# MultiHU-TD: Multifeature Hyperspectral Unmixing Based on Tensor Decomposition

arXiv: https://arxiv.org/abs/2310.03860 · HTML: https://mlsanity.com/paper/2310.03860/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 69 references that are in the map.
- First posted on arXiv 5 Oct 2023.

## Builds on (most cited first, 12 of 12)

- [An Augmented Linear Mixing Model to Address Spectral Variability for Hyperspectral Unmixing](https://mlsanity.com/paper/1810.12000/) (2018)
- [Spectral Variability in Hyperspectral Data Unmixing: A Comprehensive Review](https://mlsanity.com/paper/2001.07307/) (2020)
- [Non-local Meets Global: An Integrated Paradigm for Hyperspectral Denoising](https://mlsanity.com/paper/1812.04243/) (2018)
- [A Flexible and Efficient Algorithmic Framework for Constrained Matrix and Tensor Factorization](https://mlsanity.com/paper/1506.04209/) (2015)
- [Hyperspectral Super-Resolution: A Coupled Tensor Factorization Approach](https://mlsanity.com/paper/1804.05307/) (2018)
- [Dynamical spectral unmixing of multitemporal hyperspectral images](https://mlsanity.com/paper/1510.04238/) (2015)
- [Hyperspectral Super-Resolution with Coupled Tucker Approximation: Recoverability and SVD-based algorithms](https://mlsanity.com/paper/1811.11091/) (2018)
- [A Low-rank Tensor Regularization Strategy for Hyperspectral Unmixing](https://mlsanity.com/paper/1803.06355/) (2018)
- [Learning Endmember Dynamics in Multitemporal Hyperspectral Data Using a State-Space Model Formulation](https://mlsanity.com/paper/1911.12020/) (2019)
- [Improved Hyperspectral Unmixing With Endmember Variability Parametrized Using an Interpolated Scaling Tensor](https://mlsanity.com/paper/1901.00463/) (2019)
- [Tensor Analysis with n-Mode Generalized Difference Subspace](https://mlsanity.com/paper/1909.01954/) (2019)
- [Brain-Computer Interface with Corrupted EEG Data: A Tensor Completion Approach](https://mlsanity.com/paper/1806.05017/) (2018)

## Abstract (arXiv)

Hyperspectral unmixing allows representing mixed pixels as a set of pure materials weighted by their abundances. Spectral features alone are often insufficient, so it is common to rely on other features of the scene. Matrix models become insufficient when the hyperspectral image (HSI) is represented as a high-order tensor with additional features in a multimodal, multifeature framework. Tensor models such as canonical polyadic decomposition allow for this kind of unmixing but lack a general framework and interpretability of the results. In this article, we propose an interpretable methodological framework for low-rank multifeature hyperspectral unmixing based on tensor decomposition (MultiHU-TD) that incorporates the abundance sum-to-one constraint in the alternating optimization alternating direction method of multipliers (ADMM) algorithm and provide in-depth mathematical, physical, and graphical interpretation and connections with the extended linear mixing model. As additional features, we propose to incorporate mathematical morphology and reframe a previous work on neighborhood patches within MultiHU-TD. Experiments on real HSIs showcase the interpretability of the model and the analysis of the results. Python and MATLAB implementations are made available on GitHub.