Iterative grouping median filter for removal of fixed value impulse noise

IET Image ProcessingVolume 13, Issue 6 p. 946-953 Research ArticleFree Access Iterative grouping median filter for removal of fixed value impulse noise Jiayi Chen, Jiayi Chen orcid.org/0000-0001-5943-4709 School of Information Engineering, Guangdong Medical University, Zhanjiang, Guangdong, 524023 People's Republic of ChinaSearch for more papers by this authorYinwei Zhan, Corresponding Author Yinwei Zhan ywzhan@gdut.edu.cn School of Computer Science and Technology, Guangdong University of Technology, Guangzhou, 510006 People's Republic of ChinaSearch for more papers by this authorHuiying Cao, Huiying Cao School of Information Engineering, Guangdong Medical University, Zhanjiang, Guangdong, 524023 People's Republic of ChinaSearch for more papers by this authorGangqiang Xiong, Gangqiang Xiong School of Information Engineering, Guangdong Medical University, Zhanjiang, Guangdong, 524023 People's Republic of ChinaSearch for more papers by this author Jiayi Chen, Jiayi Chen orcid.org/0000-0001-5943-4709 School of Information Engineering, Guangdong Medical University, Zhanjiang, Guangdong, 524023 People's Republic of ChinaSearch for more papers by this authorYinwei Zhan, Corresponding Author Yinwei Zhan ywzhan@gdut.edu.cn School of Computer Science and Technology, Guangdong University of Technology, Guangzhou, 510006 People's Republic of ChinaSearch for more papers by this authorHuiying Cao, Huiying Cao School of Information Engineering, Guangdong Medical University, Zhanjiang, Guangdong, 524023 People's Republic of ChinaSearch for more papers by this authorGangqiang Xiong, Gangqiang Xiong School of Information Engineering, Guangdong Medical University, Zhanjiang, Guangdong, 524023 People's Republic of ChinaSearch for more papers by this author First published: 12 April 2019 https://doi.org/10.1049/iet-ipr.2018.6331Citations: 7AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract Due to the limitation of existing filters in detection and removal of fixed value impulse noise, the authors propose an iterative grouping median filter (IGMF) according to the characteristics of noise intensity and distribution. It sorts the noise-free pixels in neighbourhood by intensity, divides the sorted pixels into groups depending on the intensity differences of adjacent pixels, and finally takes the median of the maximum group as the intensity of noisy pixel. This noise removal strategy is performed iteratively and takes full advantage of the previous denoising results. Experiments show that IGMF outperforms the existing state-of-the-art filters in terms of visual perception, peak signal to noise ratio and structural similarity index at various noise densities. 1 Introduction An impulse noise usually corrupts an image in two versions of fixed values and random values. The former one of fixed values, which is well-known as the so-called salt and pepper noise, randomly replaces pixels with extreme intensity values. An impulse noise severely affects the image quality during image acquisition, transmission, and processing. Thus, denoising is a must before any subsequent manipulation. A mean filter [1-3] as a low-pass filter is unable to preserve edges and details, so a median filter is usually used to remove impulse noises. A standard median filter [4] that removes noises with the median of neighbour pixels is still unable to well protecting the edges and details. A weighted median filter [5-7] tried to improve the standard median filter by weighting the neighbour pixels, but all the pixels in the whole image were processed uniformly without local treatment. So, further improvements were contributed in literatures [5, 8-33] in order to effectively remove impulse noises. Nonetheless, all these works even introduce new disadvantages while dealing with the drawback in the previous methods, or obtain little improvement to the previous methods, and thus are not necessarily effective. In order to further improve the denoising performance, here, we propose an iterative grouping median filter (IGMF) with a novel noise detection technique based on intensity and distribution, followed by an iterative noise removal technique based on smoothly varying intensities. The remainder of this paper is organised as follows. In Section 2, the recent related works are stated. Our method is described in Section 3 for the noise detection part and Section 4 for the noise removal part. Experimental analysis is conducted in Section 5. Finally, we make a conclusion in Section 6. 2 Related works The median filter, closely integrated with a noise-detection technique, is called switching median filter, such as [8-14]. A median filter using a boundary discriminative noise detection was proposed in [12], but its major drawback lies in introducing blur effect at high noise densities due to the usage of a large denoising neighbourhood. Inspired by [12], an improved noise-detection technique, called boundary discriminative noise detection by elimination, was proposed in [13], which retains the advantages of the filter in [12] while suppressing noises effectively. To improve the performance, the composite application of median filter was proposed, such as [15, 16]. An extremely fast adaptive high-performance filter (FAHPF) proposed in [15] removes noises by an overlapping median filter embedded with the mean filter. However, it has the drawback of low-pass filtering due to the usage of mean filter at its last phase. Specifically, the weighted median is an improved version of median [17-19]. The authors in [18] introduced an adaptive switching weighted median filter (ASWMF), which removes the noises by taking support from the weighted median of neighbourhood of adaptive size. An adaptive dynamically weighted median filter (ADWMF) in [19], by using the weighted operator derived from Gaussian Surface, performs the noise removal by weighted median of neighbour noise-free pixels, and yields high-quality denoised image. In an attempt to further improve the denoising performance, especially at high noise densities, the hybrid filters [5, 20-24] were proposed. A switching median-mean filter (SMMF) proposed in [24] removes noises by an iterative median filter followed by a mean filter, or by an iterative mean filter followed by a median filter. These hybrid filters show good robustness in noise removal by integrating median filter with mean filter and achieve good performance to some extent. Putting aside median filters, some scholars in turn focused on improving the mean filter for fixed value impulse noise, such as [25-29]. A new adaptive weighted mean filter (AWMF) proposed in [28] enlarges the neighbourhood until the maximum and the minimum intensities of it equal to those of the successive former one, respectively, and removes noises by the weighted mean of pixels in the current neighbourhood. However, these improved mean filters are still subject to the drawback of low-pass filtering and are not necessarily effective. Recently, because of its robust decision for noise detection and removal, the decision-based median filters [30-33] were proposed to remove impulse noises at high densities. Probabilistic decision-based filter (PDBF) in [33] first proposed the patch median of neighbourhood of adaptive size for noise removal; the patch median is an improved version of median, which avoids the possibility of averaging two pixels in the middle while searching for median value. From the literatures, one can summarise the characteristics of impulse noise and original pixel in an image as follows. (i) The noisy pixels take extreme intensity values, i.e. 0 and 255. (ii) A noisy pixel drastically differs from its neighbour noise-free pixels in intensity; in other words, it does not vary smoothly in respect to the neighbour pixels. (iii) An original image consists of locally smoothly varying regions separated by edges. 3 Noise detection based on intensity and distribution It is reasonable to identify the pixels with extreme intensity values as noises, such as [11, 15, 23, 24, 30, 33]. However, it should be noticed that a certain number of noise-free pixels may also take extreme intensity values; thus, they would also be identified as noises and be destroyed. Based on the characteristics of impulse noise and noise-free pixels mentioned at the end of Section 2, and supposing a white flat neighbourhood corrupted by impulse noise, some new findings are concluded from experiments. (i) The number of noisy pixels with intensity 0 is approximately equal to that of noisy pixels with intensity 255. (ii) Excluding noisy pixels, other noise-free pixels are also with intensity 255; thus, the pixels with intensity 255, including noisy and noise-free pixels, account for the majority. In other words, the number of pixels with intensity 255 is greater than that of pixels with intensity 0. (iii) The noises with intensity 255 in the white flat neighbourhood are assimilated and lost, for their intensities are the same as noise-free pixels. The characteristics just mentioned are similar for the black flat neighbourhood. According to the above analysis and findings, the noise candidates identified by extreme intensity values further undergo a detection with another decision, with the aim to discriminate the noise-free pixels with extreme intensity values from the noisy pixels. Specifically, for a pixel p in image f, let (f(p)∈[0, 255]) be its intensity, and Np(k) be its neighbourhood of size k × k. For a pixel p with f(p) = 255, if the pixels with intensity 255 in its Np(k) account for the majority, and here we set n255 > T1, it can be inferred that the Np(k) locates at a white flat region, and the p is noise free, or else it is noisy. The decision of noise detection is similar for pixel p with f(p) = 0. For the optimal values of k and T1, we conduct a simulation with IGMF on BSD68 dataset corrupted by noise of density 0.5, the result of which is shown in Fig. 1. The result shows how the denoising performance depends on noise detection with various values of k and T1. Based on the result, we prefer to take k = 5 and T1 = 20. Fig. 1Open in figure viewerPowerPoint Average PSNRs on BSD68 dataset of IGMF with various neighbourhood size k and threshold T1 for noise detection 4 Iterative noise removal based on smoothly varying intensities The noise-free pixels in a neighbourhood may not vary all smoothly in intensity, for the neighbourhood may cover parts of several flat regions separated by edges, such as Fig. 2a. Obviously, intensity estimation of a noisy pixel simply by taking the median of its neighbour noise-free pixels would inevitably cause a deviation between estimated value and original value, and thus, something must be done to reduce the deviation. Fig. 2Open in figure viewerPowerPoint Specific illustration of noise removal based on smoothly varying intensities (a) Neighbourhood covers parts of two flat regions, (b) Intensities of (a) with centre intensity being 41, (c) (b) corrupted by noise of density 0.5 4.1 Noise removal based on smoothly varying intensities It is experimentally found that if the neighbour pixels differ greatly in intensity, they are likely to locate at different flat regions separated by edges; and in such conditions, the centre pixel highly tends to locate at the maximum region in statistical significance and has no or weak correlation with other regions. Based on this finding, the noise removal can be improved by considering only the pixels in maximum region for the intensity estimation of noisy pixel. Specifically, for a noisy pixel p, a new noise removal method can be described as follows. Step 1 Sort the noise-free pixels in Np(k) by the intensity, and obtain a sorted vector S. Step 2 Check each pair of adjacent pixels across the S, i.e. S(i) and S(i + 1), if |S(i) − S(i + 1)| > T2, then S is cut-off between S(i) and S(i + 1), and thus, divided into groups. Step 3 Take the median of maximum group as the intensity of p. Similar to the simulation results in Fig. 1 for searching for the optimal values of k and T1, by vast trial and error methods on BSD68 dataset, the optimal threshold of T2 takes 38. A specific illustration of the new noise removal method is shown in Fig. 2. Fig. 2a shows a neighbourhood Np(5) obtained from image Lenna, which is located at 403–407 of height and 343–347 of width. The intensities of Np(5) are shown in Fig. 2b, and the intensity of centre pixel p is 41. The Np(5) corrupted by impulse noise of density 0.5 is shown in Fig. 2c, with pixel p corrupted. The intensity estimation of p is given as follows. Step 1 In Np(5), sort the noise-free pixels and obtain S = [30, 32, 34, 41, 42, 47, 52, 57, 74, 122, 128]. Step 2 Check the difference of each pair of adjacent pixels across the S. It can be found that |S(9) – S(10)| = 48 > T2. Thus, the S is cut-off between S(9) and S(10), and thus, divided into groups, i.e. S1 = [30, 32, 34, 41, 42, 47, 52, 57, 74] and S2 = [122 128]. Step 3 The median of maximum group S1, i.e. 42, is taken as the intensity of p. Compared to the median 47 of S, which is used by many existing filters for noise removal, the result (i.e. 42) of the proposed method is more close to the original intensity (i.e. 41) of p. 4.2 Noise removal by iterative method Empirically, there is a strong correlation between pixel intensity and its spatial location in a small neighbourhood. Thus, noise removal using small neighbourhood is highly preferred; however, this direct approach fails in image with a high density of noises, in which, pixels of small neighbourhood may be all corrupted, and the median of noise-free pixels could not be computed. A straightforward solution is to consider large neighbourhood, but increasing the neighbourhood size may directly lead to blurring and unnecessary distortion in the denoised image. Furthermore, when the increased neighbourhood size has reached the predefined maximum, and the neighbourhood still contains no noise-free pixels, a portion of existing filters replaces the intensity of noisy pixel with the median or mean of the pixels of just previously processed in neighbourhood, such as [15, 23, 26, 32]. However, this would render the denoised image suffering streaking effect. Actually, the problems just mentioned can be addressed and substantial performance improvements can be obtained through the iterative method as follows. Denoted by R the noise recognition matrix, by which, a pixel p is identified as noise with R(p) = 1, or noise-free with R(p) = 0. Step 1 For each pixel p with R(p) = 1, if Np(3) contains pixels with R() = 0, then, process p by the method proposed in Section 4.1, and set R(p) = 0, or else let it unchanged. Step 2 For each pixel p with R(p) = 1, process it as step 1, but by using Np(5). Step 3 For each pixel p with R(p) = 1, process it as step 1, but by using Np(7). Step 4 For each pixel p with R(p) = 1, replace its intensity with the median of Np(5) excluding f(p). It is noteworthy that the denoising processing in steps 2, 3, and 4 takes full advantage of the previous denoising results; and the processing of step 4 ensures avoiding the streaking effect encountered by many existing filters; furthermore, the iterative method and taking full advantage of the previous denoising results make it easy to remove almost all the noises without expanding the neighbourhood to very large. 5 Simulation results and analysis We carry out the experiments by using Matlab R2013b in a machine: Intel(R) Core(TM) i7-7700 CPU @ 3.60 GHZ, 8 GB RAM. The Set12 and BSD68 datasets, several images of which are shown in Figs. 3 and 4, are used for experiments. In terms of visual perception, peak signal to noise ratio (PSNR), structural similarity index (SSIM) [34], and computational time at various noise densities, we investigate the performance of the proposed IGMF with respect to some state-of-the-art filters proposed recently, which are FAHPF [15], ASWMF [18], ADWMF [19], SMMF [24], AWMF [28], and PDBF [33]. Greater PSNR and SSIM imply better denoising performance. Fig. 3Open in figure viewerPowerPoint Several images of Set12 (a) Lenna, (b) Boat, (c) Barbara, (d) Peppers Fig. 4Open in figure viewerPowerPoint Several images of BSD68 (a) Test004, (b) Test018, (c) Test051, (d) Test066 The PSNR and SSIM are defined by (1) (2)C1 = (K1L)2, C2 = (K2L)2 Here f is the original image, g is the denoised image, and m and n are the numbers of rows and columns of these images. The stabilising constant C1 and C2 are calculated with the dynamic range, L = 255 and by default K1 and K2 are selected as 0.01 and 0.03, respectively; the uf and σf are the mean and standard deviation of f, respectively; and denoted by σfg the covariance of f and g. 5.1 Evaluate by visual perception Figs. 5-12 show the improvements in visual appearances gained by IGMF against existing filters for the images Boat and Test066 corrupted by noise of density 0.8, Peppers and Test018 corrupted by noise of density 0.9. Fig. 5Open in figure viewerPowerPoint Visual perception of IGMF versus state-of-the-art filters on Boat (a) Noisy image of density 0.8, denoised images of, (b) FAHPF, (c) ASWMF, (d) ADWMF Fig. 6Open in figure viewerPowerPoint Visual perception of IGMF versus state-of-the-art filters on Boat; denoised images of (a) SMMF, (b) AWMF, (c) PDBF, (d) IGMF Fig. 7Open in figure viewerPowerPoint Visual perception of IGMF versus state-of-the-art filters on Test066 (a) Noisy image of density 0.8, denoised images of, (b) FAHPF, (c) ASWMF, (d) ADWMF Fig. 8Open in figure viewerPowerPoint Visual perception of IGMF versus state-of-the-art filters on Test066; denoised images of (a) SMMF, (b) AWMF, (c) PDBF, (d) IGMF Fig. 9Open in figure viewerPowerPoint Visual perception of IGMF versus state-of-the-art filters on Peppers (a) Noisy image of density 0.9, denoised images of, (b) FAHPF, (c) ASWMF, (d) ADWMF Fig. 10Open in figure viewerPowerPoint Visual perception of IGMF versus state-of-the-art filters on Peppers; denoised images of (a) SMMF, (b) AWMF, (c) PDBF, (d) IGMF Fig. 11Open in figure viewerPowerPoint Visual perception of IGMF versus state-of-the-art filters on Test018 (a) Noisy image of density 0.9, denoised images of, (b) FAHPF, (c) ASWMF, (d) ADWMF Fig. 12Open in figure viewerPowerPoint Visual perception of IGMF versus state-of-the-art filters on Test018; denoised images of (a) SMMF, (b) AWMF, (c) PDBF, (d) IGMF In Figs. 5 and 6, the results produced by FAHPF and SMMF verify that they indeed have a good capability of noise removal; however, they still have slight blurred effect in the denoised images. The PDBF and AWMF suffer serious blur effect, although they remove the noises thoroughly. From the edges which separate the objects and background, as well as the sharpness of details, it can be concluded that denoised image of superior quality can be produced by IGMF rather than the other filters. In Figs. 7 and 8, the AWMF and PDBF have destroyed the edges of image. ASWMF and ADWMF suffer from an incomplete noise removal, although they preserve the edges of image well. Comparatively, the IGMF outperforms the other filters by removing thoroughly the impulse noises without introducing blur effect, while the edges can be well preserved. In Figs. 9 and 10, obviously, the ADWMF fails to remove noises thoroughly, and the denoising results given by PDBF and AWMF have serious blur effect, and thus, they fail to restore the images well. The FAHPF and SMMF do well in preserving the edges of image; however, slight blur effect can still be seen in the denoised images. The superior performance of the IGMF can easily be seen from the edges which separate the objects from the background; the IGMF outperforms the existing filters by preserving the edges and the clarity of the details very well. The capability of IGMF in preserving the details and edges, while removing noises, is verified again by the simulation on the image Test018. In Figs. 11 and 12, residual noises can be seen in the denoised images produced by ADWMF and ASWMF, although they preserve well the edges and clarity of image. The PDBF and AWMF show a poor visual perception in image denoising. The denoised image produced by IGMF is visually sharper and more distinctive than those obtained by the other filters. The above careful investigations of the results prove the capability of IGMF in producing higher quality image when compared to other filters. In essence, the substantial performance gains of IGMF lie on its highly accurate noise detection; together with the performance gains derived from the noise removal, the IGMF has entirely yielded a better performance to that of exiting filters consistently. 5.2 Evaluate by PSNR and SSIM Inspecting the results reveal the power of IGMF in denoising objectively and quantitatively, this is supported by the PSNR and SSIM that are shown in Table 1 for Lenna, Table 2 for Boat, Table 3 for Barbara, and Table 4 for Peppers, under noise densities ranging from 0.1 to 0.9. Table 1. PSNR and SSIM of IGMF versus state-of-the-art filters on Lenna Noise density, % 10 30 50 70 90 10 30 50 70 90 PSNR, dB SSIM, % FAHPF 43.0 36.9 33.2 30.1 25.6 99.8 99.1 97.9 95.4 86.8 ASWMF 42.4 36.2 32.4 29.1 24.5 99.8 99.0 97.7 94.7 83.9 ADWMF 42.3 36.3 32.7 29.9 23.1 99.7 99.1 97.4 94.8 84.2 SMMF 41.7 36.7 33.6 30.9 26.6 99.8 99.1 97.9 95.6 87.1 AWMF 37.8 34.9 32.4 29.4 23.8 99.4 98.7 97.3 93.9 79.4 PDBF 33.6 33.0 30.7 28.0 22.9 98.0 97.5 95.2 90.7 75.3 IGMF 43.7 37.6 34.1 31.5 28.9 99.8 99.2 98.3 96.7 93.6 Table 2. PSNR and SSIM of IGMF versus state-of-the-art filters on Boat Noise density, % 10 30 50 70 90 10 30 50 70 90 PSNR, dB SSIM, % FAHPF 38.9 32.9 29.7 26.9 23.1 99.5 98.1 95.9 91.8 78.4 ASWMF 38.8 32.9 29.3 26.3 22.4 99.5 98.1 95.8 91.2 76.0 ADWMF 38.1 32.7 29.4 26.9 22.4 99.5 98.0 95.2 90.3 77.5 SMMF 37.5 32.8 30.1 27.7 23.6 99.4 98.1 95.9 91.9 77.5 AWMF 33.9 31.3 29.2 26.4 21.7 98.8 97.6 95.2 89.2 68.2 PDBF 29.5 29.0 28.4 25.1 20.9 96.3 95.3 93.8 84.0 62.2 IGMF 39.3 33.6 30.4 28.0 25.7 99.6 98.4 96.7 93.8 88.4 Table 3. PSNR and SSIM of IGMF versus state-of-the-art filters on Barbara Noise density, % 10 30 50 70 90 10 30 50 70 90 PSNR, dB SSIM, % FAHPF 33.8 28.5 25.7 23.6 20.9 98.9 95.8 91.6 86.0 73.7 ASWMF 33.7 28.4 25.4 23.1 20.3 98.8 95.7 91.4 85.4 71.5 ADWMF 33.4 28.3 25.7 23.9 20.5 98.8 95.5 91.3 85.5 72.8 SMMF 33.3 28.6 26.1 24.3 21.8 98.7 95.8 92.0 86.3 74.1 AWMF 31.9 28.4 26.2 24.2 20.8 98.3 95.9 92.1 85.9 67.4 PDBF 25.2 24.9 23.9 22.7 19.9 90.3 88.8 84.9 79.2 61.7 IGMF 34.5 29.1 26.4 24.4 22.6 99.0 96.4 92.9 88.6 82.2 Table 4. PSNR and SSIM of IGMF versus state-of-the-art filters on Peppers Noise density, % 10 30 50 70 90 10 30 50 70 90 PSNR, dB SSIM, % FAHPF 41.4 35.7 32.4 29.9 25.5 99.5 98.4 96.9 94.3 86.3 ASWMF 40.8 35.1 31.7 28.9 24.4 99.5 98.2 96.5 93.3 83.2 ADWMF 40.3 35.2 32.3 29.2 18.4 99.5 98.1 96.5 93.1 65.7 SMMF 40.9 36.0 33.2 30.7 26.4 99.5 98.5 97.2 94.9 87.2 AWMF 36.2 34.6 32.1 28.9 22.8 98.4 98.2 96.9 93.7 79.3 PDBF 32.7 32.4 30.4 27.7 22.1 97.9 97.3 95.0 90.6 74.8 IGMF 42.2 36.5 33.3 31.0 28.6 99.6 98.7 97.4 95.5 92.2 In Table 1, the AWMF and PDBF show poor performance by the results of PSNR and SSIM, and PDBF always achieves the smallest PSNR and SSIM. The performances of FAHPF, ADWMF, and ASWMF are close to each other. SMMF shows good performance by the results of PSNR and SSIM. The IGMF relatively show better performance than others by larger values of PSNR and SSIM. By comparing to other filters, Table 2 shows that the PDBF and AWMF could not achieve a good denoising result, especially for image corrupted with noises of low densities. The SMMF indeed has a good capability of denoising, which is supported by the values of PSNR and SSIM shown in Table 2. However, compared to the results achieved by the other filters, the IGMF still stands in advantage. From the results on texture image Barbara presented in Table 3, PDBF still show poor performance at all noise densities; ASWMF lags behind others at high noise densities. The results of FAHPF, AWMF, and ADWMF are close to each other. Although the results of SMMF and AWMF are so close to that of IGMF, the IGMF behaves better than others at all noise densities. In Table 4, the PDBF and AWMF show worse performance than others in terms of PSRN and SSIM. The values of PSNR and SSIM of ADWMF drop drastically at high noise densities. Except for the comparable results produced by the SMMF at medium noise densities, IGMF shows superior performance to the others by competitive results of PSNR and SSIM. Furthermore, by using graphical representation for conveniently comparison, the above observations and statements are confirmed again by the average results of PSNR and SSIM on BSD68 dataset of IGMF versus state-of-the-art filters, see Fig. 13. The curves in Fig. 13a show the average PSNR of each filter on all images of BSD68 dataset at each noise density, and similarly, the curves in Fig. 13b show the average SSIM. These results are in line with above studies. Fig. 13Open in figure viewerPowerPoint IGMF versus state-of-the-art filters on BSD68 in terms of the average values of (a) PSNR and, (b) SSIM The IGMF consistently yields appreciable performance gains under noise density ranging from 0.1 to 0.9. These curves reveal the effectiveness of IGMF in producing higher quality and sharper images. Meanwhile, it is indicated that the accurate noise detection and robust noise removal of IGMF count for much more than that of the other filters in denoising results. In a word, these values and curves indicate that the IGMF outperforms the other filters in denoising. This is due to the fact that on the one hand, noise detection by IGMF can correctly discriminate the noisy pixels from the noise-free pixels, and on the other hand, noise removal by IGMF can improve the intensity estimation of noisy pixels and preserve the edges and details well. As a matter of fact, higher PSNR and SSIM values for IGMF under high noise densities are strongly associated with these improvements in IGMF. 5.3 Evaluate by computational time In terms of computational time, we investigate the efficiency of IGMF with existing state-of-the-art filters on BSD68 dataset. The average results, achieved by various methods, are shown in Table 5. Table 5. Average computational time of IGMF versus state-of-the-art filters on BSD68 dataset Noise density, % 10 20 30 40 50 60 70 80 90 Time, s FAHPF 1.191 2.182 3.196 4.316 5.360 6.421 7.432 8.523 9.991 ASWMF 0.380 0.724 1.048 1.390 1.698 1.996 2.296 2.632 3.095 ADWMF 1.696 2.323 3.071 4.023 4.929 5.658 6.121 6.423 6.649 SMMF 0.348 0.647 0.948 1.279 1.587 1.892 2.191 2.479 2.792 AWMF 1.818 1.580 1.524 1.486 1.486 1.500 1.532 1.575 1.622 PDBF 0.232 0.433 0.635 0.848 0.732 0.620 0.737 0.876 1.073 IGMF 0.336 0.630 0.938 1.223 1.507 1.779 2.046 2.329 2.634 For each filter, increasing noise density often leads to increasing computational time; however, the AWMF is an exception. The FAHPF and ADWMF are highly computationally demanding. The PDBF does the best in the computational time; the reason behind this lies in its simple processing strategies, from the above investigations, however, it shows poor performance in denoising. The IGMF, SMMF, and AWMF are also computationally efficient; they are close to each other in computational time. Comparatively, although no significant superiority in computational time is shown by IGMF to the PDBF, SMMF, and AWMF, the IGMF always achieves better denoising performance than all others. 6 Conclusion Inspired by the advantages and disadvantages of existing filters, we propose an IGMF for removal of fixed value impulse noise. According to the characteristics of fixed value impulse noise in intensity and distribution, the proposed method correctly discriminates the noisy pixels from noisy image. The intensity of noisy pixel is replaced by the median of noise-free pixels in the maximum subgroup, which is derived by means of sorting the neighbour noise-free pixels and then dividing them into groups depending on the intensity difference between each pair of adjacent pixels across the sorted result. Furthermore, the noise removal technique is performed iteratively and takes full advantage of the previous denoising results. The simulation results have shown that the proposed method has better capability in noise detection and removal, and surpass the existing filters in denoising performance. 7 Acknowledgment We would like to thank the editors and anonymous reviewers for their constructive suggestions to the improvements of this paper. This work was supported by the National Natural Science Foundation of China [grant numbers 61170320]; the Science and Technology Program of Guangdong Province in China [grant numbers 2017B010110015]; the Project of Science and Technology Program of Guangzhou [grant number 201604016034]; the Medical Scientific Research Foundation of Guangdong Province in China [grant number B2018190]; the Project of Science and Technology Program of Zhanjiang City in China [grant number 2017B01142]. 8 References 1Lin P.H., Chen B.H., and Cheng F.C. et al: 'A morphological mean filter for impulse noise removal', J. Disp. Technol., 2016, 12, (4), pp. 344– 350 2Jomaa H., Mabrouk R., and Khlifa N. et al: 'Denoising of dynamic PET images using a multi-scale transform and non-local means filter', Biomed. Signal Process. Control, 2018, 41, pp. 69– 80 3Rakshit M., and Das S.: 'An efficient ECG denoising methodology using empirical mode decomposition and adaptive switching mean filter', Biomed. Signal Process. 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