Accelerated graph-based spectral polynomial filters

TL;DR

This paper introduces accelerated graph spectral polynomial filters using Krylov subspace methods like LOBPCG to improve denoising efficiency without eigendecomposition.

Contribution

It proposes a novel approach to accelerate spectral polynomial filtering on graphs by integrating Krylov subspace solvers such as LOBPCG.

Findings

Enhanced denoising performance with reduced computational cost

Effective approximation of spectral filters without eigendecomposition

Demonstrated improvements over traditional polynomial filtering methods

Abstract

Graph-based spectral denoising is a low-pass filtering using the eigendecomposition of the graph Laplacian matrix of a noisy signal. Polynomial filtering avoids costly computation of the eigendecomposition by projections onto suitable Krylov subspaces. Polynomial filters can be based, e.g., on the bilateral and guided filters. We propose constructing accelerated polynomial filters by running flexible Krylov subspace based linear and eigenvalue solvers such as the Block Locally Optimal Preconditioned Conjugate Gradient (LOBPCG) method.