A large number of applications in decentralized signal processing includes projecting a vector of noisy observations onto a subspace dictated by prior information about the field being monitored. Accomplishing such a task in a centralized fashion in networks is prone to a number of issues such as large power consumption, congestion at certain nodes and suffers from robustness issues against possible node failures. Decentralized subspace projection is an alternative method to address those issues. Recently, it has been shown that graph filters (GFs) can be implemented to perform decentralized subspace projection. However, most of the existing methods have focused on designing GFs for symmetric topologies. However, in this article, motivated by the typical scenario of asymmetric communications in Wireless Sensor Networks, we study the optimal design of graph shift operators to perform decentralized subspace projection for asymmetric topologies. Firstly, the existence of feasible solutions (graph shift operators) to achieve an exact projection is characterized, and then an optimization problem is proposed to obtain the shift operator. We also provide an ADMM-based decentralized algorithm for the design of the shift operator. In the case where achieving an exact projection is not feasible due to the sparse connectivity, we provide an efficient solution to compute the projection matrix with high accuracy by using a set of parallel graph filters.

中文翻译：

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高效分散子空间投影的非对称移位算子设计

在分散信号处理中的大量应用包括将噪声观测的向量投影到子空间上，该子空间由关于所监视场的先验信息指示。在网络中以集中方式完成这样的任务容易产生许多问题，例如大功率消耗，某些节点处的拥塞并且遭受针对可能的节点故障的鲁棒性问题。分散子空间投影是解决这些问题的另一种方法。近来，已经显示出可以实现图形滤波器（GF）以执行分散的子空间投影。但是，大多数现有方法都集中在设计用于对称拓扑的GF。但是，在本文中，受无线传感器网络中非对称通信的典型情况的影响，我们研究图移位算子的最佳设计，以执行非对称拓扑的分散子空间投影。首先，描述了实现精确投影的可行解（图形移位算子）的存在，然后提出了一个优化问题来获得移位算子。我们还为移位运算符的设计提供了基于ADMM的分散算法。在由于稀疏连接而无法实现精确投影的情况下，我们提供了一种有效的解决方案，可通过使用一组并行图形滤波器来高精度地计算投影矩阵。然后提出了一个优化问题来获得移位算子。我们还为移位运算符的设计提供了基于ADMM的分散算法。在由于稀疏连接而无法实现精确投影的情况下，我们提供了一种有效的解决方案，可通过使用一组并行图形滤波器来高精度地计算投影矩阵。然后提出了一个优化问题来获得移位算子。我们还为移位运算符的设计提供了基于ADMM的分散算法。在由于稀疏连接而无法实现精确投影的情况下，我们提供了一种有效的解决方案，可通过使用一组并行图形滤波器来高精度地计算投影矩阵。