Graph Signal Processing with Applications to Network Topology Inference

Advancing a holistic theory of networks necessitates fundamental breakthroughs in modeling, identification, and controllability of distributed network processes – often conceptualized as signals defined on the vertices of a graph. Under the assumption that the signal properties are related to the topology of the graph where they are supported, the goal of graph signal processing (GSP) is to develop algorithms that fruitfully leverage this relational structure. 

After presenting the fundamentals of GSP we then address the problem of network topology inference from graph signal observations. It is assumed that the unknown graph encodes direct relationships between signal elements, which we aim to recover from observable indirect relationships generated by a diffusion process on the graph. Leveraging results from GSP and sparse recovery, efficient topology inference algorithms with theoretical guarantees are developed.