On Detecting Low-pass Graph Signals under Partial Observations

TL;DR

This paper introduces a method to detect low-pass graph signals from partial observations without needing the graph topology, aiding in preprocessing and improving robustness of graph signal processing tasks.

Contribution

It proposes a novel blind detection algorithm for low-pass graph signals under partial observations, without requiring prior knowledge of the graph structure.

Findings

The detector accurately identifies low-pass signals in partial observation scenarios.

The method enhances robustness of GSP algorithms by pre-screening signals.

Sample complexity bounds are established for the detection process.

Abstract

The application of graph signal processing (GSP) on partially observed graph signals with missing nodes has gained attention recently. This is because processing data from large graphs are difficult, if not impossible due to the lack of availability of full observations. Many prior works have been developed using the assumption that the generated graph signals are smooth or low pass filtered. This paper treats a blind graph filter detection problem under this context. We propose a detector that certifies whether the partially observed graph signals are low pass filtered, without requiring the graph topology knowledge. As an example application, our detector leads to a pre-screening method to filter out non low pass signals and thus robustify the prior GSP algorithms. We also bound the sample complexity of our detector in terms of the class of filters, number of observed nodes, etc. Numerical experiments verify the efficacy of our method.