椒盐噪声去噪方案（滤波器）

1）EWmF（2022）：Exponentially Weighted Mean Filter，指数加权均值滤波器

参考文献：Enginoğlu S, Erkan U, Memiş S. Exponentially Weighted Mean Filter for Salt-and-Pepper Noise Removal[C]//International Conference on Artificial Intelligence and Big Data in Digital Era. Springer, Cham, 2022: 435-446.

源代码：https://github.com/serdarenginoglu/EWmF

摘要：This paper defines an exponentially weighted mean using an exponentially decreasing sequence of simple fractions based on distance. It then proposes a cutting-edge salt-and-pepper noise (SPN) removal filter—i.e., Exponentially Weighted Mean Filter (EWmF). The proposed method incorporates a pre-processing step that detects noisy pixels and calculates threshold values based on the possible noise density. Moreover, to denoise the images operationalizing the calculated threshold values, EWmF employs the exponentially weighted mean (ewmean) in 1-approximate Von Neumann neighbourhoods for low noise densities and k-approximate Moore neighbourhoods for middle or high noise densities. Furthermore, it ultimately removes the residual SPN in the processed images by relying on their SPN densities. The numerical and visual results obtained with MATLAB R2021a manifest that EWmF outperforms nine state-of-the-art SPN filters.

本文利用基于距离的简单分数的指数递减序列定义了指数加权平均值。然后，它提出了一个尖端的盐和胡椒噪声（SPN）去除过滤器--即指数加权平均值过滤器（EWmF）。所提出的方法包含了一个预处理步骤，即检测噪声像素并根据可能的噪声密度计算出阈值。此外，为了将计算出的阈值用于图像去噪，EWmF在1个近似的冯-诺伊曼邻域中采用指数加权平均值（ewmean）来处理低噪声密度，在k个近似的摩尔邻域中处理中等或高噪声密度。此外，它通过依靠SPN密度最终消除了处理后图像中的残留SPN。用MATLAB R2021a得到的数值和视觉结果表明，EWmF优于九个最先进的SPN滤波器。

2）IBLF（2022）：Intensity Bound Limit Filter，强度边界限制滤波器

参考文献：Satti P, Shrotriya V, Garg B, et al. Intensity bound limit filter for high density impulse noise removal[J]. Journal of Ambient Intelligence and Humanized Computing, 2022: 1-23.

源代码：https://github.com/piyushsatti/NERD/blob/main/IBLF.m

摘要：Digital images captured by electronic products are highly susceptible to salt & pepper noise during image acquisition, enrolment, preparation, and transmission phases. Therefore, it is essential to utilize superior image restoration methods to mitigate these effects. Additionally, in the restoration process, the preservation of edge data is essential as overall image quality can be severely degraded if the edge restoration processes underperform. In this paper, a novel two-stage intensity bound limit filter is proposed in which the denoised image is obtained via first stage generation of Intensity bound limit images and second stage recombination of the generated bound images. An interesting point to note is that the bound images preserve vital image edge data by extracting the infimum and supremum pixel values for any locality in the image. These separated bound images are subsequently utilized in a recombination stage to obtain the filtered image. Using this method, significant improvements in the boundary estimation are achieved especially in higher noise densities. Qualitative and quantitative analyses have been performed for standard, medical, and the Kodak image dataset which contains multiple colored images. Results show that the proposed algorithm outperforms state-of-the-art filters in terms of image detail restoration and overall noise removal. With respect to peak signal to noise ratio, an average improvement of 0.76 dB for standard images, 0.9 dB for medical images, and 1.03 db for Kodak dataset has been observed. A high-level hardware architecture has also been provided for the same.

由电子产品捕获的数字图像在图像采集、注册、准备和传输阶段极易受到盐和胡椒噪声的影响。因此，利用优秀的图像修复方法来减轻这些影响是至关重要的。此外，在修复过程中，保留边缘数据是至关重要的，因为如果边缘修复过程表现不佳，整体图像质量会严重下降。本文提出了一种新型的两阶段强度界限滤波器，其中去噪图像是通过第一阶段生成强度界限图像和第二阶段重组生成的界限图像获得的。值得注意的一点是，边界图像通过提取图像中任何位置的下限和上限的像素值来保留重要的图像边缘数据。这些分离的边界图像随后被用于重新组合阶段，以获得过滤后的图像。使用这种方法，边界估计得到了明显的改善，特别是在较高的噪声密度下。对标准、医疗和包含多个彩色图像的柯达图像数据集进行了定性和定量的分析。结果表明，所提出的算法在图像细节恢复和整体噪音去除方面优于最先进的过滤器。在峰值信噪比方面，观察到标准图像的平均改进为0.76分贝，医疗图像为0.9分贝，而柯达数据集为1.03分贝。同时还提供了一个高水平的硬件架构。

3）DAMRmF（2021）：Different Adaptive Modified Riesz Mean Filter，差分自适应修正Riesz均值滤波器

参考文献：Memiş S, Erkan U. Different Adaptive Modified Riesz Mean Filter For High-Density Salt-and-Pepper Noise Removal in Grayscale Images[J]. Avrupa Bilim ve Teknoloji Dergisi, 2021 (23): 359-367.

源代码：https://github.com/sametmemis/DAMRmF

摘要：This paper proposes a new filter, Different Adaptive Modified Riesz Mean Filter (DAMRmF), for high-density salt-and-pepper noise (SPN) removal. DAMRmF operationalizes a pixel weight function and adaptivity condition of Adaptive Median Filter (AMF). In the simulation, the proposed filter is compared with Adaptive Frequency Median Filter (AFMF), Three-Values-Weighted Method (TVWM), Unbiased Weighted Mean Filter (UWMF), Different Applied Median Filter (DAMF), Adaptive Weighted Mean Filter (AWMF), Adaptive Cesáro Mean Filter (ACmF), Adaptive Riesz Mean Filter (ARmF), and Improved Adaptive Weighted Mean Filter (IAWMF) for 20 traditional test images with noise levels from 60% to 90%. The results show that DAMRmF outperforms the state-of-the-art filters in terms of Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity (SSIM) values. Moreover, DAMRmF also performs better than the state-of-the-art filters concerning mean PSNR and SSIM results. We finally discuss DAMRmF for further research.

本文提出了一种新的滤波器，即不同的自适应修正里兹平均滤波器（DAMRmF），用于去除高密度的盐和胡椒噪声（SPN）。DAMRmF实现了像素权重函数和自适应中值滤波器（AMF）的自适应性条件。在模拟中，所提出的滤波器与自适应频率中值滤波器（AFMF）、三值加权法（TVWM）、无偏加权平均滤波器（UWMF）、不同应用中值滤波器（DAMF）进行了比较。自适应加权平均滤波（AWMF）、自适应切萨罗平均滤波（ACmF）、自适应里兹平均滤波（ARmF）和改进的自适应加权平均滤波（IAWMF），用于20幅噪声水平为60%至90%的传统测试图像。 结果显示，DAMRmF在峰值信噪比（PSNR）和结构相似度（SSIM）值方面优于最先进的过滤器。 此外，DAMRmF在平均PSNR和SSIM结果方面也比最先进的过滤器表现得更好。 我们最后讨论了DAMRmF的进一步研究。

4）ANN（2021）：ANN Based Removal for Salt and Pepper Noise

摘要：Salt and pepper noise (SPN) with high intensity are difficult to removal. Both spatial and deep learning-based filters are used in SPN removal. However, according to the authors' information, there is no ANN-based filter for SPN removal. In this study, we propose an ANN- based SPN filter (ANN-bF). ANN network model was created by using the attributes of the nearest pixel values to the noisy pixel to be filtered. The features of 8 noiseless pixels closest to the noisy pixel were used in the creation of the training set. There are 3 attributes for each pixel. These are 1- the noise-free pixel value, 2- the distance in the x direction, 3- the distance in the y direction. A total of 24 attributes are used in the network input. The network output is the value of the noisy pixel before the noise is added (original value). The proposed method has been compared with Adaptive Riesz Mean Filter (ARmF), Different Adaptive Modified Riesz Mean Filter (DAMRmF), Adaptive Cesáro Mean Filter (ACmF), Improved Adaptive Weighted Mean Filter (IAWMF), Iterative Mean Filter (IMF). Comparison using Peak Signal-to-Noise Ratio (PSNR), Structural Similarity Index Map (SSIM), Image Enhancement Factor (IEF) quality metrics has been made. The ANN structure created gave better results than the state-of-the-art methods in removing SPN.

高强度的盐和胡椒噪声（SPN）很难去除。基于空间和深度学习的滤波器都被用于去除SPN。然而，根据作者的资料，目前还没有基于ANN的滤波器用于去除SPN。在这项研究中，我们提出了一个基于ANN的SPN滤波器（ANN-bF）。ANN网络模型是通过使用与要过滤的噪声像素最近的像素值的属性来创建的。最接近噪声像素的8个无噪声像素的特征被用于创建训练集。每个像素有3个属性。这些属性是：1-无噪音像素值；2-X方向的距离；3-Y方向的距离。总共有24个属性被用于网络输入。网络输出是加入噪声前的噪声像素值（原始值）。所提出的方法已经与自适应雷兹平均滤波（ARmF）、不同的自适应修正雷兹平均滤波（DAMRmF）、自适应切萨罗平均滤波（ACmF）、改进的自适应加权平均滤波（IAWMF）、迭代平均滤波（IMF）进行了比较。 使用峰值信噪比（PSNR）、结构相似度指数图（SSIM）、图像增强因子（IEF）等质量指标进行了比较。 创建的ANN结构在去除SPN方面比最先进的方法效果更好。

5）MMAPF（2020）：Min–Max Average Pooling Filter，最小—最大均值池化滤波器

参考文献：Satti P, Sharma N, Garg B. Min-max average pooling based filter for impulse noise removal[J]. IEEE Signal Processing Letters, 2020, 27: 1475-1479.

源代码：https://github.com/piyushsatti/NERD/blob/main/MMAPF.m

摘要：Image corruption is a common phenomenon which occurs due to electromagnetic interference, and electric signal instabilities in a system. In this letter, a novel multi procedure Min-Max Average Pooling based Filter is proposed for removal of salt, and pepper noise that betide during transmission. The first procedure functions as a pre-processing step that activates for images with low noise corruption. In latter procedure, the noisy image is divided into two instances, and passed through multiple layers of max, and min pooling which allow restoration of intensity transitions in an image. The final procedure recombines the parallel processed images from the previous procedures, and performs average pooling to remove all residual noise. Experimental results were obtained using MATLAB software, and show that the proposed filter significantly improves edges over exiting literature. Moreover, Peak Signal to Noise Ratio was improved by 1.2 dB in de-noising of medical images corrupted by medium to high noise densities.

摘要：图像损坏是一种常见的现象，由于电磁干扰和系统中的电信号不稳定而发生。在这封信中，我们提出了一种新型的基于最小-最大平均池的多程序过滤器，用于去除传输过程中出现的盐和胡椒噪声。第一个程序作为预处理步骤，对低噪音的图像进行激活。在后一程序中，噪声图像被分为两个实例，并通过多层最大和最小池，允许恢复图像中的强度转换。最后的程序是重新组合前面程序中的平行处理的图像，并执行平均池化以消除所有的残余噪声。实验结果是用MATLAB软件获得的，并表明所提出的过滤器比现有的文献明显改善了边缘。此外，在对被中高噪声密度破坏的医学图像进行去噪时，峰值信噪比提高了1.2dB。

6）AFMF（2020）：Adaptive Frequency Median Filter，自适应频率中值滤波器

参考文献：Erkan U, Enginoğlu S, Thanh D N H, et al. Adaptive frequency median filter for the salt and pepper denoising problem[J]. IET Image Processing, 2020, 14(7): 1291-1302.

源代码：https://www.mathworks.com/matlabcentral/fileexchange/76784-afmf-for-salt-and-pepper-noise-removal

摘要：In this article, we propose an Adaptive Frequency Median Filter (AFMF) to remove the salt and pepper noise (SPN). AFMF uses the same adaptive condition of Adaptive Median Filter (AMF). However, AFMF employs frequency median to restore grey values of the corrupted pixels instead of the median of AMF. The frequency median can exclude noisy pixels from evaluating a grey value of the centre pixel of the considered window, and it focuses on the uniqueness of grey values. Hence, the frequency median produces a grey value closer to the original grey value than the one by the median of AMF. Therefore, AFMF outperforms AMF. In experiments, we tested the proposed method on a variety of natural images of the MATLAB library, as well as the TESTIMAGES dataset. Additionally, we also compared the denoising results of AFMF to the ones of other state-of-the-art denoising methods. The results showed that AFMF denoises more effectively than the other methods.

在这篇文章中，我们提出了一个自适应频率中值滤波器（AFMF）来去除盐和胡椒噪声（SPN）。AFMF使用了自适应中值滤波器（AMF）的相同自适应条件。然而，AFMF采用频率中值来恢复受损像素的灰度值，而不是AMF的中值。频率中值可以在评估所考虑的窗口的中心像素的灰度值时排除嘈杂的像素，而且它注重灰度值的唯一性。因此，频率中值产生的灰度值比AMF的中值更接近原始灰度值。因此，AFMF优于AMF。在实验中，我们在MATLAB库中的各种自然图像以及TESTIMAGES数据集上测试了提议的方法。此外，我们还将AFMF的去噪结果与其他最先进的去噪方法的结果进行了比较。结果表明，AFMF的去噪效果比其他方法更有效。

7）ACmF（2020）：Adaptive Cesáro mean Filter，自适应的cesáro均值滤波器

参考文献：Enginoğlu S, Erkan U, Memiş S. Adaptive cesáro mean filter for salt-and-pepper noise removal[J]. El-Cezeri, 2020, 7(1): 304-314.

源代码：https://github.com/sametmemis/ACmF/tree/279bbb0bf6823e88468fdab60fec99524e58920e

摘要：In this study, we propound a salt-and-pepper noise (SPN) removal method, i.e. Adaptive Cesáro Mean Filter (ACmF), and provide some of its basic notions. We then apply ACmF to several test images whose noise densities range from 10% to 90%: 15 traditional test images (Baboon, Boat, Bridge, Cameraman, Elaine, Flintstones, Hill, House, Lake, Lena, Living Room, Parrot, Peppers, Pirate, and Plane) and 40 test images, provided in the TESTIMAGES Database. Afterwards, we compare ACmF with the state-of-art methods, such as Adaptive Weighted Mean Filter (AWMF), Different Applied Median Filter (DAMF), and Noise Adaptive Fuzzy Switching Median Filter (NAFSMF). The results by The Peak Signal to Noise Ratio (PSNR) and Structural Similarity (SSIM) show that ACmF performs better than the methods mentioned above. Moreover, we also compare the running time data of these algorithms. These results show that ACmF outperforms the methods except for DAMF. We finally discuss the need for further research.

在这项研究中，我们提出了一种去除盐和胡椒噪声（SPN）的方法，即自适应切萨罗平均滤波器（ACmF），并提供了它的一些基本概念。然后，我们将ACmF应用于噪声密度在10%到90%之间的几张测试图像。15张传统测试图像（狒狒、船、桥、摄影师、Elaine、打火石、山、房子、湖、Lena、客厅、鹦鹉、辣椒、海盗和飞机）和40张测试图像，提供在TESTIMAGES数据库。之后，我们将ACmF与自适应加权平均滤波（AWMF）、不同应用中值滤波（DAMF）和噪声自适应模糊切换中值滤波（NAFSMF）等最先进的方法进行比较。峰值信噪比（PSNR）和结构相似度（SSIM）的结果表明，ACmF比上述方法表现得更好。此外，我们还比较了这些算法的运行时间数据。这些结果表明，除DAMF外，ACmF的表现优于其他方法。最后我们讨论了进一步研究的必要性。

8）IAWMF（2020）：Improved Adaptive Weighted Mean Filter，改进的自适应加权中值滤波器

参考文献：Erkan U, Thanh D N H, Enginoğlu S, et al. Improved adaptive weighted mean filter for salt-and-pepper noise removal[C]//2020 International Conference on Electrical, Communication, and Computer Engineering (ICECCE). IEEE, 2020: 1-5.

源代码：https://www.mathworks.com/matlabcentral/fileexchange/79724-iawmf-for-salt-and-pepper-noise-removal

摘要：Abstract:In this study, we propose an improved adaptive weighted mean filter (IAWMF) to remove salt-and-pepper noise. The most prominent advantage of IAWMF is its ability to take into account the weights of noise-free pixels in the adaptive window. Hence, the new grey value occurs closer to the original grey value of the centre pixel than the grey value computed by the adaptive weighted mean filter (AWMF). Moreover, the proposed method utilises the advantage of AWMF to reduce the error of detecting noisy pixels. In the experiments, we compare the denoising results of the proposed method with other state-of-the-art image denoising methods. The results confirm that IAWMF outperforms other methods.

摘要:在这项研究中，我们提出了一种改进的自适应加权平均滤波器（IAWMF）来去除盐和胡椒的噪声。IAWMF最突出的优点是它能够考虑到自适应窗口中无噪声像素的权重。因此，新的灰度值比自适应加权平均滤波器（AWMF）计算的灰度值更接近中心像素的原始灰度值。此外，所提出的方法利用了AWMF的优势来减少检测噪声像素的误差。在实验中，我们将所提方法的去噪结果与其他最先进的图像去噪方法进行比较。结果证实，IAWMF优于其他方法。

9）IMF（2019）：Iterative Mean Filter，迭代中值滤波器

参考文献：Thanh D N H, Engínoğlu S. An iterative mean filter for image denoising[J]. IEEE Access, 2019, 7: 167847-167859.

源代码：https://github.com/uerkan80/IMF

摘要：We propose an Iterative Mean Filter (IMF) to eliminate the salt-and-pepper noise. IMF uses the mean of gray values of noise-free pixels in a fixed-size window. Unlike other nonlinear filters, IMF does not enlarge the window size. A large size reduces the accuracy of noise removal. Therefore, IMF only uses a window with a size of 3×3 . This feature is helpful for IMF to be able to more precisely evaluate a new gray value for the center pixel. To process high-density noise effectively, we propose an iterative procedure for IMF. In the experiments, we operationalize Peak Signal-to-Noise Ratio (PSNR), Visual Information Fidelity, Image Enhancement Factor, Structural Similarity (SSIM), and Multiscale Structure Similarity to assess image quality. Furthermore, we compare denoising results of IMF with ones of the other state-of-the-art methods. A comprehensive comparison of execution time is also provided. The qualitative results by PSNR and SSIM showed that IMF outperforms the other methods such as Based-on Pixel Density Filter (BPDF), Decision-Based Algorithm (DBA), Modified Decision-Based Untrimmed Median Filter (MDBUTMF), Noise Adaptive Fuzzy Switching Median Filter (NAFSMF), Adaptive Weighted Mean Filter (AWMF), Different Applied Median Filter (DAMF), Adaptive Type-2 Fuzzy Filter (FDS): for the IMAGESTEST dataset - BPDF (25.36/0.756), DBA (28.72/0.8426), MDBUTMF (25.93/0.8426), NAFSMF (29.32/0.8735), AWMF (32.25/0.9177), DAMF (31.65/0.9154), FDS (27.98/0.8338), and IMF (33.67/0.9252); and for the BSDS dataset - BPDF (24.95/0.7469), DBA (26.84/0.8061), MDBUTMF (26.25/0.7732), NAFSMF (27.26/0.8191), AWMF (28.89/0.8672), DAMF (29.11/0.8667), FDS (26.85/0.8095), and IMF (30.04/0.8753).

我们提出了一个迭代平均滤波器（IMF）来消除盐和胡椒的噪声。IMF使用一个固定大小的窗口中无噪声像素的灰度值的平均值。与其他非线性滤波器不同，IMF不扩大窗口的大小。大的尺寸会降低去除噪声的准确性。因此，IMF只使用大小为3×3的窗口。这一特点有助于IMF能够更精确地评估中心像素的新灰度值。为了有效地处理高密度的噪声，我们为IMF提出了一个迭代程序。在实验中，我们将峰值信噪比（PSNR）、视觉信息保真度、图像增强因子、结构相似度（SSIM）和多尺度结构相似度作为操作指标，以评估图像质量。此外，我们将IMF的去噪结果与其他最先进的方法进行比较。还提供了执行时间的综合比较。PSNR和SSIM的定性结果显示，IMF优于其他方法，如基于像素密度滤波器（BPDF）、基于决策的算法（DBA）、修正的基于决策的非修剪中值滤波器（MDBUTMF）、噪声自适应模糊切换中值滤波器（NAFSMF）、自适应加权平均值滤波器（AWMF）、不同应用中值滤波器（DAMF）、自适应2型模糊滤波器（FDS）。对于IMAGESTEST数据集--BPDF（25. 36/0.756）、DBA（28.72/0.8426）、MDBUTMF（25.93/0.8426）、NAFSMF（29.32/0.8735）、AWMF（32.25/0.9177）、DAMF（31.65/0.9154）、FDS（27.98/0.8338）和IMF（33.67/0.9252）；而对于BSDS数据集-BPDF（24. 95/0.7469），DBA（26.84/0.8061），MDBUTMF（26.25/0.7732），NAFSMF（27.26/0.8191），AWMF（28.89/0.8672），DAMF（29.11/0.8667），FDS（26.85/0.8095），和IMF（30.04/0.8753）。

10）ARmF（2019）：Adaptive Riesz Mean Filter，自适应Riesz均值滤波器

参考文献：Enginoğlu S, Erkan U, Memiş S. Pixel similarity-based adaptive Riesz mean filter for salt-and-pepper noise removal[J]. Multimedia Tools and Applications, 2019, 78(24): 35401-35418.

源代码：https://github.com/serdarenginoglu/ARmF

摘要：In this study, we propose a new method, i.e. Adaptive Riesz Mean Filter (ARmF), by operationalizing pixel similarity for salt-and-pepper noise (SPN) removal. Afterwards, we compare the results of ARmF, A New Adaptive Weighted Mean Filter (AWMF), Different Applied Median Filter (DAMF), Noise Adaptive Fuzzy Switching Median Filter (NAFSMF), Based on Pixel Density Filter (BPDF), Modified Decision-Based Unsymmetric Trimmed Median Filter (MDBUTMF) and Decision-Based Algorithm (DBA) by using Peak Signal-to-Noise Ratio (PSNR), Structural Similarity (SSIM), Image Enhancement Factor (IEF), and Visual Information Fidelity (VIF) for 20 traditional test images (Lena, Cameraman, Barbara, Baboon, Peppers, Living Room, Lake, Plane, Hill, Pirate, Boat, House, Bridge, Elaine, Flintstones, Flower, Parrot, Dark-Haired Woman, Blonde Woman, and Einstein), 40 test images in the TESTIMAGES Database, and 200 RGB test images from the UC Berkeley Dataset ranging in noise density from 10% to 90%. Moreover, we compare the running time of these algorithms. These results show that ARmF outperforms the methods mentioned above. We finally discuss the need for further research.

在这项研究中，我们提出了一种新的方法，即自适应Riesz平均滤波（ARmF），通过操作像素的相似性来去除盐和胡椒的噪声（SPN）。之后，我们通过使用峰值信噪比（PSNR）、结构相似度（SSIM）来比较ARmF、新的自适应加权中值过滤器（AWMF）、不同应用中值过滤器（DAMF）、噪声自适应模糊开关中值过滤器（NAFSMF）、基于像素密度过滤器（BPDF）、修正的基于决策的不对称修剪中值过滤器（MDBUTMF）和基于决策的算法（DBA）的结果。图像增强因子（IEF）和视觉信息保真度（VIF），适用于20张传统测试图像（Lena, Cameraman, Barbara, Baboon, Peppers, Living Room, Lake, Plane, Hill, Pirate, Boat, House, Bridge, Elaine, Flintstones, Flower, Parrot, Dark-Hairred Woman, Blonde Woman, and Einstein）、TESTIMAGES数据库的40张测试图像和UC Berkeley数据集的200张RGB测试图像，噪声密度从10%到90%不等。此外，我们还比较了这些算法的运行时间。这些结果表明，ARmF优于上述方法。最后我们讨论了进一步研究的必要性。