# Online Unmixing of Multitemporal Hyperspectral Images accounting for Spectral Variability

arXiv: https://arxiv.org/abs/1510.05893 · HTML: https://mlsanity.com/paper/1510.05893/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Oct 2015.

## Built on by (most cited first, 6 of 6)

- [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)
- [Transformer for Multitemporal Hyperspectral Image Unmixing](https://mlsanity.com/paper/2407.10427/) (2024)
- [Multitemporal Latent Dynamical Framework for Hyperspectral Images Unmixing](https://mlsanity.com/paper/2505.20902/) (2025)
- [A Copula-Guided Temporal Dependency Method for Multitemporal Hyperspectral Images Unmixing](https://mlsanity.com/paper/2509.11096/) (2025)
- [Hyperspectral Unmixing Hierarchies](https://mlsanity.com/paper/2604.16969/) (2026)

## Abstract (arXiv)

Hyperspectral unmixing is aimed at identifying the reference spectral signatures composing an hyperspectral image and their relative abundance fractions in each pixel. In practice, the identified signatures may vary spectrally from an image to another due to varying acquisition conditions, thus inducing possibly significant estimation errors. Against this background, hyperspectral unmixing of several images acquired over the same area is of considerable interest. Indeed, such an analysis enables the endmembers of the scene to be tracked and the corresponding endmember variability to be characterized. Sequential endmember estimation from a set of hyperspectral images is expected to provide improved performance when compared to methods analyzing the images independently. However, the significant size of hyperspectral data precludes the use of batch procedures to jointly estimate the mixture parameters of a sequence of hyperspectral images. Provided that each elementary component is present in at least one image of the sequence, we propose to perform an online hyperspectral unmixing accounting for temporal endmember variability. The online hyperspectral unmixing is formulated as a two-stage stochastic program, which can be solved using a stochastic approximation. The performance of the proposed method is evaluated on synthetic and real data. A comparison with independent unmixing algorithms finally illustrates the interest of the proposed strategy.