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Quantum and impulse noise filtering from breast mammogram images
c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 0 8 ( 2 0 1 2 ) 1062–1069
journal homepage: www.intl.elsevierhealth.com/journals/cmpb
Quantum and impulse noise filtering from breast mammogram images Nawazish Naveed a , Ayyaz Hussain b , M. Arfan Jaffar a,c,∗ , Tae-Sun Choi c a b c
National University of Computer & Emerging Sciences, Islamabad, Pakistan International Islamic University, Islamabad, Pakistan Gwangju Institute of Science and Technology, South Korea
a r t i c l e
i n f o
a b s t r a c t
Article history:
Recent advances in the field of image processing have shown that level of noise highly affect
Received 7 October 2011
the quality and accuracy of classification when working with mammographic images. In this
Received in revised form
paper, we have proposed a method that consists of two major modules: noise detection and
18 June 2012
noise filtering. For detection purpose, neural network is used which effectively detect the
Accepted 17 July 2012
noise from highly corrupted images. Pixel values of the window and some other features
Keywords:
used. The weighted average value of these three filters is filled on noisy pixels. The proposed
are used as feature for the training of neural network. For noise removal, three filters are Quantum
technique has been tested on salt & pepper and quantum noise present in mammogram
Impulse
images. Peak signal to noise ratio (PSNR) and structural similarity index measure (SSIM) are
Breast mammograms
used for comparison of proposed technique with different existing techniques. Experiments
Neural network
shows that proposed technique produce better results as compare to existing methods. © 2012 Elsevier Ireland Ltd. All rights reserved.
1.
Introduction
Classification accuracy of mammogram images is adversely affected by the noise present in the image. Study reveals that overall accuracy of systems decrease significantly with increase in noise and this decrease can become as significant as 21% drop in quality [1]. The effect of the noise element becomes more prominent in the task of microcalcification detection and mass discrimination. This decrease can be as significant as drop from 89% to 67% in the case of micro-calcifications from 93% to 79% in the case of mass discrimination performance [1]. Image restoration, being a significant step of image processing, works on image reconstruction by removing noise, blurriness, etc. to make them human perceptible [2]. This noise can be added due to several factors during acquisition,
∗
preprocessing or any other stage of image processing. Liu and Li, in their reviews [3], have divided spatial image restoration techniques into two main categories namely conventional and blind image restoration. The first classification comprises of those approaches which use well known information about image degradation. Such techniques resolve several issues like motion blur degradation, distortion, additive noise, etc. However, in real life such information is often not available readily. Making such approaches is difficult to apply. The second set of techniques attempt to reconstruct the image in the absence of any prior information about image attributes [3]. No information about degradation process is available to such techniques as well. This set of techniques is recently gaining more prominence. One major accomplishment of these techniques is to remove the noise or blurriness without affecting the image details in adverse manner. As it is common knowledge that image smoothing and tail preservation are in conflict
Corresponding author at: Gwangju Institute of Science and Technology, South Korea. E-mail addresses: [email protected] (N. Naveed), [email protected] (A. Hussain), [email protected] (M. Arfan Jaffar), [email protected] (T.-S. Choi). 0169-2607/$ – see front matter © 2012 Elsevier Ireland Ltd. All rights reserved. http://dx.doi.org/10.1016/j.cmpb.2012.07.002
c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 0 8 ( 2 0 1 2 ) 1062–1069
with each other since smoothening will ultimately damage edge information whereas any attempt to sharpen the edges will result in noise enhancement [4]. In our work, we have presented NN based noise detection and filtering technique deploying three filters for noise removal and detail preservation. Mammogram images are generally afflicted by quantum/Poisson noise [5]. The algorithm discussed for noise removal has used Anscombe Transform (AT) and Wiener filter followed by an image enhancement algorithm. This image enhancement algorithm works on modulation Transfer Function based inverse filter. Sarah and Maytham used Takagi neuro-fuzzy filter for noise removal in images corrupted with impulsive and Poisson noise [6]. Tukey [7], Pitas et al. [8] have used median filtering to remove this kind of noise. If the noise level in images is low, median filter can perform reasonably well. However, its performance deteriorates when noise level reaches or moves above 0.5. This filter is also responsible for removing vital details such as sharp edges and thin lines. Center weighted media (CWM) filters are one of the promising approaches studied and investigated in this particular class [9]. A set of weighting parameters is used in WM filters which control the performance to preserve image details beyond losing a certain threshold. A CWM is merely a specialized case of WM filters. A noise adaptive soft switching median (NASM) filter was presented by Eng et al. [4] which achieved much improved performance at the cost of low detail loss. However it also faced the same dilemma of performance deterioration with increase in noise volume and probability. BDND is a switching median filter with impulse noise detection. BDND first classifies the pixels of a localized window, centering on the current pixel, into three groups-lower intensity impulse noise, uncorrupted pixels, and higher intensity impulse noise. NNID is an approach to detect the impulse noise from the corrupted image using feed forward neural network (FFNN). NNID is a modified version of the arithmetic mean filter, used for impulse noise detection. There are yet other machine learning based noise removal filters present in literature [10] to handle impulse noise. For instance, Detail Preserving Fuzzy Filter for impulse noise removal (DPFF) [11], the modified histogram based fuzzy filter (MHBFF) [12], genetic based fuzzy image filter (GFIF) [13], fuzzy impulse noise detection and reduction method (FIDRM) [14] and modified histogram based fuzzy filter (MHFF) [15], fuzzy based impulse noise reduction method (FBINR) [22] and a hybrid image restoration approach: fuzzy logic and directional weighted median based uniform impulse noise removal [21] are some of the examples of such algorithms. Recently FIDRM and FRINR are used for impulse noise reduction. Both these methods work on random valued impulse noise. DPFF and MHFF are good for salt and pepper noise as well as long tailed impulse noise but not well suited for quantum/Poisson noise. Proposed technique not only removes these kinds of noise yet it preserves image details as well. The purpose of our proposed technique is to deliver more accurate results while preserving the image detail in terms of noise detection and filtering. For this purpose, we have deployed a structured mechanism of neural network (NN) along with a combination of filters such as non local mean (NLM) filter, adaptive wiener filter and frost filter based
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method. The technique performs much better filtering of impulse noise while preserving image details for gray scale images corrupted with salt and pepper noise. The contributions of this technique include: • A technique using neural network based impulse noise detection which uses image contents and some other features for accurate detection of noise is proposed. • For noise removal and detail preservation, a combination of efficient filters is proposed.
2.
Noise model
Two types of noises in mammogram images, which are addressed in this paper, are salt and pepper and quantum/Poisson noise can be modeled as in the following way.
2.1.
Quantum/Poisson noise model
The most significant kind of noise in mammogram images is quantum noise. This noise is added in the images during acquisition due to low count X-ray photons. Being signal dependent in nature, it can be described by Poisson distribution [5]. Gaussian model is used to represent electronic noise and later this can be used in digital mammographic image g as an additive term, according to equation. g=u+n
(1a)
where u is the mammographic image blurred by the acquisition system modulation transfer function and corrupted by quantum noise, and n is the additive Gaussian noise incorporated to the digitized mammographic image g. The distribution of Poisson noise can be represented by Eq. (1b)
f (k; ) =
k e− k!
(1b)
where k is the number of occurrences of an event and is a positive real number. The image containing quantum noise is given below. The nature of quantum noise is such that it affects all the pixels of the image with very low variation which is difficult to be experienced by naked eye. However the images below in Fig. 1 are the original and quantum noise added mammogram images.
2.2.
Salt and pepper noise model
With this kind of noise, one pixel is assigned either minimum or maximum intensity value. In case of impulse noise, this type is considered to be most simple and most widely used. Other pixels can have any value from allowed dynamic limit when we use random values impulse noise model. In our work, our main area of attention is separation of both these kind of noises from 8-bit gray scale images. Let x(i, j) and y(i, j) be the pixel values at position (i, j) of the original and noisy image, respectively. Where p is the
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Fig. 1 – Quantum noise added image. (a) Original image. (b) Noisy image (Poisson noise).
probability of impulse noise model. This can be described in this way.
x(i, j) =
o(i, j)
1−p
(i, j)
p
3.1.
Impulse noise detection
The impulse noise detector serves as a switch for the filter. This filter becomes active for only those pixels which have (2) Input Image
where (i, j) is the noisy pixel at position (i, j) and o(i, j) is the probability of non noisy pixel in the original image. The noisy pixel (i, j) can get value between 0 and 255 for 8-bit grayscale image.
Neural Network base Noise Detector
Take WF X WF Window
Proposed technique
Our proposed work comprises of two steps i.e. noise detection and separation. Neural networks are used for detection purposes. First of all, training of NN is performed for which data is given below. After training, NN becomes capable of separation of noisy pixels from non-noisy ones. This trained NN perform filtering so that noisy pixels can be separated for removal. A combination of frost, non local mean and adaptive wiener filter is used for denoising the image. All the three filters are considered as efficient in terms of their performance. The filtering is performed over a window of variable size depending upon noise density. Initially, a window of size 3 × 3 is selected. The size of window is increased with increase in noise threshold. This increase takes place on a level of one pixel in each direction. With increase in window size, more and more noisy pixels keep on filtering. Detailed architecture of proposed system for noise detection and filtering is given in Fig. 2. It is composed of NN based noise detector, Adaptive Size Window Calculator, and combination of filters. Detail steps of noise detection and filtering are given below.
Noise Map and Noise Density
Move Window 1 pixel ahead
3.
Determine Maximum Window Size
Determine WF Size
Adaptive Wiener Filter
Non local Mean Filter
Frost filter
Weighted Mean Value
Fig. 2 – Proposed system architecture.
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large window size and can differentiate edges with the help of small window size. Combining all these three filters using weighted average, gives us an approach which is efficient on one hand and preserve necessary image details on the other hand. This has been our motivation to use these three filters in combination. The detail of these filters is given below.
Table 1 – Neural network parameters. No. of input neurons No. of hidden layer No. of hidden layer neurons Threshold No. of output layer neurons
14 1 5 0.5 1
been marked as noisy. This detector is NN based as described above. There are 14 inputs which are fed to back propagation neural networks. First we have taken 3 × 3 window (9 pixel values)and is transformed into a single column format. Then absolute difference of maximum and minimum pixel value in the window is taken. If this value is higher than the threshold, it means window contains either noise or edgy pixels. Maximum of absolute difference of center pixel from all pixels of the window is considered to check whether region is smooth or noisy. After that, absolute difference of median and mean of the window from central pixel is extracted. Last feature is absolute background difference. In our proposed technique, NN is used to detect impulse noise. Parameters used for neural network shown in Table 1. In order to create training data, salt and pepper noise with 50% probability was added in images. After that, we have extracted features discussed above over whole image. Each movement creates a new input vector. This process yields almost 128 × 128 samples. Each sample has all fourteen values of the input vector. The state of central pixel is given as a target for each sample. The training of NN is performed over this sample. In the beginning, random values are assigned as weights to hidden and output layer. Each ample is fed as input and its output is calculated. Difference of each output against the target is accumulated over all samples. Mean square error (MSE) is used as a metric to measure performance. The resultant MSE is used to update weights of hidden and output layer weights. If MSE becomes less than a certain threshold, the whole process stops. In this way neural net is trained on the dataset. When neural net is trained, it is tested with a test image. Once the training is complete, NN is saved and used for detection of noisy pixels. Output of the neural network is a value between 0 and 1. So by applying a threshold T, we decide whether a pixel is noisy or not.
noisymap(i, j) =
3.2.
1, if output > T 0, else
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(3)
Noise filtering
For noise removal, we propose a combination of frost, adaptive wiener and non local mean (NLM) filter for the removal of noise. All the above mentioned filters are considered as efficient for different noise filtering problems but these filters have not been applied together in one framework for noise removal in mammogram images. It is worthwhile to mention that Wiener filter has already been used for noise removal from mammogram images and proved as efficient for the purpose [5]. As for as frost filter is concerned, its particular trait of replacing central pixel value with the weighted sum of all pixels in n × n window makes it a very efficient filter to detect salt and pepper noise. Non local mean filter due to its varying window size can cover large uniform space very quickly with
3.2.1.
Frost filter
This is an adaptive and exponentially weighted averaging filter. In this filter, the coefficient of variation is the ratio of the local standard deviation to the local mean of the degraded image. Being a ratio based filter [16], it uses weighted sum of values within n × n window to replace central pixel. As the difference between central and other pixels decreases, the weighting factor also decreases and vice versa. Frost filter follows the following formula:
DN =
n×n
k˛e−˛|t|
(4)
where ˛=
4 2 n¯ 2
n¯I2
k = normalization constant; ¯I = local mean; = local variance; ¯ = image coefficient of variation value |t| = |X − Xo | + |Y − Yo | where |X − Xo | is the modulus of difference from average value in x direction and |Y − Yo | is the difference of modulus from average value in y direction n = moving kernel size.
3.2.2.
Weiner filter
This particular method calculates local mean and variance of each pixel using the formulas [17]. =
1 a(n1 , n2 ) NM n1 ,n2 ∈
(5)
The above equation gives the estimate of the mean value using a neighborhood of size N by M. The value of this mean is used to calculate the variance of the image using equation below. 2 =
1 a2 (n1 , n2 ) − 2 NM n1 ,n2 ∈
(6)
where is the N-by-M local neighborhood of each pixel in the image A, apply pixel wise Wiener filter using following estimates b(n1 , n2 ) = +
2 − vz (a(n1 , n2 ) − ) 2
(7)
where 2 is the noise variance.
3.2.3.
Non local mean (NLM) filter
The NLM filter [18] averages similar image pixels defined according to their local intensity similarity. For an image Y, at
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Table 2 – Suggested window size for the estimated noise density level p [19]. WD1 × WD1
Noise density 0% < p ≤ 20% 20% < p ≤ 40% >40%
3×3 5×5 7×7
any given point p, the filtered value computed by NLM is the weighted average of all pixels in the image using this equation: NLM(Y(p)) =
w(p, q)Y(q)
∀q ∈
0 ≤ w(p, q) ≤ 1,
(8)
w(p, q) = 1
We take window size adaptive to handle the different ratio of noise. As the noise density increases in case of salt and paper noise, we increase the window size to get it smoother. Readjustments in the window size also help in identifying edges from the blank space. In order to detect edges, a small window size of 3 × 3 is applied. With the smallest window size possible we can differentiate between noise and the edge. Pseudo code of getting adaptive window size as suggested in Table 2 is given below Initially take a 3 × 3 window centered on current pixel. WF = 3 Set WD1 according to While (Nc < Sin AND WF ≤ WD1 ) OR (Nc = 0) Increase the size of WF by 1 pixel in each direction
∀q ∈
where p be the point to be filtered and q is the pixels in the neighborhood of radius Rsearch . The weights w(p, q) are based on the similarity between the neighborhoods Np and Nq of pixels p and q. Ni is defined as a square neighborhood window centered around pixel i with a user-defined radius Rsim . The similarity w(p, q) is then calculated as: w(p, q) =
1 −(d(p,q)/h2 ) e Z(p)
(9)
where Z(p) is called normalizing constant and can be calculated as: Z(p) =
−(d(p,q)/h2 )
4.
Experiments and results
(10)
e
∀q
and h is an exponential decay control parameter and d is a Gaussian weighted Euclidian distance of all the pixels of each neighborhood:
Take non-noisy pixels from the current window. Apply all three filters using non-noisy pixels only. Take mean of the result of all three filters and replace it with central pixel. Move the window 1 pixel ahead. where Nc the number of is uncorrupted pixels within the filtering window and Sin is half of the total number of pixels in the filtering window. Where noise density is the count of number of 1s on the binary decision map obtained in the noise detection stage.
2
d(p, q) = G˛ Y(Np ) − Y(Nq ) Rsim
(11)
where G˛ represents the Gaussian weighting function which is normalized at zero (0) mean and standard deviation ˛ (normally set to 1). The center pixel of the Gaussian weighting window is adjusted as the same value that the pixels at a distance 1 to avoid over-weighting effects. When p = q then the self similarity is very high, this may causes the over-weighting effect. To address this problem w(p, p) is calculated in this way: w(p, q) = max(w(p, q) ∀q = / p)
(12)
Classification accuracy is measured in the presence of noise in the mammogram images and it is observed that presence of noise badly affect the classification accuracy. We have extracted texture features from breast mammogram images of MIAS dataset and used different classifiers like neural network (NN), Bayesian, K-nearest neighbor (KNN) and support vector machine (SVM). Table 3 shows the comparison of classification accuracy in the presence/absence of noise in mammogram images. Table 3 also shows that the presence of noise also hampers abnormality type detection significantly. With the removal of noise, classification efficiency considerably improves for the given image. This is one reason why we should perform noise removal before feature extraction. Recent techniques first detect the noise and then filter it from images. Their quality is actually a mirror of quality of noise detection approach used. The reason behind better performance of our proposed method also lies in the better noise detection mechanism. A very strong feature set is used to perform detection which results in better results. These features
Table 3 – Classification accuracy with and without noise. Technique
NN + features Bayesian + features KNN + features SVM + features
Mammogram with Poisson noise accuracy (%) 58.2 59.1 76.4 81.2
Mammogram with salt and pepper noise (10%) accuracy (%) 56.3 57.5 75.7 80.6
Mammogram with accuracy (%) without noise 63.6 63.1 88.3 98.3
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Table 4 – Comparison of missed detection and false alarms of proposed technique with BDND [19], NASM [4], and NNID [20] for mammogram image. Density (salt and pepper noise)
No. of missed detection (MD) Proposed
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0 0 0 0 0 2 4 7 13
BDND
NASM
0 0 0 0 0 0 0 21 190
60 141 368 862 2031 4641 11,232 35,017 124,927
No. of false alarm (FA) NNID
Proposed
BDND
NASM
0 0 0 0 1 2 3 6 9
0 2 1 5 7 6 10 10 5
2742 755 436 272 178 131 93 404 2609
1 1 0 0 0 0 0 0 0
NNID 3 2 0 1 0 0 0 0 0
Table 5 – PSNR comparisons of different techniques at noise density 0.1–0.9 and Poisson noise. Density of salt and pepper noise
PSNR of noisy image
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Poisson noise
PSNR (NLM)
16.427 13.438 12.676 10.4355 9.4818 8.7099 7.9864 7.4358 6.9023 30.887
PSNR (Frost)
31.188 30.466 28.586 26.792 24.38 21.701 20.176 19.816 18.5 38.635
have strong ability to differentiate noisy pixels from non-noisy ones. The results clearly highlight that using NN with proposed set of inputs performs better than any other methods present in literature. Different filters have been used for noise removal. The proposed method takes average of the result obtained from all three filters. It is also noted through experiments that features/details remain preserved after applying these filters. We have used state of the art methods for comparison purpose against our proposed technique. Different impulse noise ratios of salt and pepper noise have been used to demonstrate the effectiveness of our model. Various subjective as well as quantitative measures have been used to validate the results. The quantitative measures used are peaksignal-to-noise-ratio (PSNR) and structural similarity index
PSNR (Wiener)
30.741 30.239 27.354 26.643 25.972 22.868 20.03 19.337 18.342 34.557
PSNR (combined)
30.273 30.936 27.772 26.324 23.716 22.617 20.571 19.623 19.122 34.705
32.108 31.441 28.948 27.756 26.118 23.015 21.932 20.074 19.969 40.125
measure (SSIM), which can be defined by the following equation. PSNR(F, O) = 10 × log10
S2 MSE(F, O)
(13)
Original image is represented by O and restored image is F of size NM. Maximum possible intensity value is S (for 8-bit images the maximum is 255) and MSE is mean square error defined by the following equation. 1 2 (O(i, j) − F(i, j)) MN M
MSE(F, O) =
N
(14)
i=1 j=1
Table 6 – Comparison of de-noising methods for mammogram image degraded with impulse and quantum/Poisson noise having corruption rate for impulse noise , where = 0.1 to 0.9. Method
Noisy image Ayyaz et al. [21] MHBFF DPFF FBINR Proposed
Quality measure
PSNR SSIM PSNR SSIM PSNR SSIM PSNR SSIM PSNR SSIM PSNR SSIM
Noise corruption rate
Poisson noise
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
15.426 0.231 38.10 0.885 34.103 0.839 35.612 0.865 37.753 0.910 38.189 0.912
12.439 0.125 35.213 0.817 34.117 0.836 35.009 0.817 34.154 0.883 35.466 0.890
10.675 0.0808 33.17 0.791 34.064 0.829 34.312 0.694 32.466 0.872 33.585 0.882
9.4356 0.0572 31.981 0.765 34.008 0.815 33.464 0.494 31.524 0.845 32.793 0.865
8.4817 0.0405 30.102 0.679 33.913 0.773 32.438 0.295 29.277 0.814 30.39 0.839
7.7098 0.0292 27.052 0.648 33.678 0.666 31.273 0.158 27.18 0.732 27.70 0.765
6.9864 0.0184 25.150 0.543 33.267 0.451 30.133 0.082 26.79 0.571 26.17 0.627
6.4359 0.0133 23.562 0.513 32.567 0.208 29.01 0.038 25.32 0.428 24.81 0.468
5.903 0.0091 21.71 0.253 31.15 0.0681 28.02 0.0175 23.44 0.313 22.51 0.382
30.887 0.7592 – – – – – – – – 40.12 0.932
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Fig. 3 – (a) Original image. (b) Corrupted with Poisson noise (PSNR = 30.887). (c) Denoised by Frost (PSNR = 34.557). (d) Wiener (PSNR = 34.705). (e) NLM filter (PSNR = 38.635). (f) Combined filtering (PSNR = 40.125).
SSIM(x, y) =
(2x y + c1 )(2xy + c2 ) (2x
+ 2y
+ c1 )(x2
+ y2
+ c2 )
(15)
where x , y are the averages of x and y, x2 , y2 are the variances of x, y and xy is the covariance of x and y. c1 = (k1 L)2 , c2 = (k2 L)2 , are two variables to stable the division with weak denominator, L is the dynamic range of the pixel-values (typically this is 2#bits per pixel − 1) and k1 = 0.01 and k2 = 0.03 by default. The proposed neural network based noise detection technique compared with following three techniques NNID [20], BDND [19] and NASM [4] are given. In Table 4, a comparative analysis of noise detection performance of our proposed technique with competitive techniques based on missed detection and false alarm. Table 4 clearly represents that proposed technique gives superior results for mass detection that all other techniques for mammogram images. The superior advantage of this technique is in its equally good performance to NNID [20]. As far as a false alarm for mammogram images is concerned, the proposed technique outperforms all other competitive approaches in most of the cases. Results of proposed technique for PSNR with respect to all three individual techniques are presented in Table 5. The test image for this experimentation was corrupted with
various noise rates in the range of 0.1–0.9. The test image was taken from MIAS dataset and the image reference number is mdb009. The same image has been used to achieve the results shown in Table 6. In Table 6, we have evaluated and compared the results of proposed technique with all other techniques for PSNR and SSIM. The results again highlight the superiority of our technique for images corrupted with noise ratios below 0.6 for PSNR. However, the technique performs much better for its detail preserving capability as it gives much accurate noise detection over whole range of impulse noise corrupted images as well as for quantum noise. Fig. 3 presents the visual results of the individual filters and combined filters are given. Visual results show that the proposed technique preserves the feature details.
5.
Conclusion
In this paper, we have presented a neural network based noise detection scheme along with a noise removal technique which combines three different filters (Frost, NLM and adaptive Wiener). Average value of all three filters is filled to approximate the non-noisy values of the noisy pixels detected by
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the noise detection process. The technique has been subjected to extensive experimentation and results were evaluated and compared with different leading noise detection and filtering techniques from literature for various quality measures. The results clearly show superiority of proposed work against leading techniques both in terms of noise detection and filtering based on well-known quantitative measures PSNR and SSIM. This noise detection as described in this paper is prelude to the future work where ultimately binary classification is achieved after background and noise removal as performed in this paper. The work described in this paper can be further enhanced in several aspects. The particular model suggested in this paper is effective for salt pepper noise but cannot work with quantum noise due to its peculiar nature (quantum noise spans over all the pixels of the image). Any further contribution can refine the model in such a way that quantum noise detection is performed as well. The data on which the experimentation has been performed is only composed of benign and malign images. Further experimentation can be performed by adding additional class of normal images and observing what impact it can create. Such experimentation can further determine the suitability of proposed model for commercial applications. Moreover, in proposed work, the neural network is trained on only one image of size 128 × 128 pixels in overlapping fashion. One can evaluate the result by adding noise in multiple images and then getting pixels from all those images for training the neural net.
Conflict of interest No conflict of interest.
Acknowledgement This work was supported by the Bio Imaging Research Center at Gwangju Institute of Science and Technology (GIST) Korea.
references
[1] R.S. Saunders Jr., J.A. Baker, D.M. Delong, J.P. Johnson, E. Samei, Does image quality matter? Impact of resolution and noise on mammographic task performance, Medical Physics 34 (October (10)) (2007) 3971–3981. [2] A.M. Mirza, A. Chaudhry, B. Munir, Spatially adaptive image restoration using fuzzy punctual kriging, Journal of Computer Science and Technology 22 (4) (2007) 580–589. [3] P. Liu, H. Li, Fuzzy techniques in image restoration research – a survey (invited paper), International Journal of Computational Cognition 2 (June (2)) (2004) 131–149. [4] H.-L. Eng, K.-K. Ma, Noise adaptive soft-switching median filter, IEEE Transactions on Image Processing 10 (February (2)) (2001) 242–251. [5] L.C. dos Santos Romualdo, Mammography images restoration by quantum noise reduction and inverse MTF filtering, Proceedings,.ieeecomputersociety.org/10.1109/SIBGRAPI.2009.12.
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[6] S.B. Aziz, M.A. Shahed, Impulsive and Poisson noises removal using Takagi neuro-fuzzy network, Scientific Journal of King Faisal University (Basic and Applied Sciences) 11 (1) (2010) 1431. [7] J.W. Tukey, Exploratory Data Analysis, Addison-Wesley, Reading, MA, 1971. [8] I. Pitas, A. Venetsanopoulos, Nonlinear Digital Filters: Principles and Application, Kluwer, Norwell, MA, 1990. [9] S.J. Ko, S.J. Lee, Center weighted median filters and their applications to image enhancement, IEEE Transactions on Circuits and Systems 15 (September (9)) (1991) 984–993. [10] M. Senthil Arumugam, M.V.C. Rao, A. Chandramohan, A new and improved version of particle swarm optimization algorithm with global–local best parameters, Knowledge and Information Systems 16 (3) (2008) 331–357. [11] A. Hussain, M. Arfan Jaffar, A.M. Mirza, A. Chaudhry, Detail preserving fuzzy filter for impulse noise removal, International Journal of Innovative Computing, Information and Control (IJICIC) 5 (December (12)) (2009). [12] A. Hussain, M. Arfan Jaffar, A.B. Siddiqui, M. Nazir, A.M. Mirza, Modified histogram based fuzzy filter, Lecture Notes in Computer Science 5496/2009 (2009) 277–284. [13] C.-S. Lee, S.-M. Guo, C.-Y. Hsu, Genetic-based fuzzy image filter and its applications to image processing, IEEE Transactions on Systems Man and Cybernetics 35 (August (4)) (2005) 694–711. [14] S. Schulte, M. Nachtegael, V. de Witte, D. Van der Weken, E.E. Kerre, A fuzzy impulse noise detection and reduction method, IEEE Transactions on Image Processing 15 (May (5)) (2006) 1153–1162. [15] S. Masood, A. Hussain, M. Arfan Jaffar, A.M. Mirza, T.-S. Choi, Fuzzy random impulse noise reduction technique based on statistical estimators, International Journal of Innovative Computing, Information and Control (IJICIC) 7 (June (6)) (2011) 3395–3406. [16] V.S. Frost, J.A. Stiles, K.S. Shanmugam, J.C. Holtzman, A model for radar image & its application to adaptive digital filtering for multiplicative noise, IEEE Transaction on Pattern Analysis and Machine Intelligence PMAI-4 (1982) 175–216. [17] J.S. Lim, Two-dimensional Signal and Image Processing, Prentice Hall, Englewood Cliffs, NJ, 1990, p. 548, equations 9.44–9.46. [18] A. Buades, B. Coll, J.M. Morel, A review of image denoising algorithms, with a new one, Multiscale Modeling and Simulation 4 (2) (2005) 490–530. [19] P.-E. Ng, K.-K. Ma, Senior Member, IEEE, A switching median filter with boundary discriminative noise detection for extremely corrupted images, IEEE Transactions on Image Processing 15 (June (6)) (2006). [20] G. Kaliraj, S. Baskar, An efficient approach for the removal of impulse noise from the corrupted image using neural network based impulse detector, Image and Vision Computing 28 (2010) 458–466. [21] A. Hussain, M. Arfan Jaffar, A.M. Mirza, A hybrid image restoration approach: fuzzy logic and directional weighted median based uniform impulse noise removal, Knowledge and Information System 24 (July (1)) (2010) 77–90. [22] A. Hussain, S.M. Bhatti, M. Arfan Jaffar, Fuzzy based impulse noise reduction method, Multimedia Tools and Application (2011), http://dx.doi.org/10.1007/s11042-011-0829-7.
journal homepage: www.intl.elsevierhealth.com/journals/cmpb
Quantum and impulse noise filtering from breast mammogram images Nawazish Naveed a , Ayyaz Hussain b , M. Arfan Jaffar a,c,∗ , Tae-Sun Choi c a b c
National University of Computer & Emerging Sciences, Islamabad, Pakistan International Islamic University, Islamabad, Pakistan Gwangju Institute of Science and Technology, South Korea
a r t i c l e
i n f o
a b s t r a c t
Article history:
Recent advances in the field of image processing have shown that level of noise highly affect
Received 7 October 2011
the quality and accuracy of classification when working with mammographic images. In this
Received in revised form
paper, we have proposed a method that consists of two major modules: noise detection and
18 June 2012
noise filtering. For detection purpose, neural network is used which effectively detect the
Accepted 17 July 2012
noise from highly corrupted images. Pixel values of the window and some other features
Keywords:
used. The weighted average value of these three filters is filled on noisy pixels. The proposed
are used as feature for the training of neural network. For noise removal, three filters are Quantum
technique has been tested on salt & pepper and quantum noise present in mammogram
Impulse
images. Peak signal to noise ratio (PSNR) and structural similarity index measure (SSIM) are
Breast mammograms
used for comparison of proposed technique with different existing techniques. Experiments
Neural network
shows that proposed technique produce better results as compare to existing methods. © 2012 Elsevier Ireland Ltd. All rights reserved.
1.
Introduction
Classification accuracy of mammogram images is adversely affected by the noise present in the image. Study reveals that overall accuracy of systems decrease significantly with increase in noise and this decrease can become as significant as 21% drop in quality [1]. The effect of the noise element becomes more prominent in the task of microcalcification detection and mass discrimination. This decrease can be as significant as drop from 89% to 67% in the case of micro-calcifications from 93% to 79% in the case of mass discrimination performance [1]. Image restoration, being a significant step of image processing, works on image reconstruction by removing noise, blurriness, etc. to make them human perceptible [2]. This noise can be added due to several factors during acquisition,
∗
preprocessing or any other stage of image processing. Liu and Li, in their reviews [3], have divided spatial image restoration techniques into two main categories namely conventional and blind image restoration. The first classification comprises of those approaches which use well known information about image degradation. Such techniques resolve several issues like motion blur degradation, distortion, additive noise, etc. However, in real life such information is often not available readily. Making such approaches is difficult to apply. The second set of techniques attempt to reconstruct the image in the absence of any prior information about image attributes [3]. No information about degradation process is available to such techniques as well. This set of techniques is recently gaining more prominence. One major accomplishment of these techniques is to remove the noise or blurriness without affecting the image details in adverse manner. As it is common knowledge that image smoothing and tail preservation are in conflict
Corresponding author at: Gwangju Institute of Science and Technology, South Korea. E-mail addresses: [email protected] (N. Naveed), [email protected] (A. Hussain), [email protected] (M. Arfan Jaffar), [email protected] (T.-S. Choi). 0169-2607/$ – see front matter © 2012 Elsevier Ireland Ltd. All rights reserved. http://dx.doi.org/10.1016/j.cmpb.2012.07.002
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with each other since smoothening will ultimately damage edge information whereas any attempt to sharpen the edges will result in noise enhancement [4]. In our work, we have presented NN based noise detection and filtering technique deploying three filters for noise removal and detail preservation. Mammogram images are generally afflicted by quantum/Poisson noise [5]. The algorithm discussed for noise removal has used Anscombe Transform (AT) and Wiener filter followed by an image enhancement algorithm. This image enhancement algorithm works on modulation Transfer Function based inverse filter. Sarah and Maytham used Takagi neuro-fuzzy filter for noise removal in images corrupted with impulsive and Poisson noise [6]. Tukey [7], Pitas et al. [8] have used median filtering to remove this kind of noise. If the noise level in images is low, median filter can perform reasonably well. However, its performance deteriorates when noise level reaches or moves above 0.5. This filter is also responsible for removing vital details such as sharp edges and thin lines. Center weighted media (CWM) filters are one of the promising approaches studied and investigated in this particular class [9]. A set of weighting parameters is used in WM filters which control the performance to preserve image details beyond losing a certain threshold. A CWM is merely a specialized case of WM filters. A noise adaptive soft switching median (NASM) filter was presented by Eng et al. [4] which achieved much improved performance at the cost of low detail loss. However it also faced the same dilemma of performance deterioration with increase in noise volume and probability. BDND is a switching median filter with impulse noise detection. BDND first classifies the pixels of a localized window, centering on the current pixel, into three groups-lower intensity impulse noise, uncorrupted pixels, and higher intensity impulse noise. NNID is an approach to detect the impulse noise from the corrupted image using feed forward neural network (FFNN). NNID is a modified version of the arithmetic mean filter, used for impulse noise detection. There are yet other machine learning based noise removal filters present in literature [10] to handle impulse noise. For instance, Detail Preserving Fuzzy Filter for impulse noise removal (DPFF) [11], the modified histogram based fuzzy filter (MHBFF) [12], genetic based fuzzy image filter (GFIF) [13], fuzzy impulse noise detection and reduction method (FIDRM) [14] and modified histogram based fuzzy filter (MHFF) [15], fuzzy based impulse noise reduction method (FBINR) [22] and a hybrid image restoration approach: fuzzy logic and directional weighted median based uniform impulse noise removal [21] are some of the examples of such algorithms. Recently FIDRM and FRINR are used for impulse noise reduction. Both these methods work on random valued impulse noise. DPFF and MHFF are good for salt and pepper noise as well as long tailed impulse noise but not well suited for quantum/Poisson noise. Proposed technique not only removes these kinds of noise yet it preserves image details as well. The purpose of our proposed technique is to deliver more accurate results while preserving the image detail in terms of noise detection and filtering. For this purpose, we have deployed a structured mechanism of neural network (NN) along with a combination of filters such as non local mean (NLM) filter, adaptive wiener filter and frost filter based
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method. The technique performs much better filtering of impulse noise while preserving image details for gray scale images corrupted with salt and pepper noise. The contributions of this technique include: • A technique using neural network based impulse noise detection which uses image contents and some other features for accurate detection of noise is proposed. • For noise removal and detail preservation, a combination of efficient filters is proposed.
2.
Noise model
Two types of noises in mammogram images, which are addressed in this paper, are salt and pepper and quantum/Poisson noise can be modeled as in the following way.
2.1.
Quantum/Poisson noise model
The most significant kind of noise in mammogram images is quantum noise. This noise is added in the images during acquisition due to low count X-ray photons. Being signal dependent in nature, it can be described by Poisson distribution [5]. Gaussian model is used to represent electronic noise and later this can be used in digital mammographic image g as an additive term, according to equation. g=u+n
(1a)
where u is the mammographic image blurred by the acquisition system modulation transfer function and corrupted by quantum noise, and n is the additive Gaussian noise incorporated to the digitized mammographic image g. The distribution of Poisson noise can be represented by Eq. (1b)
f (k; ) =
k e− k!
(1b)
where k is the number of occurrences of an event and is a positive real number. The image containing quantum noise is given below. The nature of quantum noise is such that it affects all the pixels of the image with very low variation which is difficult to be experienced by naked eye. However the images below in Fig. 1 are the original and quantum noise added mammogram images.
2.2.
Salt and pepper noise model
With this kind of noise, one pixel is assigned either minimum or maximum intensity value. In case of impulse noise, this type is considered to be most simple and most widely used. Other pixels can have any value from allowed dynamic limit when we use random values impulse noise model. In our work, our main area of attention is separation of both these kind of noises from 8-bit gray scale images. Let x(i, j) and y(i, j) be the pixel values at position (i, j) of the original and noisy image, respectively. Where p is the
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Fig. 1 – Quantum noise added image. (a) Original image. (b) Noisy image (Poisson noise).
probability of impulse noise model. This can be described in this way.
x(i, j) =
o(i, j)
1−p
(i, j)
p
3.1.
Impulse noise detection
The impulse noise detector serves as a switch for the filter. This filter becomes active for only those pixels which have (2) Input Image
where (i, j) is the noisy pixel at position (i, j) and o(i, j) is the probability of non noisy pixel in the original image. The noisy pixel (i, j) can get value between 0 and 255 for 8-bit grayscale image.
Neural Network base Noise Detector
Take WF X WF Window
Proposed technique
Our proposed work comprises of two steps i.e. noise detection and separation. Neural networks are used for detection purposes. First of all, training of NN is performed for which data is given below. After training, NN becomes capable of separation of noisy pixels from non-noisy ones. This trained NN perform filtering so that noisy pixels can be separated for removal. A combination of frost, non local mean and adaptive wiener filter is used for denoising the image. All the three filters are considered as efficient in terms of their performance. The filtering is performed over a window of variable size depending upon noise density. Initially, a window of size 3 × 3 is selected. The size of window is increased with increase in noise threshold. This increase takes place on a level of one pixel in each direction. With increase in window size, more and more noisy pixels keep on filtering. Detailed architecture of proposed system for noise detection and filtering is given in Fig. 2. It is composed of NN based noise detector, Adaptive Size Window Calculator, and combination of filters. Detail steps of noise detection and filtering are given below.
Noise Map and Noise Density
Move Window 1 pixel ahead
3.
Determine Maximum Window Size
Determine WF Size
Adaptive Wiener Filter
Non local Mean Filter
Frost filter
Weighted Mean Value
Fig. 2 – Proposed system architecture.
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large window size and can differentiate edges with the help of small window size. Combining all these three filters using weighted average, gives us an approach which is efficient on one hand and preserve necessary image details on the other hand. This has been our motivation to use these three filters in combination. The detail of these filters is given below.
Table 1 – Neural network parameters. No. of input neurons No. of hidden layer No. of hidden layer neurons Threshold No. of output layer neurons
14 1 5 0.5 1
been marked as noisy. This detector is NN based as described above. There are 14 inputs which are fed to back propagation neural networks. First we have taken 3 × 3 window (9 pixel values)and is transformed into a single column format. Then absolute difference of maximum and minimum pixel value in the window is taken. If this value is higher than the threshold, it means window contains either noise or edgy pixels. Maximum of absolute difference of center pixel from all pixels of the window is considered to check whether region is smooth or noisy. After that, absolute difference of median and mean of the window from central pixel is extracted. Last feature is absolute background difference. In our proposed technique, NN is used to detect impulse noise. Parameters used for neural network shown in Table 1. In order to create training data, salt and pepper noise with 50% probability was added in images. After that, we have extracted features discussed above over whole image. Each movement creates a new input vector. This process yields almost 128 × 128 samples. Each sample has all fourteen values of the input vector. The state of central pixel is given as a target for each sample. The training of NN is performed over this sample. In the beginning, random values are assigned as weights to hidden and output layer. Each ample is fed as input and its output is calculated. Difference of each output against the target is accumulated over all samples. Mean square error (MSE) is used as a metric to measure performance. The resultant MSE is used to update weights of hidden and output layer weights. If MSE becomes less than a certain threshold, the whole process stops. In this way neural net is trained on the dataset. When neural net is trained, it is tested with a test image. Once the training is complete, NN is saved and used for detection of noisy pixels. Output of the neural network is a value between 0 and 1. So by applying a threshold T, we decide whether a pixel is noisy or not.
noisymap(i, j) =
3.2.
1, if output > T 0, else
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(3)
Noise filtering
For noise removal, we propose a combination of frost, adaptive wiener and non local mean (NLM) filter for the removal of noise. All the above mentioned filters are considered as efficient for different noise filtering problems but these filters have not been applied together in one framework for noise removal in mammogram images. It is worthwhile to mention that Wiener filter has already been used for noise removal from mammogram images and proved as efficient for the purpose [5]. As for as frost filter is concerned, its particular trait of replacing central pixel value with the weighted sum of all pixels in n × n window makes it a very efficient filter to detect salt and pepper noise. Non local mean filter due to its varying window size can cover large uniform space very quickly with
3.2.1.
Frost filter
This is an adaptive and exponentially weighted averaging filter. In this filter, the coefficient of variation is the ratio of the local standard deviation to the local mean of the degraded image. Being a ratio based filter [16], it uses weighted sum of values within n × n window to replace central pixel. As the difference between central and other pixels decreases, the weighting factor also decreases and vice versa. Frost filter follows the following formula:
DN =
n×n
k˛e−˛|t|
(4)
where ˛=
4 2 n¯ 2
n¯I2
k = normalization constant; ¯I = local mean; = local variance; ¯ = image coefficient of variation value |t| = |X − Xo | + |Y − Yo | where |X − Xo | is the modulus of difference from average value in x direction and |Y − Yo | is the difference of modulus from average value in y direction n = moving kernel size.
3.2.2.
Weiner filter
This particular method calculates local mean and variance of each pixel using the formulas [17]. =
1 a(n1 , n2 ) NM n1 ,n2 ∈
(5)
The above equation gives the estimate of the mean value using a neighborhood of size N by M. The value of this mean is used to calculate the variance of the image using equation below. 2 =
1 a2 (n1 , n2 ) − 2 NM n1 ,n2 ∈
(6)
where is the N-by-M local neighborhood of each pixel in the image A, apply pixel wise Wiener filter using following estimates b(n1 , n2 ) = +
2 − vz (a(n1 , n2 ) − ) 2
(7)
where 2 is the noise variance.
3.2.3.
Non local mean (NLM) filter
The NLM filter [18] averages similar image pixels defined according to their local intensity similarity. For an image Y, at
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Table 2 – Suggested window size for the estimated noise density level p [19]. WD1 × WD1
Noise density 0% < p ≤ 20% 20% < p ≤ 40% >40%
3×3 5×5 7×7
any given point p, the filtered value computed by NLM is the weighted average of all pixels in the image using this equation: NLM(Y(p)) =
w(p, q)Y(q)
∀q ∈
0 ≤ w(p, q) ≤ 1,
(8)
w(p, q) = 1
We take window size adaptive to handle the different ratio of noise. As the noise density increases in case of salt and paper noise, we increase the window size to get it smoother. Readjustments in the window size also help in identifying edges from the blank space. In order to detect edges, a small window size of 3 × 3 is applied. With the smallest window size possible we can differentiate between noise and the edge. Pseudo code of getting adaptive window size as suggested in Table 2 is given below Initially take a 3 × 3 window centered on current pixel. WF = 3 Set WD1 according to While (Nc < Sin AND WF ≤ WD1 ) OR (Nc = 0) Increase the size of WF by 1 pixel in each direction
∀q ∈
where p be the point to be filtered and q is the pixels in the neighborhood of radius Rsearch . The weights w(p, q) are based on the similarity between the neighborhoods Np and Nq of pixels p and q. Ni is defined as a square neighborhood window centered around pixel i with a user-defined radius Rsim . The similarity w(p, q) is then calculated as: w(p, q) =
1 −(d(p,q)/h2 ) e Z(p)
(9)
where Z(p) is called normalizing constant and can be calculated as: Z(p) =
−(d(p,q)/h2 )
4.
Experiments and results
(10)
e
∀q
and h is an exponential decay control parameter and d is a Gaussian weighted Euclidian distance of all the pixels of each neighborhood:
Take non-noisy pixels from the current window. Apply all three filters using non-noisy pixels only. Take mean of the result of all three filters and replace it with central pixel. Move the window 1 pixel ahead. where Nc the number of is uncorrupted pixels within the filtering window and Sin is half of the total number of pixels in the filtering window. Where noise density is the count of number of 1s on the binary decision map obtained in the noise detection stage.
2
d(p, q) = G˛ Y(Np ) − Y(Nq ) Rsim
(11)
where G˛ represents the Gaussian weighting function which is normalized at zero (0) mean and standard deviation ˛ (normally set to 1). The center pixel of the Gaussian weighting window is adjusted as the same value that the pixels at a distance 1 to avoid over-weighting effects. When p = q then the self similarity is very high, this may causes the over-weighting effect. To address this problem w(p, p) is calculated in this way: w(p, q) = max(w(p, q) ∀q = / p)
(12)
Classification accuracy is measured in the presence of noise in the mammogram images and it is observed that presence of noise badly affect the classification accuracy. We have extracted texture features from breast mammogram images of MIAS dataset and used different classifiers like neural network (NN), Bayesian, K-nearest neighbor (KNN) and support vector machine (SVM). Table 3 shows the comparison of classification accuracy in the presence/absence of noise in mammogram images. Table 3 also shows that the presence of noise also hampers abnormality type detection significantly. With the removal of noise, classification efficiency considerably improves for the given image. This is one reason why we should perform noise removal before feature extraction. Recent techniques first detect the noise and then filter it from images. Their quality is actually a mirror of quality of noise detection approach used. The reason behind better performance of our proposed method also lies in the better noise detection mechanism. A very strong feature set is used to perform detection which results in better results. These features
Table 3 – Classification accuracy with and without noise. Technique
NN + features Bayesian + features KNN + features SVM + features
Mammogram with Poisson noise accuracy (%) 58.2 59.1 76.4 81.2
Mammogram with salt and pepper noise (10%) accuracy (%) 56.3 57.5 75.7 80.6
Mammogram with accuracy (%) without noise 63.6 63.1 88.3 98.3
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Table 4 – Comparison of missed detection and false alarms of proposed technique with BDND [19], NASM [4], and NNID [20] for mammogram image. Density (salt and pepper noise)
No. of missed detection (MD) Proposed
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0 0 0 0 0 2 4 7 13
BDND
NASM
0 0 0 0 0 0 0 21 190
60 141 368 862 2031 4641 11,232 35,017 124,927
No. of false alarm (FA) NNID
Proposed
BDND
NASM
0 0 0 0 1 2 3 6 9
0 2 1 5 7 6 10 10 5
2742 755 436 272 178 131 93 404 2609
1 1 0 0 0 0 0 0 0
NNID 3 2 0 1 0 0 0 0 0
Table 5 – PSNR comparisons of different techniques at noise density 0.1–0.9 and Poisson noise. Density of salt and pepper noise
PSNR of noisy image
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Poisson noise
PSNR (NLM)
16.427 13.438 12.676 10.4355 9.4818 8.7099 7.9864 7.4358 6.9023 30.887
PSNR (Frost)
31.188 30.466 28.586 26.792 24.38 21.701 20.176 19.816 18.5 38.635
have strong ability to differentiate noisy pixels from non-noisy ones. The results clearly highlight that using NN with proposed set of inputs performs better than any other methods present in literature. Different filters have been used for noise removal. The proposed method takes average of the result obtained from all three filters. It is also noted through experiments that features/details remain preserved after applying these filters. We have used state of the art methods for comparison purpose against our proposed technique. Different impulse noise ratios of salt and pepper noise have been used to demonstrate the effectiveness of our model. Various subjective as well as quantitative measures have been used to validate the results. The quantitative measures used are peaksignal-to-noise-ratio (PSNR) and structural similarity index
PSNR (Wiener)
30.741 30.239 27.354 26.643 25.972 22.868 20.03 19.337 18.342 34.557
PSNR (combined)
30.273 30.936 27.772 26.324 23.716 22.617 20.571 19.623 19.122 34.705
32.108 31.441 28.948 27.756 26.118 23.015 21.932 20.074 19.969 40.125
measure (SSIM), which can be defined by the following equation. PSNR(F, O) = 10 × log10
S2 MSE(F, O)
(13)
Original image is represented by O and restored image is F of size NM. Maximum possible intensity value is S (for 8-bit images the maximum is 255) and MSE is mean square error defined by the following equation. 1 2 (O(i, j) − F(i, j)) MN M
MSE(F, O) =
N
(14)
i=1 j=1
Table 6 – Comparison of de-noising methods for mammogram image degraded with impulse and quantum/Poisson noise having corruption rate for impulse noise , where = 0.1 to 0.9. Method
Noisy image Ayyaz et al. [21] MHBFF DPFF FBINR Proposed
Quality measure
PSNR SSIM PSNR SSIM PSNR SSIM PSNR SSIM PSNR SSIM PSNR SSIM
Noise corruption rate
Poisson noise
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
15.426 0.231 38.10 0.885 34.103 0.839 35.612 0.865 37.753 0.910 38.189 0.912
12.439 0.125 35.213 0.817 34.117 0.836 35.009 0.817 34.154 0.883 35.466 0.890
10.675 0.0808 33.17 0.791 34.064 0.829 34.312 0.694 32.466 0.872 33.585 0.882
9.4356 0.0572 31.981 0.765 34.008 0.815 33.464 0.494 31.524 0.845 32.793 0.865
8.4817 0.0405 30.102 0.679 33.913 0.773 32.438 0.295 29.277 0.814 30.39 0.839
7.7098 0.0292 27.052 0.648 33.678 0.666 31.273 0.158 27.18 0.732 27.70 0.765
6.9864 0.0184 25.150 0.543 33.267 0.451 30.133 0.082 26.79 0.571 26.17 0.627
6.4359 0.0133 23.562 0.513 32.567 0.208 29.01 0.038 25.32 0.428 24.81 0.468
5.903 0.0091 21.71 0.253 31.15 0.0681 28.02 0.0175 23.44 0.313 22.51 0.382
30.887 0.7592 – – – – – – – – 40.12 0.932
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Fig. 3 – (a) Original image. (b) Corrupted with Poisson noise (PSNR = 30.887). (c) Denoised by Frost (PSNR = 34.557). (d) Wiener (PSNR = 34.705). (e) NLM filter (PSNR = 38.635). (f) Combined filtering (PSNR = 40.125).
SSIM(x, y) =
(2x y + c1 )(2xy + c2 ) (2x
+ 2y
+ c1 )(x2
+ y2
+ c2 )
(15)
where x , y are the averages of x and y, x2 , y2 are the variances of x, y and xy is the covariance of x and y. c1 = (k1 L)2 , c2 = (k2 L)2 , are two variables to stable the division with weak denominator, L is the dynamic range of the pixel-values (typically this is 2#bits per pixel − 1) and k1 = 0.01 and k2 = 0.03 by default. The proposed neural network based noise detection technique compared with following three techniques NNID [20], BDND [19] and NASM [4] are given. In Table 4, a comparative analysis of noise detection performance of our proposed technique with competitive techniques based on missed detection and false alarm. Table 4 clearly represents that proposed technique gives superior results for mass detection that all other techniques for mammogram images. The superior advantage of this technique is in its equally good performance to NNID [20]. As far as a false alarm for mammogram images is concerned, the proposed technique outperforms all other competitive approaches in most of the cases. Results of proposed technique for PSNR with respect to all three individual techniques are presented in Table 5. The test image for this experimentation was corrupted with
various noise rates in the range of 0.1–0.9. The test image was taken from MIAS dataset and the image reference number is mdb009. The same image has been used to achieve the results shown in Table 6. In Table 6, we have evaluated and compared the results of proposed technique with all other techniques for PSNR and SSIM. The results again highlight the superiority of our technique for images corrupted with noise ratios below 0.6 for PSNR. However, the technique performs much better for its detail preserving capability as it gives much accurate noise detection over whole range of impulse noise corrupted images as well as for quantum noise. Fig. 3 presents the visual results of the individual filters and combined filters are given. Visual results show that the proposed technique preserves the feature details.
5.
Conclusion
In this paper, we have presented a neural network based noise detection scheme along with a noise removal technique which combines three different filters (Frost, NLM and adaptive Wiener). Average value of all three filters is filled to approximate the non-noisy values of the noisy pixels detected by
c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 0 8 ( 2 0 1 2 ) 1062–1069
the noise detection process. The technique has been subjected to extensive experimentation and results were evaluated and compared with different leading noise detection and filtering techniques from literature for various quality measures. The results clearly show superiority of proposed work against leading techniques both in terms of noise detection and filtering based on well-known quantitative measures PSNR and SSIM. This noise detection as described in this paper is prelude to the future work where ultimately binary classification is achieved after background and noise removal as performed in this paper. The work described in this paper can be further enhanced in several aspects. The particular model suggested in this paper is effective for salt pepper noise but cannot work with quantum noise due to its peculiar nature (quantum noise spans over all the pixels of the image). Any further contribution can refine the model in such a way that quantum noise detection is performed as well. The data on which the experimentation has been performed is only composed of benign and malign images. Further experimentation can be performed by adding additional class of normal images and observing what impact it can create. Such experimentation can further determine the suitability of proposed model for commercial applications. Moreover, in proposed work, the neural network is trained on only one image of size 128 × 128 pixels in overlapping fashion. One can evaluate the result by adding noise in multiple images and then getting pixels from all those images for training the neural net.
Conflict of interest No conflict of interest.
Acknowledgement This work was supported by the Bio Imaging Research Center at Gwangju Institute of Science and Technology (GIST) Korea.
references
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