Geodesic Gramian Denoising Applied to the Images Contaminated With Noise Sampled From Diverse Probability Distributions

TL;DR

This paper introduces a novel Gramian-based denoising method that effectively removes noise from images sampled from diverse distributions by operating on image patches and the underlying manifold, improving preservation of image features.

Contribution

The paper presents a new Gramian-based filtering scheme that denoises images contaminated with various noise distributions by leveraging patch manifolds, enhancing robustness over existing methods.

Findings

Effective noise removal across multiple distributions

Preserves image smoothness and features

Improves performance when combined with BM3D and K-SVD

Abstract

As quotidian use of sophisticated cameras surges, people in modern society are more interested in capturing fine-quality images. However, the quality of the images might be inferior to people's expectations due to the noise contamination in the images. Thus, filtering out the noise while preserving vital image features is an essential requirement. Current existing denoising methods have their own assumptions on the probability distribution in which the contaminated noise is sampled for the method to attain its expected denoising performance. In this paper, we utilize our recent Gramian-based filtering scheme to remove noise sampled from five prominent probability distributions from selected images. This method preserves image smoothness by adopting patches partitioned from the image, rather than pixels, and retains vital image features by performing denoising on the manifold underlying the patch space rather than in the image domain. We validate its denoising performance, using three benchmark computer vision test images applied to two state-of-the-art denoising methods, namely BM3D and K-SVD.