# Hyperspectral unmixing with spectral variability using adaptive bundles and double sparsity

arXiv: https://arxiv.org/abs/1804.11132 · HTML: https://mlsanity.com/paper/1804.11132/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Apr 2018.

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

- [Endmember-Guided Unmixing Network (EGU-Net): A General Deep Learning Framework for Self-Supervised Hyperspectral Unmixing](https://mlsanity.com/paper/2105.10194/) (2021)
- [Dynamical Hyperspectral Unmixing with Variational Recurrent Neural Networks](https://mlsanity.com/paper/2303.10566/) (2023)
- [Spectral Variability Augmented Sparse Unmixing of Hyperspectral Images](https://mlsanity.com/paper/2110.09744/) (2021)
- [A General Framework for Group Sparsity in Hyperspectral Unmixing Using Endmember Bundles](https://mlsanity.com/paper/2505.14634/) (2025)
- [Hyperspectral Unmixing with 3D Convolutional Sparse Coding and Projected Simplex Volume Maximization](https://mlsanity.com/paper/2512.05674/) (2025)

## Abstract (arXiv)

Spectral variability is one of the major issue when conducting hyperspectral unmixing. Within a given image composed of some elementary materials (herein referred to as endmember classes), the spectral signature characterizing these classes may spatially vary due to intrinsic component fluctuations or external factors (illumination). These redundant multiple endmember spectra within each class adversely affect the performance of unmixing methods. This paper proposes a mixing model that explicitly incorporates a hierarchical structure of redundant multiple spectra representing each class. The proposed method is designed to promote sparsity on the selection of both spectra and classes within each pixel. The resulting unmixing algorithm is able to adaptively recover several bundles of endmember spectra associated with each class and robustly estimate abundances. In addition, its flexibility allows a variable number of classes to be present within each pixel of the hyperspectral image to be unmixed. The proposed method is compared with other state-of-the-art unmixing methods that incorporate sparsity using both simulated and real hyperspectral data. The results show that the proposed method can successfully determine the variable number of classes present within each class and estimate the corresponding class abundances.