论文标题
事实证明，线性二次近距离混合物的盲目盲源分离
Provably robust blind source separation of linear-quadratic near-separable mixtures
论文作者
论文摘要
在这项工作中，我们通过偏离通常的线性模型并专注于线性季度（LQ）模型来考虑盲源分离（BSS）的问题。我们提出了两种可被证明可靠且在计算上可进行的算法，以在可分离性假设下解决此问题，这些假设需要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SNPA方案的迭代局固有的产品项明确建模，可以减轻混合的非线性贡献，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，即使在存在噪声的情况下也是如此。第二算法是一种蛮力（BF）算法，该算法用作SNPALQ的后处理步骤。它使得可以丢弃SNPALQ提取的虚假（混合）样品，从而扩大了其适用性。与SNPALQ相比，在更易于检查和更温和的条件下，BF对噪声表现出强大的噪声。我们表明，有和没有BF后处理的SNPALQ与现实的数值实验相关。
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.
