A new fuzzy-based decision algorithm for high-density impulse noise removal

This paper proposes a new efficient fuzzy-based decision algorithm (FBDA) for the restoration of images that are corrupted with high density of impulse noises. FBDA is a fuzzy-based switching median filter in which the filtering is applied only to corrupted pixels in the image while the uncorrupted pixels are left unchanged. The proposed algorithm computes the difference measure for each pixel based on the central pixel (corrupted pixel) in a selected window and then calculates the membership value for each pixel based on the highest difference. The algorithm then eliminates those pixels from the window with very high and very low membership values, which might represent the impulse noises. Median filter is then applied to the remaining pixels in the window to get the restored value for the current pixel position. The proposed algorithm produces excellent results compared to conventional method such as standard median filter (SMF) as well as some advanced techniques such as adaptive median filters (AMF), efficient decision-based algorithm (EDBA), improved efficient decision-based algorithm (IDBA) and boundary discriminative noise detection (BDND) switching median filter. The efficiency of the proposed algorithm is evaluated using different standard images. From experimental analysis, it has been found that FBDA produces better results in terms of both quantitative measures such as PSNR, SSIM, IEF and qualitative measures such as Image Quality Index (IQI).     

Directional switching median filter using boundary discriminative noise detection by elimination

We propose an accurate and efficient noise detection algorithm for impulse noise removal, called the boundary discriminative noise detection by elimination (BDNDE), which retains the good characteristics of the BDND filter proposed by Ng and Ma (in IEEE Trans. Image Process. 15(6):1506?C1516, 2006) while suppressing noise effectively. In order to determine whether a pixel is corrupted, the algorithm first sets the minimum and maximum boundary (threshold) values based on the localized window centered on the pixel. The thresholding helps in achieving low false-alarm and miss-detection rate (even in random noise), even up to 90% noise densities. Extensive simulation results, conducted on gray scale images under a wide range (from 10 to 90%) of noise corruption, clearly demonstrate that our enhanced switching median filter gives better results compared to existing BDND median-based filters, in terms of suppressing impulse noise while preserving image details. The proposed method is algorithmically simple and faster, compared to existing BDND, and more suitable for real-time implementation and application. The new method has shown superior performance in terms of subjective quality in the filtered image as well as objective quality in the peak signal-to-noise ratio (PSNR) measurement to that of the BDND filter.     

A new adaptive switching filter with directional impulse detection

A novel adaptive switching filter （ASF） based on directional detection is proposed for denoising the images that are highly corrupted by impulse noise. The proposed algorithm employs an efficient noise detection mechanism. It first employs an efficient method to estimate the differences between the current pixel and its neighbors aligned with 28 directions. The current noise pixel is replaced by a median or a mean value within an adaptive filter window with respect to different noise densities. Experimental results show that the proposed approach can not only achieve very low miss-detection ratio and false-alarm ratio even up to high noise corruption, but also preserve the detailed information of an image very well.     

Using Sorted Switching Median Filter to remove high-density impulse noises

We propose a novel Sorted Switching Median Filter (i.e. SSMF) for effectively denoising extremely corrupted images while preserving the image details. The center pixel is considered as “uncorrupted” or “corrupted” noise in the detecting stage. The corrupted pixels that possess more noise-free surroundings will have higher processing priority in the SSMF sorting and filtering stages to rescue the heavily noisy neighbors. Five noise models are considered to assess the performance of the proposed SSMF algorithm. Several extensive simulation results conducted on both grayscale and color images with a wide range (from 10% to 90%) of noise corruption clearly show that the proposed SSMF substantially outperforms all other existing median-based filters.     

An effective 2-stage method for removing impulse noise in images

In this paper, a robust 2-stage impulse noise removal system is proposed to remove impulse noise from extremely corrupted images. The contributions are in two-fold. First, a neuro-fuzzy based impulse noise detector (NFIDET) is introduced to identify the noisy pixels. NFIDET is a powerful noise detector that can handle image corruption even up to 90% with zero miss and false detection rate with a simple neuro-fuzzy structure. This is the best result among the other impulse noise detectors in the literature. Second, this paper presents a new approach for weight calculation of adaptive weighted mean filter by using robust statistical model. An adaptive robust weighted mean (ARWM) filter removes a detected noisy pixel by adaptively determining filtering window size and replacing a noisy pixel with the weighted mean of the noise-free pixels in its window. A Geman–McClure robust estimation function is used to estimate the weights of the pixels. Simulation results also show that the proposed robust filter substantially outperforms many other existing algorithms in terms of image restoration.     

Predictive-based adaptive switching median filter for impulse noise removal using neural network-based noise detector

A predictive-based adaptive switching median filter for impulse noise removal using neural network-based noise detector (PASMF) is presented. The PASMF has a noise detector stage and a noise filtering stage. The noise detector implemented using feed forward neural network detects impulse noises in the corrupted image. The filter is a modified median filter, which removes detected impulse noise from the image. In contrast to the standard median filter, the PASMF computes the median value after predicting the appropriate values for neighboring corrupted pixels of the current central pixel in the filtering window. The results show that the PASMF gives better performance visually as well as in terms of different performance measures.     

Noise adaptive soft-switching median filter

Existing state-of-the-art switching-based median filters are commonly found to be nonadaptive to noise density variations and prone to misclassifying pixel characteristics at high noise density interference. This reveals the critical need of having a sophisticated switching scheme and an adaptive weighted median filter. We propose a novel switching-based median filter with incorporation of fuzzy-set concept, called the noise adaptive soft-switching median (NASM) filter, to achieve much improved filtering performance in terms of effectiveness in removing impulse noise while preserving signal details and robustness in combating noise density variations. The proposed NASM filter consists of two stages. A soft-switching noise-detection scheme is developed to classify each pixel to be uncorrupted pixel, isolated impulse noise, nonisolated impulse noise or image object's edge pixel. "No filtering" (or identity filter), standard median (SM) filter or our developed fuzzy weighted median (FWM) filter will then be employed according to the respective characteristic type identified. Experimental results show that our NASM filter impressively outperforms other techniques by achieving fairly close performance to that of ideal-switching median filter across a wide range of noise densities, ranging from 10% to 70%     

Erratum to: Multi-scale directional-filtering-based method for follicular lymphoma grading

A new decision-based algorithm has been proposed for the restoration of digital images which are highly contaminated by the saturated impulse noise (i.e., salt-and-pepper noise). The proposed denoising algorithm performs filtering operation only to the corrupted pixels in the image, keeping uncorrupted pixels intact. The present study has used a coupled window scheme for the removal of high density noise. It has used sliding window of increasing dimension, centered at any pixel and replaced the noisy pixels consecutively by the median value of the window. However, if the entire pixels in the window are noisy, then the dimension of sliding window is increased in order to obtain the noise-free pixels for median calculation. Consequently, this algorithm has been found to be able to remove the high density salt-and-pepper noise and also preserved the fine details of the four images, Lena, Elaine, Rhythm, and Sunny, used as test images in this study (The latter two real-life images have been acquired using Sony: Steady Shot DSC- S3000). Experimentally, it has been found that the proposed algorithm yields better peak signal-to-noise ratio, image enhancement factor, structural similarity index measure and image quality index, compared with the other state-of-art median-based filters viz. standard median filter, adaptive median filter, progressive switched median filter, modified decision-based algorithm and modified decision-based unsymmetric trimmed median filter.     

一种新的图像去噪混合滤波方法

为了去除图像中混入的脉冲噪声和高斯噪声,提出了一种基于自适应中值滤波和模糊加权均值滤波的混合滤波方法.该方法首先进行噪声检测把受高斯型噪声污染的像素和受脉冲型噪声污染的像素区别开来,然后对受高斯噪声污染的像素采用模糊加权均值滤波算法,而对受脉冲噪声污染的像素则采用改进的中值滤波算法进行去噪.仿真结果证明,该方法更具有实用性和有效性.     

Efficient decision based algorithm for the removal of high density salt and pepper noise in images

In this paper, an efficient decision based scheme is proposed for the restoration of grayscale and colour images that are heavily corrupted by salt and pepper noise. The processed pixel is examined for 0 or 255; if found true, then it is considered as noisy pixel else not noisy. If found noisy the four neighbours of the noisy pixels are checked for 0 or 255. If all the four neighbours of the corrupted pixel are noisy, the mean of the four neighbours replaces the corrupted pixel. If any of the four neighbours is a non-noisy pixel, calculate the number of corrupted pixels in the current processing window. If the count is less than three then the noisy pixel is replaced by an unsymmetrical trimmed median. If the current window has more than three noisy pixels, then unsymmetrical trimmed mean replaces the corrupted pixels. If all the pixels of the current processing window are noisy then instead of unsymmetrical trimmed mean, global mean of the image is replaced as output. The uncorrupted pixel is left unchanged. The proposed algorithm is tested on various grayscale and colour images and found that it gives excellent PSNR, high IEF and lowest MSE. Also it consumes average time with excellent edge preservation even at higher noise densities. The quality of the results of proposed algorithm is superior when compared to the various state of the art methods.     

A Fuzzy Switching Median Filter of Impulses in Digital Imagery (FSMF)

This paper proposed a fuzzy-based switching technique that aims at detection and filtering of impulse noises from digital images. Two types of noise models are used to obtain the noisy images. In this two-step process, the noise-free pixels are remained unchanged. The proposed detection algorithm uses 5 \(\times \) 5 window, based on all neighboring pixels on the center of the window of a noisy pixel. Two weighted median filters are devised, and a particular one is applied selectively to the noisy pixel based on the characteristics of the neighboring pixels within the window. Instead of a single threshold, two threshold values are used in the proposed fuzzy membership function to partition the noise level, and accordingly, a filtering method is applied to restore the corrupted pixel. Experimental results show that the proposed technique outperforms the existing impulse denoising methods in terms of peak signal-to-noise ratio and visual effects, with a comparable time complexity with the existing methods.     

Fast switching based median–mean filter for high density salt and pepper noise removal

This paper proposes a fast switching based median–mean filter for high density salt and pepper noise in images. The extreme minimum value and extreme maximum value of the noisy image are used to identify the noise pixels. In the filtering stage, the corrupted pixel is replaced either by median value or mean value based on the number of noise free pixels in the filtering window. The qualitative and quantitative results show that the proposed filter outperforms the other switching based filters namely ACWMF, PSMF, AMF, DBA and MDBUTMF in terms of noise removal and edge preservation for noise densities varying from 10% to 90%.     

An improved recursive and adaptive median filter for high density impulse noise

An improved recursive and adaptive median filter (RAMF) for the restoration of images corrupted with high density impulse noise is proposed in the present paper. Adaptive operation of the filter is justified with the variation in size of working window which is centered at noisy pixels. Based on the presence of noise-free pixel(s), the size of working window changes. The noisy pixels are filtered through the replacement of their values using both noise-free pixels of the current working window and previously processed noisy pixels of that window. These processed noisy pixels are obtained recursively. The combined effort thus provides an improved platform for filtering high density impulse noise of images. Experimental results with several real-time noisy images show that the proposed RAMF outperforms other state-of-the-art filters quantitatively in terms of peak signal to noise ratio (PSNR) and image enhancement factor (IEF). The superiority of the filter is also justified qualitatively through visual interpretation.     

Using neighborhood-pixels-information and ANFIS for impulsive noise suppression

This paper introduces a novel approach for denoising the images corrupted by impulsive noise (IN) by using a new nonlinear IN suppression filter, entitled k-nearest neighborhood pixels-based Adaptive-Fuzzy Filter (k-AFF). The proposed filter is based on statistical impulse detection and nonlinear filtering which uses Adaptive-Network-Based Fuzzy Inference System (ANFIS) as a missed data interpolant over the k-nearest neighbor pixels of the corrupted pixels. The impulse detection is realized by using the well-known Kolmogorov–Smirnov-based goodness-of-fit test, which yields a decision about the impulsivity of each pixel. To demonstrate the capability of k-AFF, extensive simulations were realized revealing that the proposed filter achieves a better performance than the other filters mentioned in this paper in the cases of being effective in noise suppression and detail preservation, even when the images are highly corrupted by IN.     

Using Anfis with circular polygons for impulsive noise suppression from highly distorted images

In this paper, a novel approach is presented to the restoration of images corrupted by impulsive noise (IN), with a new nonlinear IN suppression filter, entitled circular polygons based adaptive-fuzzy filter (CF). The proposed filter is based on statistical impulse detection and nonlinear filtering which uses adaptive-network-based fuzzy inference system (Anfis) as a missed data interpolant over the circular polygons and provides estimates for the original intensity values of corrupted pixels. Impulse detection is realized by using the chi-square based goodness-of-fit test, which yields a decision about the impulsivity of each pixel. Extensive simulations were realized to demonstrate the capability of CF and they reveal that the proposed filter achieves a better performance than the other filters mentioned in this paper in the cases of being effective in noise suppression and detail preservation, also when the images are highly corrupted by IN.     

基于相关度量的高椒盐噪声软阈值直方图滤波算法

利用图像邻域相关和直方图对椒盐噪声的鲁棒性,提出了一种针对高椒盐噪声图像的软阈值直方图加权滤波算法.对邻域灰度相关进行了量化分析,定义了灰度相关函数作为信号邻域相关性的度量,并将该系数作为直方图加权滤波算法的软阈值,根据像素被判定为噪声或有效信号的概率,自行调整滤波强度,减少图像滤波处理中的细节损失.仿真结果表明,对于高椒盐噪声图像,本算法在椒盐噪声滤除方面有良好的表现.     

基于差分法的噪声检测和变分法的图像滤波算法

针对图像的椒盐噪声滤除算法中,在噪声检测阶段对噪声点的检测通常不够准确,在噪声恢复阶段,又缺乏对边缘信息的保护,文中提出了一种两步复原法,以用于复原被脉冲噪声破坏的模糊图像。算法将滤噪过程分为噪声检测和噪声恢复阶段。噪声检测过程中,在滑动窗口扩大当前的像素值和其他像素值之间的有序差异,来确定当前像素是否为噪声像素。而在噪声恢复过程中利用变分法,确保图像的边缘和细节。实验结果表明,文中所提检测、降噪方法在噪声密度较高的情况下,优于其他算法。     

Switching impulse noise filter based on Laplacian convolution and pixels grouping for color images

This paper presents a new switching filter consisting of three steps to restore color images corrupted by impulse noise. Firstly, Laplacian convolution is performed on pixels in four directions to mark the pixels which are radically different in value from neighboring pixels as noise candidates. Secondly, those missed neighboring pixels involved in the step of pixels grouping decrease the occurrence of false detection. Pixels in the observation window are separated into noisy pixels and normal pixels with a dividing threshold, whose value is assigned according to a noise density estimator. Finally, a modified arithmetic mean filter is applied to restore the polluted image. Extensive experiments show that the proposed method achieves better performance than comparative methods in terms of peak-signal-to-noise ratio and structural similarity. The proposed method can effectively remove impulse noise in which noise density is varying from 10 to 80%.     

A new efficient approach for the removal of impulse noise fromhighly corrupted images

A new framework for removing impulse noise from images is presented in which the nature of the filtering operation is conditioned on a state variable defined as the output of a classifier that operates on the differences between the input pixel and the remaining rank-ordered pixels in a sliding window. As part of this framework, several algorithms are examined, each of which is applicable to fixed and random-valued impulse noise models. First, a simple two-state approach is described in which the algorithm switches between the output of an identity filter and a rank-ordered mean (ROM) filter. The technique achieves an excellent tradeoff between noise suppression and detail preservation with little increase in computational complexity over the simple median filter. For a small additional cost in memory, this simple strategy is easily generalized into a multistate approach using weighted combinations of the identity and ROM filter in which the weighting coefficients can be optimized using image training data. Extensive simulations indicate that these methods perform significantly better in terms of noise suppression and detail preservation than a number of existing nonlinear techniques with as much as 40% impulse noise corruption. Moreover, the method can effectively restore images corrupted with Gaussian noise and mixed Gaussian and impulse noise. Finally, the method is shown to be extremely robust with respect to the training data and the percentage of impulse noise.     

脉冲噪声图像的中-均值滤波算法

由于在图像信息的获取和传输过程中,图像常常受到不同程度的脉冲噪声污染。为了有效地去除高浓度脉冲噪声,提出了一种基于中－均值滤波器的噪声去除算法。该方法根据脉冲噪声特点,设定一个简单的噪声检测算子,根据噪声检测结果设定自适应滤波窗口,同时根据噪声密度选择中值和均值滤波器。为了更加有效地保留图像的原有信息,对非噪声点不做滤波处理。仿真结果表明,所提出的中－均值滤波方法不仅能有效地去除高浓度的脉冲噪声,而且能很好地保留图像的原有信息,并具有较短的滤波处理时间。