# Tensor Decompositions for Hyperspectral Data Processing in Remote Sensing: A Comprehensive Review

arXiv: https://arxiv.org/abs/2205.06407 · HTML: https://mlsanity.com/paper/2205.06407/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 255 references that are in the map.
- First posted on arXiv 13 May 2022.

## Builds on (most cited first, 30 of 35)

- [Tensor Decomposition for Signal Processing and Machine Learning](https://mlsanity.com/paper/1607.01668/) (2016)
- [SpectralFormer: Rethinking Hyperspectral Image Classification with Transformers](https://mlsanity.com/paper/2107.02988/) (2021)
- [Tensor Ring Decomposition](https://mlsanity.com/paper/1606.05535/) (2016)
- [More Diverse Means Better: Multimodal Deep Learning Meets Remote Sensing Imagery Classification](https://mlsanity.com/paper/2008.05457/) (2020)
- [Graph Convolutional Networks for Hyperspectral Image Classification](https://mlsanity.com/paper/2008.02457/) (2020)
- [Deep Learning in Multimodal Remote Sensing Data Fusion: A Comprehensive Review](https://mlsanity.com/paper/2205.01380/) (2022)
- [An Augmented Linear Mixing Model to Address Spectral Variability for Hyperspectral Unmixing](https://mlsanity.com/paper/1810.12000/) (2018)
- [Hyperspectral Image Restoration via Total Variation Regularized Low-rank Tensor Decomposition](https://mlsanity.com/paper/1707.02477/) (2017)
- [Novel methods for multilinear data completion and de-noising based on tensor-SVD](https://mlsanity.com/paper/1407.1785/) (2014)
- [Hyperspectral pansharpening: a review](https://mlsanity.com/paper/1504.04531/) (2015)
- [A convex formulation for hyperspectral image superresolution via subspace-based regularization](https://mlsanity.com/paper/1411.4005/) (2014)
- [Non-local Meets Global: An Integrated Paradigm for Hyperspectral Denoising](https://mlsanity.com/paper/1812.04243/) (2018)
- [Tensor Robust Principal Component Analysis: Exact Recovery of Corrupted Low-Rank Tensors via Convex Optimization](https://mlsanity.com/paper/1708.04181/) (2017)
- [Weighted Low-rank Tensor Recovery for Hyperspectral Image Restoration](https://mlsanity.com/paper/1709.00192/) (2017)
- [Image Restoration for Remote Sensing: Overview and Toolbox](https://mlsanity.com/paper/2107.00557/) (2021)
- [FCCDN: Feature Constraint Network for VHR Image Change Detection](https://mlsanity.com/paper/2105.10860/) (2021)
- [Hyperspectral Super-Resolution: A Coupled Tensor Factorization Approach](https://mlsanity.com/paper/1804.05307/) (2018)
- [Hyperspectral and Multispectral Image Fusion based on a Sparse Representation](https://mlsanity.com/paper/1409.5729/) (2014)
- [Tensor N-tubal rank and its convex relaxation for low-rank tensor recovery](https://mlsanity.com/paper/1812.00688/) (2018)
- [Self-Supervised Nonlinear Transform-Based Tensor Nuclear Norm for Multi-Dimensional Image Recovery](https://mlsanity.com/paper/2105.14320/) (2021)
- [Total Variation Regularized Tensor RPCA for Background Subtraction from Compressive Measurements](https://mlsanity.com/paper/1503.01868/) (2015)
- [Hyperspectral Super-Resolution via Coupled Tensor Ring Factorization](https://mlsanity.com/paper/2001.01547/) (2020)
- [Algorithms and Comparisons of Non-negative Matrix Factorization with Volume Regularization for Hyperspectral Unmixing](https://mlsanity.com/paper/1903.04362/) (2019)
- [Invariant Attribute Profiles: A Spatial-Frequency Joint Feature Extractor for Hyperspectral Image Classification](https://mlsanity.com/paper/1912.08847/) (2019)
- [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)
- [Using Low-rank Representation of Abundance Maps and Nonnegative Tensor Factorization for Hyperspectral Nonlinear Unmixing](https://mlsanity.com/paper/2103.16204/) (2021)
- [Low-Rank Tensor Modeling for Hyperspectral Unmixing Accounting for Spectral Variability](https://mlsanity.com/paper/1811.02413/) (2018)
- [Robust Fusion of Multi-Band Images with Different Spatial and Spectral Resolutions for Change Detection](https://mlsanity.com/paper/1609.06076/) (2016)
- [Non-local tensor completion for multitemporal remotely sensed images inpainting](https://mlsanity.com/paper/1801.10240/) (2018)

## Built on by (most cited first, 9 of 9)

- [Change Detection Methods for Remote Sensing in the Last Decade: A Comprehensive Review](https://mlsanity.com/paper/2305.05813/) (2023)
- [Image Processing and Machine Learning for Hyperspectral Unmixing: An Overview and the HySUPP Python Package](https://mlsanity.com/paper/2308.09375/) (2023)
- [Unsupervised Hyperspectral and Multispectral Image Blind Fusion Based on Deep Tucker Decomposition Network with Spatial-Spectral Manifold Learning](https://mlsanity.com/paper/2409.09670/) (2024)
- [Irregular Tensor Low-Rank Representation for Hyperspectral Image Representation](https://mlsanity.com/paper/2410.18388/) (2024)
- [STAR-Net: An Interpretable Model-Aided Network for Remote Sensing Image Denoising](https://mlsanity.com/paper/2505.24327/) (2025)
- [Generalized Least Squares Kernelized Tensor Factorization](https://mlsanity.com/paper/2412.07041/) (2024)
- [Compact Multi-level-prior Tensor Representation for Hyperspectral Image Super-resolution](https://mlsanity.com/paper/2510.06098/) (2025)
- [Structured Adaptive Tensor Prediction for Streaming Data](https://mlsanity.com/paper/2606.10085/) (2026)
- [Convolution-Free Holistic Multivariance Decomposition Layer for Efficient Hyperspectral Image Classification Tensor Networks](https://mlsanity.com/paper/2608.16241/) (2026)

## Abstract (arXiv)

Owing to the rapid development of sensor technology, hyperspectral (HS) remote sensing (RS) imaging has provided a significant amount of spatial and spectral information for the observation and analysis of the Earth's surface at a distance of data acquisition devices, such as aircraft, spacecraft, and satellite. The recent advancement and even revolution of the HS RS technique offer opportunities to realize the full potential of various applications, while confronting new challenges for efficiently processing and analyzing the enormous HS acquisition data. Due to the maintenance of the 3-D HS inherent structure, tensor decomposition has aroused widespread concern and research in HS data processing tasks over the past decades. In this article, we aim at presenting a comprehensive overview of tensor decomposition, specifically contextualizing the five broad topics in HS data processing, and they are HS restoration, compressed sensing, anomaly detection, super-resolution, and spectral unmixing. For each topic, we elaborate on the remarkable achievements of tensor decomposition models for HS RS with a pivotal description of the existing methodologies and a representative exhibition on the experimental results. As a result, the remaining challenges of the follow-up research directions are outlined and discussed from the perspective of the real HS RS practices and tensor decomposition merged with advanced priors and even with deep neural networks. This article summarizes different tensor decomposition-based HS data processing methods and categorizes them into different classes from simple adoptions to complex combinations with other priors for the algorithm beginners. We also expect this survey can provide new investigations and development trends for the experienced researchers who understand tensor decomposition and HS RS to some extent.