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Linear Attention Based Deep Nonlocal Means Filtering for Multiplicative Noise Removal

Xiao Siyao, Huang Libing, Zhang Shunsheng

TL;DR

The paper tackles multiplicative speckle noise in imaging by proposing LDNLM, a linear-time, deep nonlocal means denoising method that replaces traditional similarity computations with kernelized linear attention. A CNN-based neighborhood extractor maps local patches to high-dimensional representations, from which Query, Key, and Value vectors are derived to compute attention-weighted averages, with a kernel map φ enabling $O(n)$ complexity. The approach preserves interpretability by maintaining the nonlocal denoising structure while providing visualizable representations and ablation-based insights. Experiments on simulated gamma-noise data and real SAR imagery demonstrate competitive performance against state-of-the-art methods, along with faster inference and reduced memory usage, making it practical for remote sensing and medical imaging applications.

Abstract

Multiplicative noise widely exists in radar images, medical images and other important fields' images. Compared to normal noises, multiplicative noise has a generally stronger effect on the visual expression of images. Aiming at the denoising problem of multiplicative noise, we linearize the nonlocal means algorithm with deep learning and propose a linear attention mechanism based deep nonlocal means filtering (LDNLM). Starting from the traditional nonlocal means filtering, we employ deep channel convolution neural networks to extract the information of the neighborhood matrix and obtain representation vectors of every pixel. Then we replace the similarity calculation and weighted averaging processes with the inner operations of the attention mechanism. To reduce the computational overhead, through the formula of similarity calculation and weighted averaging, we derive a nonlocal filter with linear complexity. Experiments on both simulated and real multiplicative noise demonstrate that the LDNLM is more competitive compared with the state-of-the-art methods. Additionally, we prove that the LDNLM possesses interpretability close to traditional NLM.

Linear Attention Based Deep Nonlocal Means Filtering for Multiplicative Noise Removal

TL;DR

The paper tackles multiplicative speckle noise in imaging by proposing LDNLM, a linear-time, deep nonlocal means denoising method that replaces traditional similarity computations with kernelized linear attention. A CNN-based neighborhood extractor maps local patches to high-dimensional representations, from which Query, Key, and Value vectors are derived to compute attention-weighted averages, with a kernel map φ enabling complexity. The approach preserves interpretability by maintaining the nonlocal denoising structure while providing visualizable representations and ablation-based insights. Experiments on simulated gamma-noise data and real SAR imagery demonstrate competitive performance against state-of-the-art methods, along with faster inference and reduced memory usage, making it practical for remote sensing and medical imaging applications.

Abstract

Multiplicative noise widely exists in radar images, medical images and other important fields' images. Compared to normal noises, multiplicative noise has a generally stronger effect on the visual expression of images. Aiming at the denoising problem of multiplicative noise, we linearize the nonlocal means algorithm with deep learning and propose a linear attention mechanism based deep nonlocal means filtering (LDNLM). Starting from the traditional nonlocal means filtering, we employ deep channel convolution neural networks to extract the information of the neighborhood matrix and obtain representation vectors of every pixel. Then we replace the similarity calculation and weighted averaging processes with the inner operations of the attention mechanism. To reduce the computational overhead, through the formula of similarity calculation and weighted averaging, we derive a nonlocal filter with linear complexity. Experiments on both simulated and real multiplicative noise demonstrate that the LDNLM is more competitive compared with the state-of-the-art methods. Additionally, we prove that the LDNLM possesses interpretability close to traditional NLM.
Paper Structure (13 sections, 19 equations, 8 figures, 3 tables)

This paper contains 13 sections, 19 equations, 8 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Nonlocal Denoising
  4. Interpretability
  5. Method
  6. Deep Nonlocal Means Filtering
  7. Linear Attention Based Deep Nonlocal Means Filtering
  8. Experiments
  9. On Simulation Images
  10. On Real SAR Images
  11. Ablation Study
  12. The Interpretability of LDNLM
  13. Conclusion

Figures (8)

  • Figure 1: The basic framework of LDNLM. The whole framework contains three parts: CNN based pixel information extraction, Similarity calculation & Weighted averaging and Post-processing.
  • Figure 2: Performance of each model on example simulated images containing multiplicative noise. From left to right: Noisy, Reference, NLM, BM3D, SAR-CNN, MONet, SAR-CAM and LDNLM. From top to bottom: dense residential and parking lot.
  • Figure 3: Performance of each model on real SAR images: TerraSAR-Mountain. From left (top) to right (bottom): Noisy, NLM, BM3D, SAR-CNN, MONet, SAR-CAM, CNN-NLM and LDNLM.
  • Figure 4: Performance of each model on real SAR images: TerraSAR-Urban. From left (top) to right (bottom): Noisy, NLM, BM3D, SAR-CNN, MONet, SAR-CAM, CNN-NLM and LDNLM.
  • Figure 5: Performance of each model on real SAR images: The patch indicated by the red boxes in \ref{['real_urban']}. From left (top) to right (bottom): Noisy, NLM, BM3D, SAR-CNN, MONet, SAR-CAM, CNN-NLM and LDNLM.
  • ...and 3 more figures