统计相关源信号分离模型与算法综述

Survey on statistical dependent source separation model and algorithms

统计相关源信号分离理论不仅有着广泛的应用背景,也为深入了解数据的本质结构提供了有效的分析工具.首先,重点分析和讨论一类特殊的相关源信号分离模型——独立子空间分析模型的可分离性;其次,分别介绍基于源信号稀疏性、统计测度、独立子空间分析、源信号时序结构、源信号有界性和非负性的各种相关源信号分离算法;再次,通过将加性噪声中的盲源分离和高光谱解混问题建模为统计相关源信号分离模型,表明了该方法的应用价值;最后,总结了相关源信号分离中存在的问题,并对下一步的研究思路进行了分析和展望.

The statistical dependent source separation problem is a basic and important research topic in the field of blind source separation（BSS）,because it not only has abundant potential applications,but also can gain further insights into the structure of the data.Firstly,the unified mathematical model of dependent source separation is constructed and the separability issues are discussed.Then,state-of-art algorithms to implement separation for dependent sources are surveyed from two aspects：statistical and deterministic,where the statistical method mainly includes sparsity based method,statistical measure based method,independent subspace analysis（IS A） based method and temporal structure based method.Meanwhile,the deterministic approach contains the bounded source signals based method and nonnegative source signals based method.The applications of the statistical dependent source separation problem are demonstrated by the hyperspectral unmixing problem and the BSS in the additive noise problem.Finally,some of the existing problems are listed,and the future research work is also presented.