基于面元分量分析的几何盲源分离方法
A Geometric Blind Source Separation Method Based on Facet Component Analysis
AI总结：
提出一种基于面元分量分析（FCA）的几何盲源分离方法，通过识别数据锥结构的面元而非顶点，结合数据分类与线性回归实现非负线性混合的盲分离，并利用去噪技术处理噪声数据。
摘要：
给定一组混合信号，盲源分离试图在没有或很少混合过程信息的情况下恢复源信号。我们提出了一种几何方法用于非负线性混合的盲分离，称为面元分量分析（FCA）。该方法基于数据底层锥结构的面元识别。早期工作侧重于通过顶点分量分析（VCA）定位锥的顶点，这要求每个源信号在其频谱中具有独立的峰值（互稀疏条件）。我们提出了替代条件，使得足够多的数据点落在锥的面元上，而不是聚集在顶点周围。为了找到唯一可解的条件，我们利用了数据点的几何和密度特性，并通过结合数据分类和线性回归开发了一种高效的面元识别方法。对于含噪数据，我们展示了可以采用去噪方法，如图像处理中的全变分技术和主成分分析。我们在核磁共振波谱数据上展示了计算结果，以验证我们的方法。
英文摘要：
Given a set of mixtures, blind source separation attempts to retrieve the source signals without or with very little information of the the mixing process. We present a geometric approach for blind separation of nonnegative linear mixtures termed {\em facet component analysis} (FCA). The approach is based on facet identification of the underlying cone structure of the data. Earlier works focus on recovering the cone by locating its vertices (vertex component analysis or VCA) based on a mutual sparsity condition which requires each source signal to possess a stand-alone peak in its spectrum. We formulate alternative conditions so that enough data points fall on the facets of a cone instead of accumulating around the vertices. To find a regime of unique solvability, we make use of both geometric and density properties of the data points, and develop an efficient facet identification method by combining data classification and linear regression. For noisy data, we show that denoising methods may be employed, such as the total variation technique in imaging processing, and principle component analysis. We show computational results on nuclear magnetic resonance spectroscopic data to substantiate our method.
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