A Non-Iterative Adaptive Median Filter for Image ... - IEEE Xplore

2014 International Conference on Signal Processing and Integrated Networks (SPIN)

A Non-Iterative Adaptive Median Filter for Image Denoising Vikrant Bhateja, Member, IEEE

Kartikeya Rastogi

Aviral Verma

Chirag Malhotra

Deptt. of Electronics and Comm. Engg., SRMGPC, Lucknow (U.P.), India. [email protected]

Deptt. of Electronics and Comm. Engg., SRMGPC, Lucknow (U.P.), India. [email protected]

Deptt. of Electronics and Comm. Engg., SRMGPC, Lucknow (U.P.), India. [email protected]

Deptt. of Electronics and Comm. Engg., SRMGPC, Lucknow (U.P.), India. [email protected]

have been proposed for restoration of images contaminated by salt and pepper noise. Among them, the conventional filtering approaches include: Local Statistics & Standard Median Filter (SMF) [36]-[37], Bilateral Filters [31],[38], Decision based median filtering (DMF) approaches [39]-[43], Adaptive median filters (AMF) [44]-[45] and Directional weighted median filters (DWMF) [46]-[47]. These approaches have been established to perform reliable filtering when the levels of noise contaminations are fairly low. For impulse noise levels of 50% and above, the major outcomes are edge jitter leading to compromise of fine details as well as prominent blurring [48]-[49]. Chan et al. proposed a new impulse detection and filtering method [48] that uses a 3x3 window for computation. Although the processing time is less but there occurs a heavy blurring at high noise levels. Wang et al. [49][50] proposed a modified switching median filter which was successful in preservation of edges, only at low noise levels. Vijay Kumar, et al. proposed an algorithm [51] for detection of high density salt and pepper noise using robust estimation with a variable window of size 17x17. This enhanced the complexity and also the computation time. Jayaraj, et al. presented a robust estimation technique [52] which efficiently removed the noise at low densities but reconstructed a poor quality image at higher densities using a maximum window size of 7x7. The signal-dependent rank ordered mean (SDROM) is median-based filter that can remove low level impulse noise quite effectively, but at high noise densities the rank-ordered mean gets corrupted in a local window having large number of noisy pixels. Another median-based filter, the adaptive center weighted median filter (ACWMF), performs the comparison between the center weighted medians and adaptive thresholds for detection of noisy pixels [53]. The filtering approach proposed in this paper is the improvement of our previous work [42] where filtering scheme was applied to all pixels which resulted in smoothening of image and loss of sharp image features at low noise levels. The non-iterative adaptive median filter proposed in this paper performs robust decision (to detect noisy pixels and adaptively increase the window size) by comparing the computed median with the minimum and maximum pixel values without the requirement of any preset thresholds. The obtained results demonstrated effective suppression of residual noise while satisfactorily preserving the fine details. The remaining paper is structured

Abstract— In this paper, a non-iterative adaptive median filter is proposed for denoising images contaminated with impulse noise. The proposed denoising scheme operates in two steps. Firstly, the pixels are segregated as ‘noisy’ and ‘noise-free’ so that the subsequent processing can be carried out only for the noisy pixels only in the next step. Secondly, the identified noisy pixels are replaced by the median value or by its neighboring pixel value. The term ‘adaptive’ justifies the filters’ capability to increase the size of the spatial window, depending upon the decisions made based on statistical parameters (estimated within the local window). Further, the ‘non-iterative’ feature projects that there is no need of recursive filtering to reduce the residual noise content. The proposed denoising method is tested on images with different characteristics and is found to produce better results in terms of the qualitative and quantitative measures of the image in comparison to other filtering approaches. Index Terms—non-iterative, noise detection, noise suppression, adaptive spatial window.

I. INTRODUCTION During acquisition or transmission digital images often get affected by noise. It manifests itself as erroneous intensity fluctuations which steam from imperfections of imaging devices and transmission channels [1]-[4]. Noise can seriously affect the quality of signals and images. It causes degradation of image spatial resolution, loss of image details and distortion of important image features. This distortion of features is more of concern in medical images like mammograms [5]-[11], ultrasound [12]-[13] as well as MRI [14]-[15]. Not only is this but the loss of diagnostic features equally important with ECG [16]-[20] and EEG [21]-[24] signals corrupted with noise. There are generally two kinds of noise that corrupt the digital images: one is the additive Gaussian noise and the other is the impulse noise [25]-[27]. In course of digital data traffic, impulse noise forms the main cause of error as this noise is present due to bit errors in transmission. This noise can corrupt images where the corrupted pixel takes either maximum or minimum gray level value; leading to severe degradation of image quality and loss of fine details [28]-[33]. The objective of noise suppression in such corrupted images is to filter the impulses so that the noise free image is fully restored with minimum signal distortion [34]-[35]. Several non-linear filters

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2014 International Conference on Signal Processing and Integrated Networks (SPIN)

as follows: Section II describes the concept and operation of proposed filter. Section III presents the simulation results and its discussion while Section IV concludes the work.

attain effective filtering, the above process is carried out for two iterations for images corrupted with high density impulse noise. The novelty of the proposed filter lies in the fact that a variable window size is used instead of fixed size and optimal filtering is obtained without going beyond window sizes of 9x9; In addition, the computational complexity of the proposed filter is also minimized as residual filtering can be achieved without iterative application of the filter.

II. NON-ITERATIVE ADAPTIVE MEDIAN FILTER DMF makes a rough approximation of whether a pixel is corrupted or not. Then, the non-noisy pixel values are preserved and the noisy pixels are replaced by the median value of their neighbors. Hence the output of DMF is superior to the SMF. Since, DMF uses neighborhood of fixed window size, it yields degradation in performance at high noise densities because of non-availability of uncorrupted median value within the spatial window. On the other hand, corrupted pixel values and replaced median pixel values are less correlated in AMF due use of large window sizes [42]-[43]. This leads to loss of edge information. The filter proposed in [54] uses the concept of AMF in two stages. In first stage, AMF with a predefined maximum window size is used whereas unlimited window size AMF is used in second stage. However, the problem in this method is that it processes all pixels without paying any heed to whether pixel is noisy or noise free leading to over smoothening of the image. Based on the above idea, the denoising filter proposed in this work uses a non-iterative adaptive median filter employing a variable window. The key concept of the proposed filter is to consider only the corrupted pixels as far as possible and then applying the filtering scheme to those pixels only, leaving the non-noisy pixels unprocessed. The proposed algorithm is initiated by moving a spatially adaptive window (w) of size 3x3 over the noisy image. This is followed by checking the central pixel of the spatial window to detect whether it is corrupted or uncorrupted. A pixel in an image can take values only between 0 and 255. In impulse noise corrupted image the noisy pixels generally acquire minimum or maximum pixel values i.e. either 0 or 255. So if the pixel is non noisy, leave it unprocessed otherwise, apply the adaptive median filter to it. Then, the statistical parameters within this window are extracted which include minimum (min), maximum (max) and median values (median) for the pixels. Two conditional decisions are applied at this level on the basis of the extracted statistical parameters. Thus, if the median value lies between the min and the max pixel values; it is further verified if the centre pixel x(i,j) also lies within these limits. Upon fulfillment of the former condition, the centre pixel, x(i,j) is left unprocessed {y(i,j) = x(i,j)} otherwise x(i,j) is replaced by the median value {y(i,j) = median}; where: y(i,j) denotes the restored pixel value. However, during the conditional check if the median value does not lie within the min and the max pixel values; the size of the window (w) is adaptively increased by a factor of 2. Thereafter, shifting the spatial window (centering it) to the next pixel in the noisy image. The control then transfers again to the first step, extracting the parameters within this incremented window. It is worth noting that, the increment in the window size is permissible only to a maximum limit (wmax) of 9x9; beyond which the centre pixel will be always replaced by the last processed pixel value. To

III. RESULTS AND DISCUSSIONS The proposed filter is tested using 256×256, 8-bits/pixel gray scale high detailed image of Barbara as input image. This image is corrupted by impulse noise at various densities and performance is objectively evaluated using the parameters such as Peak Signal to Noise Ratio (PSNR) in dB [55]-[58] and Structural Similarity Index (SSIM) [59]-[61] to ensure that the obtained results are in reasonable coherence with HVS [62][65]. Fig. 1. (a)-(i) shows the images which have been corrupted by the impulse noise of different intensities ranging from 10-90% respectively whereas Fig. 1. (j)-(r) shows the denoised images obtained by the proposed filter. To prove the objectivity of the proposed algorithm, experiments are carried out on further three standard images, Pepper as representatives for low detail images, Cameraman for medium detail images, Baboon for high detail images. All images are grayscale ones with intensity values in the range of [0, 255]. Images are of size 256×256. Fig. 2,3,4 shows comparison among the restored images obtained by standard DMF [40], the method proposed in work of A. Jourabloo et al. [54] and the proposed filter in this paper for three images of Pepper, Cameraman and Baboon. The quantitative performances in terms of PSNR and SSIM for all the above mentioned algorithms are shown in Table I and II, III and IV respectively. It is clear from the Table I for Barbara image that at all noise levels i.e. from 10% to 90% the performance the proposed filter outperforms the existing one; as validated by the computed values of PSNR and SSIM. The qualitative analysis from Fig. 1 proves that the level of impulse noise is considerably reduced and the visualization is also improved to a great extent in the reconstructed images. Till 50% noise density, there is very less blurring in the restored image supported with higher PSNR and SSIM values. Even on increasing the noise density (50%-90%), the performance of the proposed filter is still able to preserve the details of the image along with suppression of residual noise. Table II, III and IV illustrate increased values of quantitative parameters thereby demonstrating that the proposed filter is well suited for high noise levels. The same is also implicit from the visual quality of the restored images. Fig. 2, 3 and 4 shows images recovered from conventional DMF method [40] and the proposed filter respectively at 80% noise density. The results shows that conventional DMF fails at high noise density and even the result of method [54] are also not satisfactory and images are over-smoothened that leads to loss 80% noise density) is promising. Thus, it can be visualized from the obtained results that the proposed filter tends to improve the performance of ordinary DMF approach; yielding above satisfactory results even for high density impulse noise

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2014 International Conference on Signal Processing and Integrated Networks (SPIN)

Fig. 1. Shows the results of the proposed filter for various impulse noise densities. (a)-(i) denotes the input noisy images. (j)-(r) denotes images restored with the proposed filter. above satisfactory results even for high density impulse noise wide range of noise densities in comparison to other filtering along with preservation of fine image details. approaches.

Table I. Results of PSNR and SSIM for different filters for Barbara. PSNR (dB) SSIM

Impulse Noise Density

DMF [40]

Method [54]

Proposed Filter

DMF [40]

Method [54]

Proposed Filter

10%

32.88

33.56

37.84

0.985

0.987

0.998

20%

29.44

30.47

34.81

0.968

0.974

0.996

30%

27.22

28.41

32.67

0.945

0.956

0.994

40%

25.48

26.98

31.23

0.919

0.937

0.991

50%

23.94

25.67

29.44

0.888

0.914

0.987

60%

22.62

24.63

27.78

0.851

0.891

0.981

70%

21.33

23.54

26.12

0.797

0.858

0.971

80%

19.84

22.40

24.29

0.713

0.816

0.957

90%

17.49

20.95

23.06

0.525

0.735

0.936

REFERENCES

IV. CONCLUSION

[1]

This paper proposes a non-iterative adaptive median filter for suppression of impulse noise at high noise intensities; without incorporation of complex optimization techniques. The proposed approach performs decision to adaptively increase the window size depending upon the number of corrupted pixels within the local window to a maximum of 9x9. Simulation results show that the proposed filter offers an effective improvement in the performance of the DMF across a

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A. Jain and V. Bhateja, “An Improved Image Denoising Algorithm using Robust Estimation for High Density Salt and Pepper Noise,” Proc. of (IEEE) International Conference on Digital Convergence (ICDC-2011), Chennai (India), pp. 25-30, February, 2011. A. Garg, J. Shukla, A. Jain, and V. Bhateja, “An Optimal Spatial Domain Edge Detector for Images Corrupted with Salt and Pepper Noise,” Proc. of (IEEE) 4th International Conference on Electronics & Computer Technology (ICECT-2012), Kanyakumari (India), Vol. 1, pp. 77-81, April 2012. A. Jain and V. Bhateja, “An Iterative Non-Linear Filtering Approach for Suppression of High Density Impulse Noise in Mammographic Images,” Proc. of (IEEE) 3rd International Conference on Machine Learning and Computing (ICMLC-2011), Singapore, vol. 3, pp. 527531, February 2011.

2014 International Conference on Signal Processing and Integrated Networks (SPIN)

[4]

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P. Gupta, P. Srivastava, S. Bharadwaj and V. Bhateja,"A New Model for Performance Evaluation of Denoising Algorithms based on Image Quality Assessment," Proc. of (ACM ICPS) CUBE International Information Technology Conference & Exhibition, Pune, India, pp. 5-10, September, 2012. V. Bhateja and S. Devi, “Combination of Wavelet Analysis and NonLinear Enhancement Function for Computer Aided Detection of Microcalcifications,” Proc. of International Conference on Biomedical Engineering and Assistive Technologies (BEATs-2010), Jalandhur (India), pp.44, December 2010. V. Bhateja and S. Devi, “Mammographic Image Enhancement using Double Sigmoid Transformation Function,” Proc. of International Conference on Computer Applications, India, pp.259-264, Dec 2010. V. Bhateja and S. Devi, “An Improved Non-Linear Transformation Function for Enhancement of Mammographic Breast Masses,” Proc. of (IEEE) 3rd International Conference on Electronics & Computer Technology (ICECT-2011), India, vol. 5, pp. 341-346, April 2011. V. Bhateja and S. Devi, “A Novel Framework for Edge Detection of Microcalcifications using a Non-Linear Enhancement Operator and Morphological Filter,” Proc. of (IEEE) 3rd Int. Conf. on Electronics & Computer Technology, India, vol. 5, pp. 419-424, 2011. Siddhartha, R. Gupta and V. Bhateja, “A New UnSharp Masking Algorithm for Mammography using Non-Linear Enhancement Function,” Proc. of the (Springer) International Conference on Information Systems Design and Intelligent Applications (INDIA 2012), Vishakhapatnam, India, pp. 779-786, January 2012.

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(e) Fig. 3. Showing results of various filters on a MediumDetailed Image (a) Cameraman image corrupted by 80%; (b) original image; (c) using DMF [40]; (d) using method in [54]; (e) using Proposed filter.

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(e) Fig. 4. Showing results of various filters on a HighDetailed Image (a) Baboon image corrupted by 80%; (b) original image; (c) using DMF [40]; (d) using method in [54]; (e) using Proposed filter.

Table II. Comparison of Various Denoising Filters in terms of PSNR (in dB) and SSIM for Less Detailed Image: Peppers.

(e) Fig. 2. Showing results of various filters on a LessDetailed Image (a) Pepper image corrupted by 80%; (b) original image; (c) using DMF [40]; (d) using method in [54]; (e) using Proposed filter.

DMF [40]

Method[54]

Proposed Filter

Impulse Noise Density

PSNR

SSIM

PSNR

SSIM

PSNR

SSIM

40%

27.07

0.943

33.29

0.993

35.70

0.995

80%

14.82

0.583

28.25

0.978

30.17

0.984

Table III. Comparison of Various Denoising Filters in terms of PSNR (in dB) and SSIM for Medium Detailed Image: Cameraman.

(a)

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DMF [40]

Method[54]

Proposed Filter

Impulse Noise Density

PSNR

SSIM

PSNR

SSIM

PSNR

SSIM

40%

22.75

0.951

24.96

0.975

27.60

0.985

80%

11.82

0.643

22.55

0.955

23.09

0.962

2014 International Conference on Signal Processing and Integrated Networks (SPIN)

[22]

Table IV. Comparison of Various Denoising Filters in terms of PSNR (in dB) and SSIM for High Detailed Image: Baboon. DMF [40] Impulse Noise Density PSNR SSIM

[10]

[11]

[12]

[13]

[14]

[15]

[16]

[17]

[18]

[19]

[20]

[21]

Method[54]

Proposed Filter [23]

PSNR

SSIM

PSNR

SSIM

40%

23.08

0.905

26.54

0.942

28.56

0.967

80%

11.70

0.573

24.13

0.911

24.78

0.924

[24]

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