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Joint Independent Subspace Analysis Using Second-Order Statistics

机译:使用二阶统计量的联合独立子空间分析

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This paper deals with a novel generalization of classical blind source separation (BSS) in two directions. First, relaxing the constraint that the latent sources must be statistically independent. This generalization is well-known and sometimes termed independent subspace analysis (ISA). Second, jointly analyzing several ISA problems, where the link is due to statistical dependence among corresponding sources in different mixtures. When the data are one-dimensional, i.e., multiple classical BSS problems, this model, known as independent vector analysis (IVA), has already been studied. In this paper, we combine IVA with ISA and term this new model joint independent subspace analysis (JISA). We provide full performance analysis of JISA, including closed-form expressions for minimal mean square error (MSE), Fisher information and Cramér–Rao lower bound, in the separation of Gaussian data. The derived MSE applies also for non-Gaussian data, when only second-order statistics are used. We generalize previously known results on IVA, including its ability to uniquely resolve instantaneous mixtures of real Gaussian stationary data, and having the same arbitrary permutation at all mixtures. Numerical experiments validate our theoretical results and show the gain with respect to two competing approaches that either use a finer block partition or a different norm.
机译:本文研究了两个方向上经典盲源分离(BSS)的新颖概括。首先,放宽潜在源必须在统计上独立的约束。这种概括是众所周知的,有时也称为独立子空间分析(ISA)。其次,共同分析几个ISA问题,其中的链接是由于不同混合物中相应来源之间的统计依赖性所致。当数据是一维的,即多个经典BSS问题时,已经研究了称为独立矢量分析(IVA)的模型。在本文中,我们将IVA与ISA结合在一起,并称这种新模型联合独立子空间分析(JISA)。我们提供了JISA的完整性能分析,包括用于分离高斯数据的最小均方误差(MSE),Fisher信息和Cramér-Rao下界的闭式表达式。当仅使用二阶统计量时,派生的MSE也适用于非高斯数据。我们对IVA的先前已知结果进行了概括,包括其独特地解析实际高斯平稳数据的瞬时混合的能力,并且对所有混合具有相同的任意排列。数值实验验证了我们的理论结果,并显示了相对于两种竞争方法的收益,这两种方法要么使用更精细的块划分,要么使用不同的范数。

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