Rethinking Coupled Tensor Analysis for Hyperspectral Super-Resolution: Recoverable Modeling Under Endmember Variability

TL;DR

This paper introduces a flexible tensor decomposition model for hyperspectral super-resolution that effectively handles endmember variability, providing both interpretability and recoverability guarantees, and demonstrates superior performance over existing methods.

Contribution

Proposes the LMN block-term tensor model for hyperspectral super-resolution, addressing endmember variability while maintaining interpretability and recoverability guarantees.

Findings

The LMN model outperforms existing methods on synthetic datasets.

The approach is robust to nonlinear effects like endmember variability.

Theoretical recoverability conditions are established for the proposed model.

Abstract

This work revisits the hyperspectral super-resolution (HSR) problem, i.e., fusing a pair of spatially co-registered hyperspectral (HSI) and multispectral (MSI) images to recover a super-resolution image (SRI) that enhances the spatial resolution of the HSI. Coupled tensor decomposition (CTD)-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-$(L_r, L_r, 1)$ 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, we propose modeling spectral images using a more flexible block-term tensor decomposition with rank-$(L_r, M_r, N_r)$ 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 tradeoff 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 further validate the effectiveness and robustness of the proposed method compared with existing CTD-based approaches.