# Hyperspectral Image Unmixing with Endmember Bundles and Group Sparsity Inducing Mixed Norms

arXiv: https://arxiv.org/abs/1805.10232 · HTML: https://mlsanity.com/paper/1805.10232/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 May 2018.

## Built on by (most cited first, 14 of 14)

- [Deep Hyperspectral Unmixing using Transformer Network](https://mlsanity.com/paper/2203.17076/) (2022)
- [Hyperspectral Unmixing Based on Nonnegative Matrix Factorization: A Comprehensive Review](https://mlsanity.com/paper/2205.09933/) (2022)
- [Image Processing and Machine Learning for Hyperspectral Unmixing: An Overview and the HySUPP Python Package](https://mlsanity.com/paper/2308.09375/) (2023)
- [Dynamical Hyperspectral Unmixing with Variational Recurrent Neural Networks](https://mlsanity.com/paper/2303.10566/) (2023)
- [Hyperspectral Pixel Unmixing with Latent Dirichlet Variational Autoencoder](https://mlsanity.com/paper/2203.01327/) (2022)
- [Transformer for Multitemporal Hyperspectral Image Unmixing](https://mlsanity.com/paper/2407.10427/) (2024)
- [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)
- [The Effects of Spectral Dimensionality Reduction on Hyperspectral Pixel Classification: A Case Study](https://mlsanity.com/paper/2104.00788/) (2021)
- [Hyperspectral Unmixing Under Endmember Variability: A Variational Inference Framework](https://mlsanity.com/paper/2407.14899/) (2024)
- [A General Framework for Group Sparsity in Hyperspectral Unmixing Using Endmember Bundles](https://mlsanity.com/paper/2505.14634/) (2025)
- [MiSiSUn: Minimum Simplex Semisupervised Unmixing](https://mlsanity.com/paper/2603.20263/) (2026)
- [Hyperspectral Unmixing Hierarchies](https://mlsanity.com/paper/2604.16969/) (2026)

## Abstract (arXiv)

Hyperspectral images provide much more information than conventional imaging techniques, allowing a precise identification of the materials in the observed scene, but because of the limited spatial resolution, the observations are usually mixtures of the contributions of several materials. The spectral unmixing problem aims at recovering the spectra of the pure materials of the scene (endmembers), along with their proportions (abundances) in each pixel. In order to deal with the intra-class variability of the materials and the induced spectral variability of the endmembers, several spectra per material, constituting endmember bundles, can be considered. However, the usual abundance estimation techniques do not take advantage of the particular structure of these bundles, organized into groups of spectra. In this paper, we propose to use group sparsity by introducing mixed norms in the abundance estimation optimization problem. In particular, we propose a new penalty which simultaneously enforces group and within group sparsity, to the cost of being nonconvex. All the proposed penalties are compatible with the abundance sum-to-one constraint, which is not the case with traditional sparse regression. We show on simulated and real datasets that well chosen penalties can significantly improve the unmixing performance compared to the naive bundle approach.