# Efficient and Robust Remote Sensing Image Denoising Using Randomized Approximation of Geodesics' Gramian on the Manifold Underlying the Patch Space

arXiv: https://arxiv.org/abs/2504.10820 · HTML: https://mlsanity.com/paper/2504.10820/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 31 references that are in the map.
- First posted on arXiv 15 Apr 2025.

## Builds on (most cited first, 8 of 8)

- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [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)
- [Geodesic Gramian Denoising Applied to the Images Contaminated With Noise Sampled From Diverse Probability Distributions](https://mlsanity.com/paper/2203.02600/) (2022)

## Abstract (arXiv)

Remote sensing images are widely utilized in many disciplines such as feature recognition and scene semantic segmentation. However, due to environmental factors and the issues of the imaging system, the image quality is often degraded which may impair subsequent visual tasks. Even though denoising remote sensing images plays an essential role before applications, the current denoising algorithms fail to attain optimum performance since these images possess complex features in the texture. Denoising frameworks based on artificial neural networks have shown better performance; however, they require exhaustive training with heterogeneous samples that extensively consume resources like power, memory, computation, and latency. Thus, here we present a computationally efficient and robust remote sensing image denoising method that doesn't require additional training samples. This method partitions patches of a remote-sensing image in which a low-rank manifold, representing the noise-free version of the image, underlies the patch space. An efficient and robust approach to revealing this manifold is a randomized approximation of the singular value spectrum of the geodesics' Gramian matrix of the patch space. The method asserts a unique emphasis on each color channel during denoising so the three denoised channels are merged to produce the final image.