRI is shown under mild conditions. More importantly, the latent factors of the <inline-formula><tex-math notation="LaTeX">${\mathsf {LL1}}$</tex-math></inline-formula> model can be interpreted as the key constituents of spectral images, i.e., the endmembers’ spectral signatures and abundance maps. This connection allows us to incorporate prior information for performance enhancement. A flexible algorithmic framework that can work with a series of structural information is proposed to take advantages of the model interpretability. The effectiveness is showcased using simulated and real data.