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Extreme direction analysis for blind separation of nonnegative signals

机译：用于非负信号盲分离的极端方向分析

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摘要

Blind signal separation consists in processing a set of observed mixed signals in order to separate them into a set of components without any a priori knowledge about the mixing process. This paper deals with the blind separation of nonnegative signals. We show that, for such signals, the problem can be expressed as the identification of relevant extreme directions of a data defined polyhedral cone. Direction relevance is determined by means of a new criterion which integrates both sparseness and linear independence. In order to optimize this criterion with a low complexity, a sub-optimal but efficient algorithm based on linear programming is proposed. After a rigorous soundness proof, the steps of the proposed algorithm are detailed, its convergence is analyzed and its performance is evaluated via experiments involving two-dimensional signals.
机译：盲信号分离在于处理一组观察到的混合信号，以便将它们分离为一组组件，而无需任何关于混合过程的先验知识。本文涉及非负信号的盲分离。我们表明，对于此类信号，问题可以表示为数据定义的多面体圆锥体的相关极端方向的标识。方向相关性是通过新准则确定的，该准则整合了稀疏性和线性独立性。为了以较低的复杂度优化该准则，提出了一种基于线性规划的次优但有效的算法。经过严格的稳健性证明后，详细介绍了该算法的步骤，分析了其收敛性，并通过涉及二维信号的实验评估了其性能。

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