# A Generalized Tensor Formulation for Hyperspectral Image Super-Resolution Under General Spatial Blurring

arXiv: https://arxiv.org/abs/2409.18731 · HTML: https://mlsanity.com/paper/2409.18731/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 61 references that are in the map.
- First posted on arXiv 27 Sep 2024.

## Builds on (most cited first, 11 of 11)

- [A convex formulation for hyperspectral image superresolution via subspace-based regularization](https://mlsanity.com/paper/1411.4005/) (2014)
- [Non-local Meets Global: An Iterative Paradigm for Hyperspectral Image Restoration](https://mlsanity.com/paper/2010.12921/) (2020)
- [Blind Image Super-resolution with Elaborate Degradation Modeling on Noise and Kernel](https://mlsanity.com/paper/2107.00986/) (2021)
- [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)
- [Noisy Tensor Completion via Low-rank Tensor Ring](https://mlsanity.com/paper/2203.08857/) (2022)
- [Multi-Band Image Fusion Based on Spectral Unmixing](https://mlsanity.com/paper/1603.08720/) (2016)
- [Bayesian Image Super-Resolution with Deep Modeling of Image Statistics](https://mlsanity.com/paper/2204.00623/) (2022)
- [Hyperspectral Super-Resolution via Interpretable Block-Term Tensor Modeling](https://mlsanity.com/paper/2006.10248/) (2020)
- [Hyperspectral Super-Resolution with Coupled Tucker Approximation: Recoverability and SVD-based algorithms](https://mlsanity.com/paper/1811.11091/) (2018)
- [Unrolled Variational Bayesian Algorithm for Image Blind Deconvolution](https://mlsanity.com/paper/2110.07202/) (2021)

## Built on by (most cited first, 5 of 5)

- [Unsupervised Hyperspectral Image Super-Resolution via Self-Supervised Modality Decoupling](https://mlsanity.com/paper/2412.04802/) (2024)
- [HADAR-Based Thermal Infrared Hyperspectral Image Restoration](https://mlsanity.com/paper/2605.13664/) (2026)
- [Bayesian Fully-Connected Tensor Network for Hyperspectral-Multispectral Image Fusion](https://mlsanity.com/paper/2510.18400/) (2025)
- [Compact Multi-level-prior Tensor Representation for Hyperspectral Image Super-resolution](https://mlsanity.com/paper/2510.06098/) (2025)
- [Robust Principal Component Completion](https://mlsanity.com/paper/2603.25132/) (2026)

## Abstract (arXiv)

Hyperspectral super-resolution is commonly accomplished by the fusing of a hyperspectral imaging of low spatial resolution with a multispectral image of high spatial resolution, and many tensor-based approaches to this task have been recently proposed. Yet, it is assumed in such tensor-based methods that the spatial-blurring operation that creates the observed hyperspectral image from the desired super-resolved image is separable into independent horizontal and vertical blurring. Recent work has argued that such separable spatial degradation is ill-equipped to model the operation of real sensors which may exhibit, for example, anisotropic blurring. To accommodate this fact, a generalized tensor formulation based on a Kronecker decomposition is proposed to handle any general spatial-degradation matrix, including those that are not separable as previously assumed. Analysis of the generalized formulation reveals conditions under which exact recovery of the desired super-resolved image is guaranteed, and a practical algorithm for such recovery, driven by a blockwise-group-sparsity regularization, is proposed. Extensive experimental results demonstrate that the proposed generalized tensor approach outperforms not only traditional matrix-based techniques but also state-of-the-art tensor-based methods; the gains with respect to the latter are especially significant in cases of anisotropic spatial blurring.