Optimal Wiener-Filter Solutions for Denoising of Graph Signals on Directed Graphs

2026-06-05

AI Summary

This work addresses the challenge of denoising signals defined on directed graphs, overcoming the limitation of conventional approaches that are restricted to undirected graphs. It extends Wiener filtering theory to the directed graph setting for the first time, deriving optimal denoising solutions under both correlated and uncorrelated noise assumptions based on distinct notions of graph stationarity. The proposed framework integrates concepts from graph signal processing, classical Wiener filtering, and models of stationarity tailored to directed graphs. Experimental results on real-world temperature graph data demonstrate the effectiveness of the method, achieving significantly improved denoising performance for directed graph signals. This study thus establishes both a theoretical foundation and a practical toolset for signal processing on directed graphs.

Abstract

Graph signal processing has opened new avenues to the canonical denoising problem in interesting settings. Specifically, here we propose a Wiener-filter solution for graph signals on directed graphs. Under various stationarity assumptions combining uncorrelated and correlated noise conditions, we show optimal solutions, including a successful proof-of-concept for temperature graph.

Problem

• graph signal denoising
• directed graphs
• Wiener filter
• stationarity
• noise

Innovation

• Wiener filter
• graph signal denoising
• directed graphs
• stationarity
• graph signal processing