Graph Signal Separation with Learnable Spectral Filters

TL;DR

This paper introduces an unsupervised spectral filtering method for separating multiple graph signals from a mixture, leveraging learnable filters in the low-frequency eigenspace to recover latent components.

Contribution

It proposes a novel neural spectral filtering framework that combines classical graph spectral analysis with learnable components for source separation.

Findings

Successfully isolates individual sources using only the observed mixture and graph topology.

Operates within low-frequency eigenspaces to promote smooth signal recovery.

Provides a principled approach bridging classical analysis and neural decomposition.

Abstract

Separating multiple graph signals from a single observed mixture is an inherently ill-posed problem that traditionally relies on restrictive and handcrafted priors. This letter addresses this challenge by proposing an unsupervised learnable spectral filtering framework. Our approach reconstructs latent components by passing a fixed random input through learnable spectral filters, operating within the low-frequency eigenspace of each source-specific graph Laplacian. The architecture implicitly biases the recovered signals toward smooth patterns by confining reconstruction to these low-frequency subspaces. This acts as a structural prior, establishing a principled bridge between classical graph spectral analysis and modern neural decomposition. Numerical experiments confirm that this framework successfully isolates individual sources using solely the observed mixture and the underlying graph topology.