Blind Multichannel Deconvolution and Convolutive Extensions of Canonical Polyadic and Block Term Decompositions
Blind Multichannel Deconvolution and Convolutive Extensions of Canonical Polyadic and Block Term Decompositions
复制标题
规范多元和块项分解的盲多通道反卷积和卷积扩展
DOI：
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发表时间：
2017
影响因子：
5.4
通讯作者：
L. D. Lathauwer
中科院分区：
文献类型：
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作者：
Mikael Sørensen;Frederik Van Eeghem;L. D. Lathauwer
典型多元分解(CPD)或块项分解(BTD)等张量分解是盲信号分离的基本工具。大多数文献涉及瞬时混合/无记忆通道。在这篇文章中，我们主要讨论卷积扩张。更准确地说，我们给出了卷积CPD/BTD模型和耦合的瞬时CPD/BTD之间的联系。我们给出了卷积低阶分解问题的一个新的可辨识性条件。我们解释说，在这种情况下，CPD/BTD的卷积扩展可以用代数方法来计算，从而保证了在无噪声情况下的完美信源分离。在不精确的情况下，该算法可以用作基于优化的方法的廉价初始化。我们解释说，与无记忆的情况相比，卷积信号分离在某些情况下是可能的，尽管只有双向差异(例如，空间$时间)。
Tensor decompositions such as the canonical polyadic decomposition (CPD) or the block term decomposition (BTD) are basic tools for blind signal separation. Most of the literature concerns instantaneous mixtures/memoryless channels. In this paper, we focus on convolutive extensions. More precisely, we present a connection between convolutive CPD/BTD models and coupled but instantaneous CPD/BTD. We derive a new identifiability condition dedicated to convolutive low-rank factorization problems. We explain that under this condition, the convolutive extension of CPD/BTD can be computed by means of an algebraic method, guaranteeing perfect source separation in the noiseless case. In the inexact case, the algorithm can be used as a cheap initialization for an optimization-based method. We explain that, in contrast to the memoryless case, convolutive signal separation is in certain cases possible despite only two-way diversities (e.g., space $ imes$ time).