LAUSR

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.