# A spatial compositional model (SCM) for linear unmixing and endmember uncertainty estimation

arXiv: https://arxiv.org/abs/1509.09243 · HTML: https://mlsanity.com/paper/1509.09243/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Sep 2015.

## Built on by (most cited first, 2 of 2)

- [Rethinking Coupled Tensor Analysis for Hyperspectral Super-Resolution: Recoverable Modeling Under Endmember Variability](https://mlsanity.com/paper/2512.19489/) (2025)
- [SMILE: A Super-resolution Guided Multi-task Learning Method for Hyperspectral Unmixing](https://mlsanity.com/paper/2509.11093/) (2025)

## Abstract (arXiv)

The normal compositional model (NCM) has been extensively used in hyperspectral unmixing. However, most of the previous research has focused on estimation of endmembers and/or their variability. Also, little work has employed spatial information in NCM. In this paper, we show that NCM can be used for calculating the uncertainty of the estimated endmembers with spatial priors incorporated for better unmixing. This results in a spatial compositional model (SCM) which features (i) spatial priors that force neighboring abundances to be similar based on their pixel similarity and (ii) a posterior that is obtained from a likelihood model which does not assume pixel independence. The resulting algorithm turns out to be easy to implement and efficient to run. We compared SCM with current state-of-the-art algorithms on synthetic and real images. The results show that SCM can in the main provide more accurate endmembers and abundances. Moreover, the estimated uncertainty can serve as a prediction of endmember error under certain conditions.