Rethinking Coupled Tensor Analysis for Hyperspectral Superresolution: Recoverable Modeling under Endmember Variability

Abstract. This work revisits the hyperspectral superresolution (HSR) problem, i.e., fusing a pair of spatially co-registered hyperspectral (HSI) and multispectral (MSI) images to recover a superresolution image (SRI) that enhances the spatial resolution of the HSI. Coupled tensor decomposition–based methods have gained traction in this domain, offering recoverability guarantees under various assumptions. Existing models such as canonical polyadic decomposition (CPD) and Tucker decomposition provide strong expressive power but lack physical interpretability. The block-term decomposition model with rank-[Formula: see text] terms (the LL1 model) yields interpretable factors under the linear mixture model (LMM) of spectral images, but LMM assumptions are often violated in practice—primarily due to nonlinear effects such as endmember variability (EV). To address this issue, we propose representing spectral images using a more flexible block-term tensor model with rank-[Formula: see text] terms (the LMN model). This modeling choice retains interpretability, subsumes CPD, Tucker, and LL1 as special cases, and robustly accounts for non-ideal effects such as EV, offering a balanced trade-off between expressiveness and interpretability for HSR. Importantly, under the LMN model for HSI and MSI, recoverability of the SRI can still be established under proper conditions—providing strong theoretical support. Extensive experiments on synthetic and real datasets demonstrate the effectiveness and robustness of the proposed method.