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

arXiv: https://arxiv.org/abs/2512.19489 · HTML: https://mlsanity.com/paper/2512.19489/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 70 references that are in the map.
- First posted on arXiv 22 Dec 2025.

## Builds on (most cited first, 26 of 26)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Tensor Decomposition for Signal Processing and Machine Learning](https://mlsanity.com/paper/1607.01668/) (2016)
- [Tensor Ring Decomposition](https://mlsanity.com/paper/1606.05535/) (2016)
- [Hyperspectral pansharpening: a review](https://mlsanity.com/paper/1504.04531/) (2015)
- [Spectral Variability in Hyperspectral Data Unmixing: A Comprehensive Review](https://mlsanity.com/paper/2001.07307/) (2020)
- [A globally convergent algorithm for nonconvex optimization based on block coordinate update](https://mlsanity.com/paper/1410.1386/) (2014)
- [Fast Fusion of Multi-Band Images Based on Solving a Sylvester Equation](https://mlsanity.com/paper/1502.03121/) (2015)
- [Hyperspectral Super-Resolution: A Coupled Tensor Factorization Approach](https://mlsanity.com/paper/1804.05307/) (2018)
- [Successive Nonnegative Projection Algorithm for Robust Nonnegative Blind Source Separation](https://mlsanity.com/paper/1310.7529/) (2013)
- [Maximum Volume Inscribed Ellipsoid: A New Simplex-Structured Matrix Factorization Framework via Facet Enumeration and Convex Optimization](https://mlsanity.com/paper/1708.02883/) (2017)
- [Spectral Unmixing via Data-guided Sparsity](https://mlsanity.com/paper/1403.3155/) (2014)
- [Unsupervised and Unregistered Hyperspectral Image Super-Resolution with Mutual Dirichlet-Net](https://mlsanity.com/paper/1904.12175/) (2019)
- [Hyperspectral Super-Resolution via Coupled Tensor Ring Factorization](https://mlsanity.com/paper/2001.01547/) (2020)
- [Multi-Band Image Fusion Based on Spectral Unmixing](https://mlsanity.com/paper/1603.08720/) (2016)
- [Hyperspectral Super-Resolution via Interpretable Block-Term Tensor Modeling](https://mlsanity.com/paper/2006.10248/) (2020)
- [Super-Resolution for Hyperspectral and Multispectral Image Fusion Accounting for Seasonal Spectral Variability](https://mlsanity.com/paper/1808.10072/) (2018)
- [Hyperspectral Super-Resolution with Coupled Tucker Approximation: Recoverability and SVD-based algorithms](https://mlsanity.com/paper/1811.11091/) (2018)
- [NeurTV: Total Variation on the Neural Domain](https://mlsanity.com/paper/2405.17241/) (2024)
- [A Framework for One-Bit and Constant-Envelope Precoding over Multiuser Massive MISO Channels](https://mlsanity.com/paper/1810.03159/) (2018)
- [Fast and Structured Block-Term Tensor Decomposition For Hyperspectral Unmixing](https://mlsanity.com/paper/2205.03798/) (2022)
- [Enhancing Pure-Pixel Identification Performance via Preconditioning](https://mlsanity.com/paper/1406.5286/) (2014)
- [Joint Tensor Factorization and Outlying Slab Suppression with Applications](https://mlsanity.com/paper/1507.04436/) (2015)
- [A spatial compositional model (SCM) for linear unmixing and endmember uncertainty estimation](https://mlsanity.com/paper/1509.09243/) (2015)
- [Provably robust blind source separation of linear-quadratic near-separable mixtures](https://mlsanity.com/paper/2011.11966/) (2020)
- [Separable Quaternion Matrix Factorization for Polarization Images](https://mlsanity.com/paper/2207.14039/) (2022)
- [Multispectral Image Restoration by Generalized Opponent Transformation Total Variation](https://mlsanity.com/paper/2403.12770/) (2024)

## Built on by (most cited first, 1 of 1)

- [Unregistered Spectral Image Fusion: Unmixing, Adversarial Learning, and Recoverability](https://mlsanity.com/paper/2603.21510/) (2026)

## Abstract (arXiv)

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-(Lr, Lr, 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-(Lr, Mr, Nr) 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.