# Spectral Variability in Hyperspectral Data Unmixing: A Comprehensive Review

arXiv: https://arxiv.org/abs/2001.07307 · HTML: https://mlsanity.com/paper/2001.07307/

## Key facts

- Cited by 46 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jan 2020.

## Built on by (most cited first, 30 of 46)

- [Hyperspectral Unmixing Based on Nonnegative Matrix Factorization: A Comprehensive Review](https://mlsanity.com/paper/2205.09933/) (2022)
- [Superpixel-based and Spatially-regularized Diffusion Learning for Unsupervised Hyperspectral Image Clustering](https://mlsanity.com/paper/2312.15447/) (2023)
- [DCN-T: Dual Context Network with Transformer for Hyperspectral Image Classification](https://mlsanity.com/paper/2304.09915/) (2023)
- [Image Processing and Machine Learning for Hyperspectral Unmixing: An Overview and the HySUPP Python Package](https://mlsanity.com/paper/2308.09375/) (2023)
- [Entropic Descent Archetypal Analysis for Blind Hyperspectral Unmixing](https://mlsanity.com/paper/2209.11002/) (2022)
- [Contrastive Multi-view Subspace Clustering of Hyperspectral Images based on Graph Convolutional Networks](https://mlsanity.com/paper/2312.06068/) (2023)
- [Dynamical Hyperspectral Unmixing with Variational Recurrent Neural Networks](https://mlsanity.com/paper/2303.10566/) (2023)
- [Large-Scale Hyperspectral Image Clustering Using Contrastive Learning](https://mlsanity.com/paper/2111.07945/) (2021)
- [SUnAA: Sparse Unmixing using Archetypal Analysis](https://mlsanity.com/paper/2308.04771/) (2023)
- [Towards Lightweight Hyperspectral Image Super-Resolution with Depthwise Separable Dilated Convolutional Network](https://mlsanity.com/paper/2505.00374/) (2025)
- [Unsupervised Diffusion and Volume Maximization-Based Clustering of Hyperspectral Images](https://mlsanity.com/paper/2203.09992/) (2022)
- [Learning Semilinear Neural Operators : A Unified Recursive Framework For Prediction And Data Assimilation](https://mlsanity.com/paper/2402.15656/) (2024)
- [AE-RED: A Hyperspectral Unmixing Framework Powered by Deep Autoencoder and Regularization by Denoising](https://mlsanity.com/paper/2307.00269/) (2023)
- [UnMix-NeRF: Spectral Unmixing Meets Neural Radiance Fields](https://mlsanity.com/paper/2506.21884/) (2025)
- [Spectral Variability Augmented Sparse Unmixing of Hyperspectral Images](https://mlsanity.com/paper/2110.09744/) (2021)
- [Learning Interpretable Deep Disentangled Neural Networks for Hyperspectral Unmixing](https://mlsanity.com/paper/2310.02340/) (2023)
- [A Generalized Multiscale Bundle-Based Hyperspectral Sparse Unmixing Algorithm](https://mlsanity.com/paper/2401.13161/) (2024)
- [Sum-of-norms regularized Nonnegative Matrix Factorization](https://mlsanity.com/paper/2407.00706/) (2024)
- [Personalized Coupled Tensor Decomposition for Multimodal Data Fusion: Uniqueness and Algorithms](https://mlsanity.com/paper/2412.01102/) (2024)
- [Classification of grapevine varieties using UAV hyperspectral imaging](https://mlsanity.com/paper/2401.12851/) (2024)
- [Weighted-Sum of Gaussian Process Latent Variable Models](https://mlsanity.com/paper/2402.09122/) (2024)
- [Multiview Subspace Clustering of Hyperspectral Images based on Graph Convolutional Networks](https://mlsanity.com/paper/2403.01465/) (2024)
- [DTU-Net: A Multi-Scale Dilated Transformer Network for Nonlinear Hyperspectral Unmixing](https://mlsanity.com/paper/2503.03465/) (2025)
- [Hyperspectral Imaging](https://mlsanity.com/paper/2508.08107/) (2025)
- [Rethinking Coupled Tensor Analysis for Hyperspectral Super-Resolution: Recoverable Modeling Under Endmember Variability](https://mlsanity.com/paper/2512.19489/) (2025)
- [A Vision for Cleaner Rivers: Harnessing Snapshot Hyperspectral Imaging to Detect Macro-Plastic Litter](https://mlsanity.com/paper/2307.12145/) (2023)
- [Robust retrieval of material chemical states in X-ray microspectroscopy](https://mlsanity.com/paper/2308.04207/) (2023)
- [MultiHU-TD: Multifeature Hyperspectral Unmixing Based on Tensor Decomposition](https://mlsanity.com/paper/2310.03860/) (2023)
- [An Elliptic Kernel Unsupervised Autoencoder-Graph Convolutional Network Ensemble Model for Hyperspectral Unmixing](https://mlsanity.com/paper/2406.06742/) (2024)
- [Hyperspectral Unmixing Under Endmember Variability: A Variational Inference Framework](https://mlsanity.com/paper/2407.14899/) (2024)

## Abstract (arXiv)

The spectral signatures of the materials contained in hyperspectral images, also called endmembers (EM), can be significantly affected by variations in atmospheric, illumination or environmental conditions typically occurring within an image. Traditional spectral unmixing (SU) algorithms neglect the spectral variability of the endmembers, what propagates significant mismodeling errors throughout the whole unmixing process and compromises the quality of its results. Therefore, large efforts have been recently dedicated to mitigate the effects of spectral variability in SU. This resulted in the development of algorithms that incorporate different strategies to allow the EMs to vary within a hyperspectral image, using, for instance, sets of spectral signatures known a priori, Bayesian, parametric, or local EM models. Each of these approaches has different characteristics and underlying motivations. This paper presents a comprehensive literature review contextualizing both classic and recent approaches to solve this problem. We give a detailed evaluation of the sources of spectral variability and their effect in image spectra. Furthermore, we propose a new taxonomy that organizes existing works according to a practitioner's point of view, based on the necessary amount of supervision and on the computational cost they require. We also review methods used to construct spectral libraries (which are required by many SU techniques) based on the observed hyperspectral image, as well as algorithms for library augmentation and reduction. Finally, we conclude the paper with some discussions and an outline of possible future directions for the field.