# Low-Rank Tensor Modeling for Hyperspectral Unmixing Accounting for Spectral Variability

arXiv: https://arxiv.org/abs/1811.02413 · HTML: https://mlsanity.com/paper/1811.02413/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Nov 2018.

## Built on by (most cited first, 5 of 5)

- [Hyperspectral Unmixing Based on Nonnegative Matrix Factorization: A Comprehensive Review](https://mlsanity.com/paper/2205.09933/) (2022)
- [Tensor Decompositions for Hyperspectral Data Processing in Remote Sensing: A Comprehensive Review](https://mlsanity.com/paper/2205.06407/) (2022)
- [Dynamical Hyperspectral Unmixing with Variational Recurrent Neural Networks](https://mlsanity.com/paper/2303.10566/) (2023)
- [Learning Interpretable Deep Disentangled Neural Networks for Hyperspectral Unmixing](https://mlsanity.com/paper/2310.02340/) (2023)
- [Interpretable Hyperspectral AI: When Non-Convex Modeling meets Hyperspectral Remote Sensing](https://mlsanity.com/paper/2103.01449/) (2021)

## Abstract (arXiv)

Traditional hyperspectral unmixing methods neglect the underlying variability of spectral signatures often observed in typical hyperspectral images (HI), propagating these missmodeling errors throughout the whole unmixing process. Attempts to model material spectra as members of sets or as random variables tend to lead to severely ill-posed unmixing problems. Although parametric models have been proposed to overcome this drawback by handling endmember variability through generalizations of the mixing model, the success of these techniques depend on employing appropriate regularization strategies. Moreover, the existing approaches fail to adequately explore the natural multidimensinal representation of HIs. Recently, tensor-based strategies considered low-rank decompositions of hyperspectral images as an alternative to impose low-dimensional structures on the solutions of standard and multitemporal unmixing problems. These strategies, however, present two main drawbacks: 1) they confine the solutions to low-rank tensors, which often cannot represent the complexity of real-world scenarios; and 2) they lack guarantees that endmembers and abundances will be correctly factorized in their respective tensors. In this work, we propose a more flexible approach, called ULTRA-V, that imposes low-rank structures through regularizations whose strictness is controlled by scalar parameters. Simulations attest the superior accuracy of the method when compared with state-of-the-art unmixing algorithms that account for spectral variability.