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Provably robust blind source separation of linear-quadratic near-separable mixtures
arXiv - CS - Numerical Analysis Pub Date : 2020-11-24 , DOI: arxiv-2011.11966
Christophe Kervazo, Nicolas Gillis, Nicolas Dobigeon

In this work, we consider the problem of blind source separation (BSS) by departing from the usual linear model and focusing on the linear-quadratic (LQ) model. We propose two provably robust and computationally tractable algorithms to tackle this problem under separability assumptions which require the sources to appear as samples in the data set. The first algorithm generalizes the successive nonnegative projection algorithm (SNPA), designed for linear BSS, and is referred to as SNPALQ. By explicitly modeling the product terms inherent to the LQ model along the iterations of the SNPA scheme, the nonlinear contributions of the mixing are mitigated, thus improving the separation quality. SNPALQ is shown to be able to recover the ground truth factors that generated the data, even in the presence of noise. The second algorithm is a brute-force (BF) algorithm, which is used as a post-processing step for SNPALQ. It enables to discard the spurious (mixed) samples extracted by SNPALQ, thus broadening its applicability. The BF is in turn shown to be robust to noise under easier-to-check and milder conditions than SNPALQ. We show that SNPALQ with and without the BF postprocessing is relevant in realistic numerical experiments.

中文翻译:

线性-二次近可分离混合物的可靠的盲源分离

在这项工作中,我们通过偏离通常的线性模型并关注线性二次(LQ)模型来考虑盲源分离(BSS)问题。我们提出了两种可证明的鲁棒性和计算易处理性的算法,以在可分离性假设下解决此问题,这要求源在数据集中显示为样本。第一种算法概括了为线性BSS设计的连续非负投影算法(SNPA),被称为SNPALQ。通过沿着SNPA方案的迭代对LQ模型固有的乘积项进行显式建模,可以减轻混合的非线性影响,从而提高分离质量。SNPALQ被证明能够恢复产生数据的地面真实因素,即使存在噪声也是如此。第二种算法是蛮力(BF)算法,用作SNPALQ的后处理步骤。它可以丢弃SNPALQ提取的虚假(混合)样本,从而扩展了其适用性。与SNPALQ相比,BF在更易于检查和更温和的条件下表现出对噪声的鲁棒性。我们表明,有和没有BF后处理的SNPALQ在现实的数值实验中都是相关的。
更新日期:2020-11-25
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