With the emergence of wireless sensor networks (WSNs), many traditional signal processing tasks are required to be computed in a distributed fashion, without transmissions of the raw data to a centralized processing unit, due to the limited energy and bandwidth resources available to the sensors. In this paper, we propose a distributed independent component analysis (ICA) algorithm, which aims at identifying the original signal sources based on observations of their mixtures measured at various sensor nodes. One of the most commonly used ICA algorithms is known as FastICA, which requires a spatial pre-whitening operation in the first step of the algorithm. Such a pre-whitening across all nodes of a WSN is impossible in a bandwidth-constrained distributed setting as it requires to correlate each channel with each other channel in the WSN. We show that an explicit network-wide pre-whitening step can be circumvented by leveraging the properties of the so-called Distributed Adaptive Signal Fusion (DASF) framework. Despite the lack of such a network-wide pre-whitening, we can still obtain the $Q$ least Gaussian independent components of the centralized ICA solution, where $Q$ scales linearly with the required communication load.

翻译：随着无线传感器网络（WSNs）的出现，由于传感器可用的能量和带宽资源有限，许多传统的信号处理任务需要在分布式方式下进行计算，而无需将原始数据传输到集中处理单元。本文提出了一种分布式独立成分分析（ICA）算法，其目标是根据在不同传感器节点处测量到的混合信号观测值来识别原始信号源。最常用的ICA算法之一是FastICA，该算法在其第一步需要执行空间预白化操作。在带宽受限的分布式环境中，这种跨越WSN所有节点的预白化是不可能实现的，因为它要求将网络中的每个通道与其他每个通道进行关联。我们证明，通过利用所谓的分布式自适应信号融合（DASF）框架的特性，可以规避显式的全网预白化步骤。尽管缺乏这种全网预白化，我们仍然可以获得集中式ICA解中$Q$个最不高斯（least Gaussian）的独立成分，其中$Q$与所需的通信负载呈线性比例关系。