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

TL;DR

This work tackles denoising of remote sensing images under real-world noise without relying on training data. It introduces Efficient Geodesic Gramian Denoising (EGGD), a non-local, patch-space method that leverages a low-rank manifold of geodesic distances among patches and uses randomized SVD to approximate the leading singular values of the Gramian, enabling robust noise suppression with reduced computational load. The approach operates in the YCbCr color space with channel-specific emphasis, denoising each channel via a three-step process: patch extraction, geodesic graph construction, and projection onto leading right singular vectors, followed by Shepard-based fusion. Comparative experiments against BM3D, KSVD, ADNet, and DnCNN demonstrate that EGGD achieves competitive or superior PSNR, SSIM, and information-content metrics across multiple remote sensing categories, while requiring far fewer training data and tunable parameters. This combination of algebraic, non-local, and manifold-based techniques offers a practical, scalable solution for denoising in remote-sensing workflows with robust performance across varying noise levels.

Abstract

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.

Figures (5)

• Figure 1: A red-green-blue image
• Figure 2: Remote sensing image denoising with EGGD and four other state-of-the-art denoising methods, namely, sparse 3-D transform-domain collaborative filtering (BM3D), sparse and redundant representations over learned dictionaries (KSVD), Attention-guided Denoising Convolutional Neural Network (ADNet), and Denoising Convolutional Neural Networks (DnCNN). Each of the seven test images, namely, desert, ocean, snow, volcano, watershed, city, and cargo, of size $10^3 \times 10^3$, is imposed with a relative Gaussian noise of 2%. EGGD is executed with the parameter values ($\rho, \delta, L$) = (5, 20, 80), (7, 20, 80), and (7, 20, 80) for the channels Y, Cr, and Cb, respectively. The other four methods are executed using their recommended parameter values, or tested using pre-train ANNs given in their literature. Here, we observe that EGGD retains texture and cartoon in the denoised images most of the time than that of the other four methods.
• Figure 3: Box and whisker plots of the three similarity metrics, Shannon Entropy, denoted by ShE, Peak Signal to Noise Ratio, denoted by PSNR, and Structural Similarity Index Measure, denoted by SSIM, of the experiments of remote sensing image denoising with EGGD and four other state-of-the-art denoising methods, namely, sparse 3-D transform-domain collaborative filtering (BM3D), sparse and redundant representations over learned dictionaries (KSVD), Attention-guided Denoising Convolutional Neural Network (ADNet), and Denoising Convolutional Neural Networks (DnCNN). Seven remote sensing test images each of size $10^3 \times 10^3$ are imposed with three relative Gaussian noise levels, denoted as $\zeta$, of $2\%$, $4\%$, and $6\%$ to make noisy images, denoted by $\mathcal{U}$. For $\zeta=2\%$, EGGD is implemented with the parameter values ($\rho, \delta, L$) = (5, 20, 80), (7, 20, 80), and (7, 20, 80) for the channels Y, Cr, and Cb, respectively. For $\zeta=4\%$, EGGD is implemented with the parameter values ($\rho, \delta, L$) = (7, 20, 80), (9, 20, 80), and (9, 20, 80) for the channels Y, Cr, and Cb, respectively. For $\zeta=6\%$, EGGD is implemented with the parameter values ($\rho, \delta, L$) = (9, 20, 80), (11, 20, 80), and (11, 20, 80) for the channels Y, Cr, and Cb, respectively. For a given noise level and a method, the seven denoised images, desert, ocean, snow, volcano, watershed, city, and cargo are considered to be seven trials. Thus, we compute box and whisker plots of the values of a denoising performance metric of interest (i.e., ShE, PSNR, and SSIM) over these trials. While BM3D and KSVD are implemented using the recommended parameter values mentioned in their literature, ADNet and DnCNN are implemented using pre-train ANNs given in their literature.
• Figure 4: Remote sensing image denoising with EGGD and four other state-of-the-art denoising methods, namely, sparse 3-D transform-domain collaborative filtering (BM3D), sparse and redundant representations over learned dictionaries (KSVD), Attention-guided Denoising Convolutional Neural Network (ADNet), and Denoising Convolutional Neural Networks (DnCNN). Each of the seven test images, namely, desert, ocean, snow, volcano, watershed, city, and cargo, of size $10^3 \times 10^3$, is imposed with a relative Gaussian noise of 4%. EGGD is executed with the parameter values ($\rho, \delta, L$) = (7, 20, 80), (9, 20, 80), and (9, 20, 80) for the channels Y, Cr, and Cb, respectively. The other four methods are executed with their recommended parameter values, or tested with their given trained ANNs. Here, we observe that EGGD retains texture and cartoon in the denoised images most of the time than that of the other four methods.
• Figure 5: Remote sensing image denoising with EGGD and four other state-of-the-art denoising methods, namely, sparse 3-D transform-domain collaborative filtering (BM3D), sparse and redundant representations over learned dictionaries (KSVD), Attention-guided Denoising Convolutional Neural Network (ADNet), and Denoising Convolutional Neural Networks (DnCNN). Each of the seven test images, namely, desert, ocean, snow, volcano, watershed, city, and cargo, of size $10^3\times 10^3$, is imposed with a relative Gaussian noise of 6%. EGGD is executed with the parameter values ($\rho, \delta, L$) = (9, 20, 80), (11, 20, 80), and (11, 20, 80) for the channels Y, Cr, and Cb, respectively. The other four methods are executed with their recommended parameter values, or tested with their given trained ANNs. Here, we observe that EGGD retains texture and cartoon in the denoised images most of the time than that of the other four methods.

Theorems & Definitions (5)

• Definition 2.1
• Definition 3.1
• Definition 3.2
• Definition 3.3
• Definition 3.4