# Linear Attention Based Deep Nonlocal Means Filtering for Multiplicative Noise Removal

arXiv: https://arxiv.org/abs/2407.05087 · HTML: https://mlsanity.com/paper/2407.05087/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 45 references that are in the map.
- First posted on arXiv 6 Jul 2024.

## Builds on (most cited first, 24 of 24)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [SwinIR: Image Restoration Using Swin Transformer](https://mlsanity.com/paper/2108.10257/) (2021)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [Noise2Noise: Learning Image Restoration without Clean Data](https://mlsanity.com/paper/1803.04189/) (2018)
- [Dual Adversarial Network: Toward Real-world Noise Removal and Noise Generation](https://mlsanity.com/paper/2007.05946/) (2020)
- [Non-Local Color Image Denoising with Convolutional Neural Networks](https://mlsanity.com/paper/1611.06757/) (2016)
- [Spectral Enhanced Rectangle Transformer for Hyperspectral Image Denoising](https://mlsanity.com/paper/2304.00844/) (2023)
- [SAR image despeckling through convolutional neural networks](https://mlsanity.com/paper/1704.00275/) (2017)
- [Speckle2Void: Deep Self-Supervised SAR Despeckling with Blind-Spot Convolutional Neural Networks](https://mlsanity.com/paper/2007.02075/) (2020)
- [SAR Image Despeckling Using a Convolutional Neural Network](https://mlsanity.com/paper/1706.00552/) (2017)
- [SAR Despeckling using a Denoising Diffusion Probabilistic Model](https://mlsanity.com/paper/2206.04514/) (2022)
- [As if by magic: self-supervised training of deep despeckling networks with MERLIN](https://mlsanity.com/paper/2110.13148/) (2021)
- [Hybrid Spectral Denoising Transformer with Guided Attention](https://mlsanity.com/paper/2303.09040/) (2023)
- [Transformer-based SAR Image Despeckling](https://mlsanity.com/paper/2201.09355/) (2022)
- [Low-Dose CT Denoising via Sinogram Inner-Structure Transformer](https://mlsanity.com/paper/2204.03163/) (2022)
- [Multi-Objective CNN Based Algorithm for SAR Despeckling](https://mlsanity.com/paper/2006.09050/) (2020)
- [Unassisted Quantitative Evaluation Of Despeckling Filters](https://mlsanity.com/paper/1704.05952/) (2017)
- [OCT-GAN: Single Step Shadow and Noise Removal from Optical Coherence Tomography Images of the Human Optic Nerve Head](https://mlsanity.com/paper/2010.11698/) (2020)
- [SS-BSN: Attentive Blind-Spot Network for Self-Supervised Denoising with Nonlocal Self-Similarity](https://mlsanity.com/paper/2305.09890/) (2023)
- [DoPAMINE: Double-sided Masked CNN for Pixel Adaptive Multiplicative Noise Despeckling](https://mlsanity.com/paper/1902.02530/) (2019)

## Abstract (arXiv)

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. The source code and pre-trained model are available at https://github.com/ShowiBin/LDNLM.