Chebyshev and Conjugate Gradient Filters for Graph Image Denoising
This work addresses image denoising for 3D acquisition, offering incremental improvements in graph filtering techniques.
The paper tackles the problem of enhancing noisy 3D image views by using a higher-quality view and depth information, proposing graph-based filtering methods that achieve about 1-3 dB PSNR improvement over existing polynomial graph filters.
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.