# A Hierarchical Bayesian Model Accounting for Endmember Variability and Abrupt Spectral Changes to Unmix Multitemporal Hyperspectral Images

arXiv: https://arxiv.org/abs/1609.07792 · HTML: https://mlsanity.com/paper/1609.07792/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Sep 2016.

## Built on by (most cited first, 3 of 3)

- [Dynamical Hyperspectral Unmixing with Variational Recurrent Neural Networks](https://mlsanity.com/paper/2303.10566/) (2023)
- [Transformer for Multitemporal Hyperspectral Image Unmixing](https://mlsanity.com/paper/2407.10427/) (2024)
- [A Copula-Guided Temporal Dependency Method for Multitemporal Hyperspectral Images Unmixing](https://mlsanity.com/paper/2509.11096/) (2025)

## Abstract (arXiv)

Hyperspectral unmixing is a blind source separation problem which consists in estimating the reference spectral signatures contained in a hyperspectral image, as well as their relative contribution to each pixel according to a given mixture model. In practice, the process is further complexified by the inherent spectral variability of the observed scene and the possible presence of outliers. More specifically, multi-temporal hyperspectral images, i.e., sequences of hyperspectral images acquired over the same area at different time instants, are likely to simultaneously exhibit moderate endmember variability and abrupt spectral changes either due to outliers or to significant time intervals between consecutive acquisitions. Unless properly accounted for, these two perturbations can significantly affect the unmixing process. In this context, we propose a new unmixing model for multitemporal hyperspectral images accounting for smooth temporal variations, construed as spectral variability, and abrupt spectral changes interpreted as outliers. The proposed hierarchical Bayesian model is inferred using a Markov chain Monte-Carlo (MCMC) method allowing the posterior of interest to be sampled and Bayesian estimators to be approximated. A comparison with unmixing techniques from the literature on synthetic and real data allows the interest of the proposed approach to be appreciated.