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

2025-12-22

AI Summary

Endmember variability (EV) violates the linear mixing assumption, degrading hyperspectral super-resolution (HSR) performance. To address this, we propose LMN—a physically interpretable block-term tensor decomposition (BTD) model with theoretical guarantees. LMN unifies CP, Tucker, and LL1 decompositions to explicitly model nonlinear spectral mixing while jointly factorizing co-registered hyperspectral and multispectral image tensors. We establish, for the first time under EV, a rigorous HSR identifiability theory—proving both uniqueness and stability of the solution. Experiments on synthetic and real-world data demonstrate that LMN significantly outperforms state-of-the-art tensor-based methods, exhibits robustness to endmember variation, and achieves superior trade-offs between physical interpretability and reconstruction accuracy.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Computer Vision: Multi-modal Vision
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

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.

Problem

• Addresses hyperspectral super-resolution by fusing HSI and MSI images
• Proposes flexible LMN tensor model to handle endmember variability
• Ensures recoverability and interpretability in spectral image reconstruction

Innovation

• Proposes flexible LMN tensor decomposition model
• Balances expressiveness and interpretability for HSR
• Ensures recoverability under endmember variability conditions