Context‐based prediction filtering of impulse noise images
2016; Institution of Engineering and Technology; Volume: 10; Issue: 6 Linguagem: Inglês
10.1049/iet-ipr.2015.0702
ISSN1751-9667
Autores Tópico(s)Anomaly Detection Techniques and Applications
ResumoIET Image ProcessingVolume 10, Issue 6 p. 429-437 Research ArticlesFree Access Context-based prediction filtering of impulse noise images Arpad Gellert, Corresponding Author Arpad Gellert arpad.gellert@ulbsibiu.ro Computer Science and Electrical Engineering Department, Lucian Blaga University of Sibiu, Emil Cioran Street, No. 4, 550025 Sibiu, RomaniaSearch for more papers by this authorRemus Brad, Remus Brad Computer Science and Electrical Engineering Department, Lucian Blaga University of Sibiu, Emil Cioran Street, No. 4, 550025 Sibiu, RomaniaSearch for more papers by this author Arpad Gellert, Corresponding Author Arpad Gellert arpad.gellert@ulbsibiu.ro Computer Science and Electrical Engineering Department, Lucian Blaga University of Sibiu, Emil Cioran Street, No. 4, 550025 Sibiu, RomaniaSearch for more papers by this authorRemus Brad, Remus Brad Computer Science and Electrical Engineering Department, Lucian Blaga University of Sibiu, Emil Cioran Street, No. 4, 550025 Sibiu, RomaniaSearch for more papers by this author First published: 01 June 2016 https://doi.org/10.1049/iet-ipr.2015.0702Citations: 11AboutSectionsPDF 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 A new image denoising method for impulse noise in greyscale images using a context-based prediction scheme is presented. The algorithm replaces the noisy pixel with the value occurring with the highest frequency, in the same context as the replaceable pixel. Since it is a context-based technique, it preserves the details in the filtered images better than other methods. In the aim of validation, the authors have compared the proposed method with several existing denoising methods, many of them being outperformed by the proposed filter. 1 Introduction Digital images are often affected by different types of noise, due to various sources of interferences. There are two main noise categories: Gaussian and impulse. The first mentioned type is a statistical noise, whose values are Gaussian-distributed. On the other hand, impulse noise is independent, uncorrelated with the image pixels and randomly distributed. Digital images can be degraded by impulse noise during sensors acquisition or transmission through a faulty communication channel. Salt and pepper is a typical impulse noise composed of minimum and maximum valued pixels within the affected image. The main objective of salt-and-pepper denoising methods is preservation of unaffected pixels while restoring the missing information. In this paper we are proposing a novel technique to reduce salt-and-pepper noise from greyscale images using context-based prediction filtering (CBPF). The basic idea was to replace the pixel affected by noise with the pixel which occurred with the highest frequency in the same context as the replaceable pixel. Therefore, we search for the context in the vicinity of the noisy pixel. The frequencies of pixels occurring in a certain context have been determined like in a Markov chain. Since our method is using context information, it is a good candidate to reconstruct details in the images affected by noise. We have compared our technique with other existing denoising methods in terms of mean square error (MSE) and peak signal-to-noise ratio (PSNR), using the boat, cameraman and airplane test images. In view of the comparisons, we have predetermined the optimal CBPF configuration and also choose the best parameters of the mentioned filters. The experimental results showed that the CBPF significantly outperforms many of the salt-and-pepper noise filters existing in the literature. The paper is organised as follows. Section 2 reviews the state of the art in denoising techniques, while Section 3 introduces the proposed CBPF. Section 4 describes the experimental methodology and the obtained results are presented in Section 5. Finally, Section 6 summarises the relevant contributions and presents some further work directions. 2 Related work in impulse noise filtering Impulse noise filtering techniques can be classified into three main categories: statistical based, fuzzy and neural network based and hybrid, employing multi-stage filtering [1]. One of the most employed impulse noise removal methods is the median filter (MF), efficient only for low-noise densities. Thus, during the last decade several improved median-based filters have been developed, with better performance on high-noise levels. Many improvements focused on replacing the noisy pixel based on non-noisy pixel values. In [2], the authors proposed a method to overcome the shortcomings faced by the classical MF at high-noise densities, by considering only those pixels that are informative in the neighbourhood. A filter employing two stages was proposed in [3]; in the first stage, the noisy pixel is detected, while in the second stage noisy pixels are replaced by the mean value of a 2 × 2 area noise-free pixels. In [4], the authors suggest a decision-based algorithm which uses a 3 × 3 window for image denoising applied selectively for 0 and 255 pixel values. At high-noise densities the median value is noisy, therefore in such cases, neighbouring pixels are used to replace the noisy pixels. A modified decision-based unsymmetrical MF is proposed in [5], replacing the noisy pixel by the trimmed median value of the non-noisy pixels. When all the pixel values are 0 and 255, the noisy pixel is replaced by the mean value of the entire window. In [6], the authors recommend a modified directional-weighted-MF to reconstruct images corrupted by salt-and-pepper noise. If the central pixel of a certain window is classified as noisy, it is replaced by a weighted median value on an optimum direction. Hamza et al. present in [7] another median-based filter obtained by relaxing the order statistic for pixel substitution. Noise attenuation properties as well as edge and line preservation are statistically analysed. The trade-off between noise elimination and detail preservation is also analysed. In [8], the progressive switching MF is presented. The method uses an impulse detection algorithm before filtering, and thus, only a proportion of the pixels are filtered. Both the impulse detection and the noise filtering steps are progressively applied through several iterations. The results are showing an enhancement over traditional MFs, being particularly effective for highly corrupted images. Wang et al. present in [9] a modified switching MF, employing a two-phase denoising method. In the first phase, the adaptive vector MF detection [10] identifies pixels likely to have been corrupted by salt-and-pepper noise. In the second phase, the noisy candidates are evaluated by using four one-dimensional Laplacian operators, which allow edge preserving. The proposed approach can effectively preserve thin lines, fine details and edges. A soft-switching MF for impulse noise removal was presented in [11], while Jassim [12] proposed a Kriging interpolation filter to reduce salt-and-pepper noise from greyscale images. First, a sequential search is performed using k × k window size to determine non-noisy pixels. The non-noisy pixels are then passed to the Kriging interpolation method to predict their absent neighbour pixels detected in the first phase as being noisy. The experimental results show that the Kriging interpolation filter can achieve noise reduction without damaging edges and details. In [13], the authors present a two-stage noise adaptive fuzzy switching median filter (NAFSMF) for salt-and-pepper noise removal. The first stage uses a histogram of the corrupted image to identify the noisy pixels, while in the second stage detected pixels are filtered, leaving unprocessed the noise-free pixels. Fuzzy reasoning is employed to handle uncertainty introduced by noise, present in the extracted local information. Their simulation results show that the presented method outperforms some of the existing salt-and-pepper noise filters. In [14], Lin identifies impulse noise with support vector machine and removes it with a fuzzy filter. Some authors are using neural networks [15-21] to filter images affected by impulse noise. Nair and Shankar [22] make use of a neural network to identify impulse noise in corrupted images and a modified MF to remove the detected noise. The authors of [23] present another hybrid technique implying a neural network in the detection stage and a switching filter in the removal stage. A universal noise removal algorithm [24], working on both Gaussian and impulse noise, introduces the spatial gradient into the Gaussian filtering framework for Gaussian noise removal and integrates their directional absolute relative differences statistic for impulse noise removal and combines them into a hybrid noise filter. Another two-stage filter that removes mixed impulse and Gaussian noise is proposed in [25]. In contrast with the above presented methods, our proposed filter is context based and therefore it can better preserve and reconstruct details in images affected by impulse noise. In the last few years, context-based noise filters have also been proposed. Buades et al. presented in [26] the non-local means denoising algorithm. The estimated value of a pixel is computed as a weighted average of all the pixels in the image, whose weights depend on the similarity between the pixels. Thus, the pixels with a similar grey level neighbourhood to the replaceable pixel have larger weights in average. In fact, this averaging approach represents the main difference between the non-local means algorithm and Markov chains. In our method, the noisy pixel is replaced, instead of an average, with the most frequent pixel which occurred in similar neighbourhoods. In [27], Estrada et al. proposed a stochastic image denoising method which is based on random walks over arbitrary neighbourhoods of a given pixel. They sample a subset of random walks starting from a given pixel and use the probabilities of travelling between pairs of pixels as weights to combine them into the noise-free pixel. The size and shape of each distinct neighbourhood are determined by the configuration and similarity of nearby pixels. In contrast, in our method we considered a neighbourhood with fixed size and shape and we use it as a whole to search similar neighbourhoods. Another important difference is that we replace a noisy pixel with the most frequent pixel occurring in similar neighbourhoods. Wong et al. proposed another stochastic image denoising method in [28], which is based on Markov-chain Monte Carlo sampling. 3 Description of the proposed context-based prediction filtering Context-based prediction can be used to determine the probability of a value, as the frequency of its occurrence in a certain context and, thus, it has been successfully applied as statistical model in several computer science areas such as computational biology [29], web mining [30], ubiquitous computing [31], information retrieval [32], speech recognition [33] and even in computer architecture [34]. Similar to a Markov process, it consists of a set of N distinct states S = {S1, S2, …, SN} [35]. In the first-order model with N states, the current state depends only on the previous state (1)where qt is the state at time t, the set of transition probabilities between the states Si and Sj is A = {aij}, having aij = P[qt = Sj|qt−1 = Si], 1 ≤ i, j ≤ N, aij ≥ 0 and . Generalising, in an order R model, the current state depends on R previous states [36] (2)We can also express the order R model in a simpler form (3)The full probabilistic description requires to specify the current state and all the predecessor states [35], meaning that the current state in a sequence depends on all the previous states. In this work, we are proposing the reconstruction of greyscale images affected by impulse noise using context-based information in a similar way as in a Markov chain implementation. In Markov chains, the next state is determined based on the transition probabilities from the current context. Therefore, we have adapted the classical Markov model presented in (3), whose values are from a one-dimensional sequence, to work with the values of a two-dimensional area. In our application, the probability of a pixel value is determined as the frequency of its occurrence in the same or similar contexts. Thus, the noisy pixel represents the next state which must be predicted, the surrounding pixels represent the context, whereas the search area encodes the previous states through its pixel values. In the case of greyscale images, the states consist of pixel values ranging between 0 and 255. Thus, we adjusted the order R model as in equation (4) where (4) CS is the context size expressed as the number of pixels from one side of the context square, W and H are the width and height of the image, respectively. Since the context is surrounding one pixel, its size can have only odd values. The pixel value qx, y depends on the pixel values from the surrounding context, excepting its own value. Thus, the order of the CBPF will be R = CS2 − 1 and the context consists in R pixel values. The probability of a certain pixel value in a given context is determined as the frequency of that pixel value in the considered context occurring within the image. Equation (4) implies searching the contexts in the entire image, which leads to a major disadvantage from the timing point of view. Therefore, we limit the search area, based on the search radius SR, as in (5). Obviously, (5)we have adjusted the SR on the margins to keep it within the image and have considered noisy pixels having values of 0 or 255, as in [4]. When we have determined that a pixel is noisy (N), we have taken the context C of that pixel consisting in R pixels from the neighbourhood, and searched for that context in a larger area, with size defined by SR, as it is illustrated in Fig. 1. The noise-free pixel value occurred in that context with the highest frequency will replace the noisy pixel value N. Fig. 1Open in figure viewerPowerPoint CBPF proposed for image denoising The algorithm that replaces a noisy pixel through the presented context-based prediction technique is described in the pseudocode given in Fig. 2. Fig. 2Open in figure viewerPowerPoint Algorithm that replaces a noisy pixel through the presented context-based prediction technique The parameters of the CBP function are: the position of the current pixel, the search area defined by SR, CS which gives the order of the model and the similarity threshold T. Obviously, the noisy pixel is not part of the context. In order to improve the algorithm efficiency, we do not search for identical contexts; we accept similar contexts, measuring the similarity degree as the sum of absolute differences (6)The pseudocode given in Fig. 3 presents how we compute the sum of absolute differences.Since the noisy pixel is not part of the context, the value of the middle pixel must be avoided in the SAD computation. We have considered a context similar if the SAD value is less than a certain threshold T. We keep in Q the count of a certain pixel value that has occurred after the considered pixel. The 'Max' function returns the colour (index) of the highest element from Q. The noise-free pixel value occurred in similar contexts with the highest frequency will replace the noisy pixel value N. If there is at least one valid case, it is returned by the CBP function. If similar contexts have not been found, the initial noisy pixel is unchanged, but this case is very rare. We have checked whether a pixel is noisy with the Salt_Pepper function returning TRUE for pixels having values of 0 or 255. The CBPF algorithm is presented in the pseudocode given in Fig. 4, where the Set_Color function replaces the value of the noisy pixel (i, j) with the value returned by the CBP function. Fig. 3Open in figure viewerPowerPoint Computation of sum of absolute differences Fig. 4Open in figure viewerPowerPoint CBPF algorithm 4 Experimental methodology We have implemented our CBPF algorithm in C#, whereas the implementations of the state-of-the-art denoising methods used for comparisons were available in Matlab. The tests were performed on three 512 × 512 greyscale PNG images: boat, cameraman and airplane. We have added salt-and-pepper noise into the original images, in ratios between 10 and 90%, in steps of 10%. All the methods were compared using this set of noisy images. The performances of the denoising methods were expressed in terms of MSE and PSNR. The MSE shows the error values of a filtered image F compared with the original one O(7)where W and H are the width and height of the image, respectively. On the other hand, the PSNR estimates the quality of a denoised image with respect to the original one. The PSNR is computed as follows (8)The goal is to obtain a low MSE and a high PSNR. 5 Experimental results First, we have evaluated the CBPF by varying CS on a fixed SR = 5 and T = 500. As we have explained in Section 3, the CS can have only odd values and it must be at least 3. The MSE values obtained on the test images are presented in Fig. 5. Fig. 5Open in figure viewerPowerPoint MSE of images denoised using CBPF with different context sizes a Boat b Cameraman c Airplane images denoised using CBPF with different context sizes Fig. 5 has shown that the best value for CS is 3, the CBPF being inefficient for higher contexts. A richer context leads to higher precision, but if it is too rich, the probability to find it is low. Therefore, usually the performance is increasing together with the context up to a certain size (which in our application is 3), after which it starts to decrease. We have continued our evaluations by varying the search radius SR between 2 and 5, considering the best CS = 3 and a fixed T = 500. The MSE values obtained on the test images are presented in Fig. 6. Fig. 6Open in figure viewerPowerPoint MSE of images denoised using CBPF with different search radius values a Boat b Cameraman c Airplane One can observe that on the boat image, a CBPF with SR value of 3 is better up to 60% noise level and for SR of 4 is better only starting with 70% noise density. On the airplane image the SR of 2 is better up to 50%, while SR of 3 and 4 are very close and better starting with a noise of 60%. On the cameraman image SR 4 performs best, it being just slightly outperformed by SR 2 on a noise up to 20%. Therefore, we consider that the optimal SR value will be 4. The conclusion after this evaluation step was that the search area might be sufficiently high to find the context, but if it is too high (SR ≥ 5), the multiple pixel value choices can lead to uncertainty and thus to lower denoising ability. The next stage of our analysis consists in varying the similarity threshold T between 450 and 600, in steps of 50. As we have already explained, when we have searched for the context of the current noisy pixel, we have taken into account all the contexts whose similarity degree, computed as SAD, is less than T. Fig. 7 presents the MSE obtained for different similarity threshold values, considering the best CS = 3 and the optimal SR = 4. Fig. 7Open in figure viewerPowerPoint MSE of images denoised using CBPF with different search similarity thresholds a Boat b Cameraman c Airplane Fig. 7 showed that the best similarity threshold value is 500 up to 70% noise on the boat image and even up to 80% noise on the cameraman and airplane images. Only on very high-noise density, a threshold of 550 or 600 is slightly better. Therefore, we have considered that the optimal similarity threshold value will be T = 500. A difference of 500 in the SAD between two compared image blocks, taking into account the best CS = 3 (contexts of 8 pixels), results in a reasonable average per pixel difference of 62. Further, we have compared the optimal CBPF having SR = 4, CS = 3 and T = 500 with other denoising methods. We have included in the comparative analysis the NAFSMF [13], the decision-based algorithm (DBA) [4], the MF, the progressive switching median filter (PSMF) [8], the relaxed median filter (RMF) [7] and the analysis prior algorithm (APA) [37]. Figs. 8 and 9 present comparatively the MSE and PSNR, respectively, for all the considered methods, including our CBPF with SR = 4, CS = 3 and T = 500, on the boat, cameraman and airplane test images. Fig. 8Open in figure viewerPowerPoint Comparing the MSE on images a Boat b Cameraman c Airplane Fig. 9Open in figure viewerPowerPoint Comparing the PSNR on images a Boat b Cameraman c Airplane The MSE and PSNR results show that the CBPF outperforms the MF, PSMF and RMF denoising methods. It also partially outperformed the APA method, on noise levels up to 20%. It is less performing than the NAFSMF and DBA methods. Fig. 10 presents the cameraman image with 30% salt-and-pepper noise (a) and its denoised versions using our CBPF (b), as well as using NAFSM (c), DBA (d), MF (e), PSMF (f), RMF (g), APA (h). Fig. 10Open in figure viewerPowerPoint Denoising the Cameraman image with a 30% noise b Using the CBPF c NAFSM d DBA e MF f PSMF g RMF h APA As Fig. 10 depicts, the proposed CBPF can better remove salt-and-pepper noise than the MF, PSMF and RMF denoising methods. 6 Conclusions and further work In this paper, we have proposed a new filtering method for impulse noise on greyscale images using context-based prediction. The CBPF replaces a pixel affected by salt-and-pepper noise with the pixel which occurred in its neighbourhood, determined by the search radius input parameter, with the highest frequency in the same context as the replaceable pixel. The frequencies of pixels occurring in a certain context are determined like in a Markov chain. Since our method is using context information, it can reconstruct details in the images affected by noise better than other methods. Due to the intrinsic behaviour, it could have a significant advantage on images containing textures. The limitation of the proposed method stands in the computational time required for denoising, which recommends it only for off-line processing of images. We have analysed our CBPF by varying its parameters. The tests performed on the boat, cameraman and airplane images show that the CBPF with a context size of 3 is the optimal. In the next step, we have shown that the optimal search radius is 4. The last analysed parameter was the similarity threshold whose optimal value was 500, admitting reasonable differences between the compared image blocks. We have compared the optimal CBPF (with configuration CS = 3, SR = 4, T = 500) with other existing denoising methods in terms of MSE and PSNR. The experimental results show that the CBPF significantly outperforms the MF, the PSMF and also the RMF and it is not significantly worse than the NAFSMF and the DBA methods (see Figs. 8 and 9). It also partially outperforms, on low-noise levels, other considered algorithms. For the case of usual noise filtering conditions (noise between 0 and 30%), the proposed method is very close to the most performing denoising methods referenced. Therefore, in our opinion, this new method can be further developed, so that it could outperform all the existing methods. It is a new method, which is using context information, and has a high further development potential. Although the optimal SR is 4, there are some noise levels where an SR of 3, or even 2, is better. Therefore, as a further work direction, we will analyse the possibility to dynamically adjust the SR value and thus to adapt this input parameter to the image. 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