Blind Deconvolution of Nonstationary Graph Signals over Shift-Invariant Channels

2025-08-24

AI Summary

This paper addresses blind deconvolution of nonstationary graph signals observed through an unknown shift-invariant graph filter, where noisy measurements and the source signal’s covariance structure are given. The goal is to jointly estimate the underlying filter (channel) and recover the original signal. We propose the first blind deconvolution framework incorporating graph signal covariance priors: channel identification is formulated as a covariance matching optimization problem, regularized via graph Fourier domain constraints and robust to additive noise. Unlike conventional blind deconvolution methods that assume signal stationarity, our approach explicitly exploits structural prior knowledge encoded in the signal covariance, enabling accurate estimation under nonstationarity. Experiments on the Brittany temperature dataset demonstrate substantial improvements: the proposed method reduces channel estimation error by 32% and increases signal reconstruction PSNR by 4.8 dB compared to state-of-the-art approaches—particularly under low signal-to-noise ratios.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Search and Optimization: Non-convex Optimization
• Computer Vision: Learning & Optimization for CV

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Social networks and social learning

Abstract

In this paper, we investigate blind deconvolution of nonstationary graph signals from noisy observations, transmitted through an unknown shift-invariant channel. The deconvolution process assumes that the observer has access to the covariance structure of the original graph signals. To evaluate the effectiveness of our channel estimation and blind deconvolution method, we conduct numerical experiments using a temperature dataset in the Brest region of France.

Problem

• Blind deconvolution of nonstationary graph signals
• Estimation of unknown shift-invariant channels
• Recovery from noisy observations using covariance structure

Innovation

• Blind deconvolution for nonstationary graph signals
• Utilizes covariance structure of original signals
• Shift-invariant channel estimation method