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

TL;DR

This paper introduces a new two-step linear mixing model for spectral unmixing that is computationally efficient, robust, and capable of handling endmember variability using second-order optimization techniques.

Contribution

The work presents the first application of second-order optimization to spectral unmixing with endmember variability, offering a tractable and robust solution.

Findings

Model is competitive with state-of-the-art methods.

Performs well in blind unmixing scenarios.

Requires minimal hyperparameter tuning.

Abstract

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.