Correlation-based Graph Smoothness Measures In Graph Signal Processing

Graph smoothness is an important prior used for designing sampling strategies for graph signals as well as for regularizing the problem of graph learning. Additionally, smoothness is an appropriate assumption for graph signal processing (GSP) tasks such as filtering or signal recovery from samples. The most popular measure of smoothness is the quadratic form of the Laplacian, which naturally follows from the factor analysis approach. This paper presents a novel smoothness measure based on the graph correlation. The proposed measure enhances the applicability of graph smoothness measures across a variety of GSP tasks, by facilitating interoperability and generalizing across shift operators.