# A Tractable Two-Step Linear Mixing Model Solved with Second-Order Optimization for Spectral Unmixing under Variability

arXiv: https://arxiv.org/abs/2502.17212 · HTML: https://mlsanity.com/paper/2502.17212/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 48 references that are in the map.
- First posted on arXiv 24 Feb 2025.

## Builds on (most cited first, 11 of 11)

- [An Augmented Linear Mixing Model to Address Spectral Variability for Hyperspectral Unmixing](https://mlsanity.com/paper/1810.12000/) (2018)
- [Nonnegative Matrix Factorization for Signal and Data Analytics: Identifiability, Algorithms, and Applications](https://mlsanity.com/paper/1803.01257/) (2018)
- [Spectral Variability in Hyperspectral Data Unmixing: A Comprehensive Review](https://mlsanity.com/paper/2001.07307/) (2020)
- [On Identifiability of Nonnegative Matrix Factorization](https://mlsanity.com/paper/1709.00614/) (2017)
- [Endmember-Guided Unmixing Network (EGU-Net): A General Deep Learning Framework for Self-Supervised Hyperspectral Unmixing](https://mlsanity.com/paper/2105.10194/) (2021)
- [Robust Volume Minimization-Based Matrix Factorization for Remote Sensing and Document Clustering](https://mlsanity.com/paper/1608.04290/) (2016)
- [Hyperspectral unmixing with spectral variability using a perturbed linear mixing model](https://mlsanity.com/paper/1502.01260/) (2015)
- [Spectral Variability Aware Blind Hyperspectral Image Unmixing Based on Convex Geometry](https://mlsanity.com/paper/1904.03888/) (2019)
- [Dynamical Hyperspectral Unmixing with Variational Recurrent Neural Networks](https://mlsanity.com/paper/2303.10566/) (2023)
- [Generalized linear mixing model accounting for endmember variability](https://mlsanity.com/paper/1710.07723/) (2017)
- [Nonlinearly Preconditioned L-BFGS as an Acceleration Mechanism for Alternating Least Squares, with Application to Tensor Decomposition](https://mlsanity.com/paper/1803.08849/) (2018)

## Abstract (arXiv)

In this paper, we propose a Two-Step Linear Mixing Model (2LMM) that bridges the gap between model complexity and computational tractability. The model achieves this by introducing two distinct scaling steps: an endmember scaling step across the image, and another for pixel-wise scaling. We show that this model leads to only a mildly non-convex optimization problem, which we solve with an optimization algorithm that incorporates second-order information. To the authors' knowledge, this work represents the first application of second-order optimization techniques to solve a spectral unmixing problem that models endmember variability. Our method is highly robust, as it requires virtually no hyperparameter tuning and can therefore be used easily and quickly in a wide range of unmixing tasks. We show through extensive experiments on both simulated and real data that the new model is competitive and in some cases superior to the state of the art in unmixing. The model also performs very well in challenging scenarios, such as blind unmixing.