# Accelerated graph-based spectral polynomial filters

arXiv: https://arxiv.org/abs/1509.02468 · HTML: https://mlsanity.com/paper/1509.02468/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Sep 2015.

## Built on by (most cited first, 2 of 2)

- [Graph Filters for Signal Processing and Machine Learning on Graphs](https://mlsanity.com/paper/2211.08854/) (2022)
- [Approximating Gaussian Whittle-Matern Fields over Well-Centered Triangulations of Riemannian Manifolds](https://mlsanity.com/paper/2606.13827/) (2026)

## Abstract (arXiv)

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.