# A Copula-Guided Temporal Dependency Method for Multitemporal Hyperspectral Images Unmixing

arXiv: https://arxiv.org/abs/2509.11096 · HTML: https://mlsanity.com/paper/2509.11096/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 69 references that are in the map.
- First posted on arXiv 14 Sep 2025.

## Builds on (most cited first, 18 of 18)

- [TACTiS: Transformer-Attentional Copulas for Time Series](https://mlsanity.com/paper/2202.03528/) (2022)
- [Material Based Object Tracking in Hyperspectral Videos: Benchmark and Algorithms](https://mlsanity.com/paper/1812.04179/) (2018)
- [TACTiS-2: Better, Faster, Simpler Attentional Copulas for Multivariate Time Series](https://mlsanity.com/paper/2310.01327/) (2023)
- [Copulas as High-Dimensional Generative Models: Vine Copula Autoencoders](https://mlsanity.com/paper/1906.05423/) (2019)
- [Implicit Generative Copulas](https://mlsanity.com/paper/2109.14567/) (2021)
- [A Plug-and-Play Priors Framework for Hyperspectral Unmixing](https://mlsanity.com/paper/2012.13074/) (2020)
- [Spectral Variability Aware Blind Hyperspectral Image Unmixing Based on Convex Geometry](https://mlsanity.com/paper/1904.03888/) (2019)
- [Dynamical spectral unmixing of multitemporal hyperspectral images](https://mlsanity.com/paper/1510.04238/) (2015)
- [Kalman Filtering and Expectation Maximization for Multitemporal Spectral Unmixing](https://mlsanity.com/paper/2001.00425/) (2020)
- [Dynamical Hyperspectral Unmixing with Variational Recurrent Neural Networks](https://mlsanity.com/paper/2303.10566/) (2023)
- [A Data Dependent Multiscale Model for Hyperspectral Unmixing With Spectral Variability](https://mlsanity.com/paper/1808.01047/) (2018)
- [Online Unmixing of Multitemporal Hyperspectral Images accounting for Spectral Variability](https://mlsanity.com/paper/1510.05893/) (2015)
- [Learning Endmember Dynamics in Multitemporal Hyperspectral Data Using a State-Space Model Formulation](https://mlsanity.com/paper/1911.12020/) (2019)
- [Transformer for Multitemporal Hyperspectral Image Unmixing](https://mlsanity.com/paper/2407.10427/) (2024)
- [A Hierarchical Bayesian Model Accounting for Endmember Variability and Abrupt Spectral Changes to Unmix Multitemporal Hyperspectral Images](https://mlsanity.com/paper/1609.07792/) (2016)
- [NN-Copula-CD: A Copula-Guided Interpretable Neural Network for Change Detection in Heterogeneous Remote Sensing Images](https://mlsanity.com/paper/2303.17448/) (2023)
- [Copula Variational LSTM for High-dimensional Cross-market Multivariate Dependence Modeling](https://mlsanity.com/paper/2305.08778/) (2023)
- [Multitemporal Latent Dynamical Framework for Hyperspectral Images Unmixing](https://mlsanity.com/paper/2505.20902/) (2025)

## Abstract (arXiv)

Multitemporal hyperspectral unmixing (MTHU) aims to model variable endmembers and dynamical abundances, which emphasizes the critical temporal information. However, existing methods have limitations in modeling temporal dependency, thus fail to capture the dynamical material evolution. Motivated by the ability of copula theory in modeling dependency structure explicitly, in this paper, we propose a copula-guided temporal dependency method (Cog-TD) for multitemporal hyperspectral unmixing. Cog-TD defines new mathematical model, constructs copula-guided framework and provides two key modules with theoretical support. The mathematical model provides explicit formulations for MTHU problem definition, which describes temporal dependency structure by incorporating copula theory. The copula-guided framework is constructed for utilizing copula function, which estimates dynamical endmembers and abundances with temporal dependency. The key modules consist of copula function estimation and temporal dependency guidance, which computes and employs temporal information to guide unmixing process. Moreover, the theoretical support demonstrates that estimated copula function is valid and the represented temporal dependency exists in hyperspectral images. The major contributions of this paper include redefining MTHU problem with temporal dependency, proposing a copula-guided framework, developing two key modules and providing theoretical support. Our experimental results on both synthetic and real-world datasets demonstrate the utility of the proposed method.