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.

翻译：本文提出了一种两步线性混合模型（2LMM），该模型在模型复杂性与计算可处理性之间架起了桥梁。该模型通过引入两个不同的缩放步骤实现这一目标：一个是在整幅图像上进行端元缩放，另一个则是针对像素级的缩放。我们证明该模型仅导致一个轻度非凸的优化问题，并通过融合二阶信息的优化算法进行求解。据作者所知，本研究首次将二阶优化技术应用于解决建模端元可变性的光谱解混问题。我们的方法具有高度鲁棒性，几乎无需超参数调优，因此可便捷快速地应用于广泛的解混任务。通过在模拟数据和真实数据上的大量实验，我们证明新模型在解混性能上具有竞争力，并在某些情况下优于现有先进方法。该模型在具有挑战性的场景（如盲解混）中也表现出色。