Wide-Sense Stationarity and Spectral Estimation for Generalized Graph Signal

Abstract

We consider a probabilistic model for graph signal processing (GSP) in a generalized framework where each vertex of a graph is associated with an element from a Hilbert space. We introduce the notion of joint wide-sense stationarity in this generalized GSP (GGSP) framework, which allows us to characterize a random graph process as a combination of uncorrelated oscillation modes across both the vertex and Hilbert space domains. We also propose a method for joint power spectral density estimation in case of missing features. Experiment results corroborate the effectiveness of our estimation approach.

Quantum entangled fractional Fourier transform based on the IWOP technique

“…The HGFT combines the FT in Hilbert space and the GFT in the vertex domain, aiming to reduce signals in infinite continuous domains to form more manageable finite domains. Methods such as filtering [24]- [28], sampling [29]- [31] and estimation [32] can be included in this framework, which can be categorized based on three scenarios:…”