# Chebyshev and Conjugate Gradient Filters for Graph Image Denoising

arXiv: https://arxiv.org/abs/1509.01624 · HTML: https://mlsanity.com/paper/1509.01624/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Sep 2015.

## Built on by (most cited first, 3 of 3)

- [Graph Filters for Signal Processing and Machine Learning on Graphs](https://mlsanity.com/paper/2211.08854/) (2022)
- [Spectrally Pruned Gaussian Fields with Neural Compensation](https://mlsanity.com/paper/2405.00676/) (2024)
- [Projective Kolmogorov Arnold Neural Networks (P-KANs): Entropy-Driven Functional Space Discovery for Interpretable Machine Learning](https://mlsanity.com/paper/2509.20049/) (2025)

## Abstract (arXiv)

In 3D image/video acquisition, different views are often captured with varying noise levels across the views. In this paper, we propose a graph-based image enhancement technique that uses a higher quality view to enhance a degraded view. A depth map is utilized as auxiliary information to match the perspectives of the two views. Our method performs graph-based filtering of the noisy image by directly computing a projection of the image to be filtered onto a lower dimensional Krylov subspace of the graph Laplacian. We discuss two graph spectral denoising methods: first using Chebyshev polynomials, and second using iterations of the conjugate gradient algorithm. Our framework generalizes previously known polynomial graph filters, and we demonstrate through numerical simulations that our proposed technique produces subjectively cleaner images with about 1-3 dB improvement in PSNR over existing polynomial graph filters.