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

arXiv: https://arxiv.org/abs/2203.02600 · HTML: https://mlsanity.com/paper/2203.02600/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 33 references that are in the map.
- First posted on arXiv 4 Mar 2022.

## Builds on (most cited first, 7 of 7)

- [A Review Paper: Noise Models in Digital Image Processing](https://mlsanity.com/paper/1505.03489/) (2015)
- [A Nonlinear Dimensionality Reduction Framework Using Smooth Geodesics](https://mlsanity.com/paper/1707.06757/) (2017)
- [Bounded Manifold Completion](https://mlsanity.com/paper/1912.09026/) (2019)
- [Identifying manifolds underlying group motion in Vicsek agents](https://mlsanity.com/paper/1508.02809/) (2015)
- [Reconstruction of Fragmented Trajectories of Collective Motion using Hadamard Deep Autoencoders](https://mlsanity.com/paper/2110.10428/) (2021)
- [Dimensionality Reduction of Collective Motion by Principal Manifolds](https://mlsanity.com/paper/1508.03332/) (2015)
- [Image Denoising Using the Geodesics' Gramian of the Manifold Underlying Patch-Space](https://mlsanity.com/paper/2010.07769/) (2020)

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

- [Efficient Image Denoising by Low-Rank Singular Vector Approximations of Geodesics' Gramian Matrix](https://mlsanity.com/paper/2209.13094/) (2022)
- [Efficient and Robust Remote Sensing Image Denoising Using Randomized Approximation of Geodesics' Gramian on the Manifold Underlying the Patch Space](https://mlsanity.com/paper/2504.10820/) (2025)

## Abstract (arXiv)

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.