Chebyshev and Conjugate Gradient Filters for Graph Image Denoising

TL;DR

This paper introduces a graph-based image denoising method leveraging Chebyshev and conjugate gradient filters, utilizing a higher quality view and depth map for improved noise reduction in 3D images.

Contribution

It presents a novel framework combining Chebyshev and conjugate gradient graph filters for enhanced image denoising, generalizing previous polynomial graph filters.

Findings

Achieves 1-3 dB PSNR improvement over existing polynomial graph filters.

Produces subjectively cleaner images in numerical simulations.

Utilizes depth maps to match perspectives and improve denoising quality.

Abstract

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.