This paper introduces a new sparse unmixing technique using archetypal analysis (SUnAA). First, we design a new model based on archetypal analysis. We assume that the endmembers of interest are a convex combination of endmembers provided by a spectral library and that the number of endmembers of interest is known. Then, we propose a minimization problem. Unlike most conventional sparse unmixing methods, here the minimization problem is non-convex. We minimize the optimization objective iteratively using an active set algorithm. Our method is robust to the initialization and only requires the number of endmembers of interest. SUnAA is evaluated using two simulated datasets for which results confirm its better performance over other conventional and advanced techniques in terms of signal-to-reconstruction error. SUnAA is also applied to Cuprite dataset and the results are compared visually with the available geological map provided for this dataset. The qualitative assessment demonstrates the successful estimation of the minerals abundances and significantly improves the detection of dominant minerals compared to the conventional regression-based sparse unmixing methods. The Python implementation of SUnAA can be found at: https://github.com/BehnoodRasti/SUnAA.

翻译：本文提出了一种基于原型分析的新型稀疏解混技术（SUnAA）。首先，我们设计了一个基于原型分析的新模型。该模型假设感兴趣端元是光谱库中端元集合的凸组合，且已知感兴趣端元的数量。随后，我们提出了一个最小化问题。与大多数传统稀疏解混方法不同，本方法中的最小化问题是非凸的。我们采用活动集算法迭代优化目标函数。该方法对初始条件具有鲁棒性，且仅需已知感兴趣端元的数量。通过两个模拟数据集对SUnAA进行验证，结果表明其在信号重构误差指标上优于其他传统和先进方法。本文还将SUnAA应用于Cuprite数据集，并将结果与该数据集提供的地质图进行直观对比。定性评估表明，该方法成功估算了矿物丰度，相较于传统基于回归的稀疏解混方法，显著提升了对主导矿物的检测能力。SUnAA的Python实现代码见：https://github.com/BehnoodRasti/SUnAA。