Applied Soft Computing 13 (2013) 817–832

Contents lists available at SciVerse ScienceDirect

Applied Soft Computing journal homepage: www.elsevier.com/locate/asoc

Neuro fuzzy and punctual kriging based filter for image restoration Asmatullah Chaudhry a,b , Asifullah Khan c,∗ , Anwar M. Mirza d , Asad Ali e , Mehdi Hassan c , Jin Young Kim b a

Human Resource Development, PINSTECH, Nilore, Islamabad, Pakistan School of Electronics and Computer Engineering, Chonnam National University, Gwangju, South Korea Department of Computer and Information Sciences, PIEAS, Nilore, Islamabad, Pakistan d College of Computer and Information Sciences, King Saud University, Riyadh, Saudi Arabia e Institute of Industrial Science, University of Tokyo, Japan b c

a r t i c l e

i n f o

Article history: Received 10 January 2012 Received in revised form 16 August 2012 Accepted 31 October 2012 Available online 10 November 2012 Keywords: Image restoration Fuzzy logic Artificial neural networks (ANNs) Punctual kriging Adaptive spatial filtering Neuro fuzzy classifier (NFC)

a b s t r a c t In this paper, we present a hybrid, image restoration approach. The proposed approach combines the geostatistical interpolation of punctual kriging, artificial neural networks (ANNs), and fuzzy logic based approaches. Images degraded with Gaussian white noise are restored by first utilizing fuzzy logic for selecting pixels that needs kriging. Three fuzzy systems are employed. Both type-I and type-II fuzzy sets in addition with neuro fuzzy classifier (NFC) have been used for the detection of noisy pixels. To avoid edge pixels, a post processing technique is used to check the edge pixel connectivity up to lag 5. If the pixel under consideration is an edge pixel, it is excluded from the fuzzy map and thus not estimated. The concept of punctual kriging is then used to estimate the intensity of a noisy pixel. ANN is employed to minimize the cost function of the kriging based pixel intensity estimation procedure. ANN, in contrast to analytical methodologies, avoids both matrix inversion failure and negative weights problems. Image restoration performance based comparison has been made against adaptive Weiner filter and existing fuzzy kriging approaches. Experimental results using 450 images are used to validate the effectiveness of the proposed approach. Different image quality measures are used to compare the efficacy of the proposed NFC and fuzzy type-II approaches for detecting noisy pixels in conjunction with ANN and kriging based estimation. © 2012 Elsevier B.V. All rights reserved.

1. Introduction Image restoration has become a widely investigated field of image processing. In spite of the advances made by recent methods, it is still a challenging task as these methods have yet to achieve a desirable level of applicability in many realistic scenarios. Moreover, with the ever increasing production of digital contents such as images and videos acquired with low resolution cameras and in poor conditions. In such cases, the importance of image restoration has significantly increased. One of the primary tasks in developing image restoration techniques is noise removal without destroying edge information. Noise smoothing and edge enhancement are generally considered as conflicting tasks. Since smoothing a region might destroy an edge while sharpening edges might lead to amplification of unnecessary noise [1]. Therefore, we present a new spatial filtering technique; a neural approach based on

∗ Corresponding author at: Department of Computer and Information Sciences (DCIS), Pakistan Institute of Engineering and Applied Sciences, Nilore 45650, Islamabad, Pakistan. Tel.: +92 51 2207381; fax: +92 51 2208070. E-mail addresses: [email protected], asif [email protected] (A. Khan). 1568-4946/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.asoc.2012.10.017

punctual kriging and fuzzy logic control. This new approach takes into account this conflict and tries to remove noise, while efficiently preserving the image details and edges information. Punctual kriging, named after its developer, Krige [2] is heavily used in mining and geostatistics based applications. It is an interpolation technique that gives an optimal linear estimate of an unknown parameter at a sampling point in terms of its known values at the surrounding sampling points [3]. The estimation involves calculation of the semi-variances and modeling of semi-variograms from the sampled data. Besides this, kriging has been applied in many other fields as well. Fuzzy filters have been extensively applied in image processing over the last decade. Young Sik and Krishnapuram [4] devised fuzzy rule based multiple filters, derived from the method of weighted least squares, for noise removal. Some researchers have also investigated the use of fuzzy clustering for the removal of impulsive noise [5–7]. In [8], Farbiz and Menhaj have introduced an approach of image filtering based on fuzzy logic control. They have shown how to remove impulsive noise and smooth out Gaussian noise while, simultaneously, preserving image details and edges efficiently. Liang and Looney [9] have proposed a competition fuzzy edge detector to distinguish the noisy pixels from the edge

818

A. Chaudhry et al. / Applied Soft Computing 13 (2013) 817–832

pixels. Further, Khriji and Gabbouj [10] have recently proposed a fuzzy transformation based approach for multichannel image processing. Fuzzy spatial filters have been widely explored for restoration of images. However, with the increase of local information, the number of fuzzy rules in these filters also increases accordingly. To reduce the requirement of such complicated rules, fuzzy control is used as a complementary tool along with the existing techniques to develop better and accurate methods. This is one of the major aims of the investigations presented in this paper. In the most basic image restoration approach using neural networks, noise is removed from the image by simple filtering. Cellular neural networks by Chua and Yang [11,12] have been proposed for noise suppression. Improvements have been done for training cellular neural networks that make use of genetic algorithms by Zamparelli [13]. Generalized adaptive neural filter [14,15] is another interesting neural architecture for noise filtering. It consists of a set of neural operators based on stack filters [14] that make use of binary decomposition of gray valued data. Combination of order statistic filters and Hopfield neural network have also been developed and used by Qian et al. [16] for noise removal and image de-blurring. Suetake and Uchino [17] have proposed a radial basis function network and Wiener hybrid filter to exploit merits of both for removing noise with an arbitrary distribution. Multilevel sigmoidal activation functions [18] are used by Sivakumar et al. to model a blurred and noisy image with many gray levels without any knowledge of the statistics of the additive noise and blurring function. In [19], Widyanto et al. have proposed a method to improve recognition as well as generalization capability of back-propagation neural network as a hidden layer self-organization inspired by immune algorithm. Recently, Palmer et al. [20] have introduced a spatially regularized neural approach that makes use of local image statistics to apply varying regularization to different areas of the image by using a parallel implementation of the Hopfield neural network. Gwanggil et al. [21], have proposed deinterlacing technique based on a type-II fuzzy logic filter and have introduced application of type-II fuzzy sets for interpolation of interlaced fields. Similarly in [1] an image filtering with hybrid impulse detector is proposed. Several techniques [22–25] have also been proposed using the wavelet transform for image denoising. These methods perform a combination of statistical modeling and thresholding on wavelet coefficients at different decomposition levels to suppress noise. More recently, curvelets [26] and ridgelets [27] have been employed for line structure preservation while denoising images. Similarly, Portilla at al. [28] have proposed a method based on using scale mixtures of Gaussians in the wavelet domain for removing noise. Their idea is based on modeling the coefficients at adjacent positions and scales as a product of two independent random variables which allows it to account for empirically observed correlation between the coefficient amplitudes. Moreover, a kernel based method has also been proposed recently by Laparra et al. [29] using support vector regression in the wavelet domain. It tries to non-explicitly model the relationship between wavelet coefficients by encoding specific coefficient relations in an anisotropic kernel. Whereby, the kernel is obtained from mutual information measure computed on a database of images. The non-parametric nature of their method allows it to cope with different types of noise sources without any reformulation. Although, wavelet based methods have performed well in denoising images but they use fixed basis, which is often not suitable for images having rich amount of locally varying structural patterns specially, the natural scenes. Thus these methods introduce several visual artifacts in the reconstructed images [30]. To overcome some of the disadvantages of wavelet transform, Lei et al. [30] have recently proposed a two stage principal

Table 1 The abbreviations used in the text. FIS MSE PSNR wPSNR SSIM VMSE VPSNR BPN AWF PWFK SAFK NFC

Fuzzy inference system Mean squared error Peak signal-to-noise ratio Weighted peak signal-to-noise ratio Structural similarity index measure Variogram based mean squared error Variogram based peak signal-to-noise ratio Backpropagation neural network Adaptive Wiener filter Pham and Wagner fuzzy kriging Spatially adaptive fuzzy kriging Neuro fuzzy classifier

component analysis (PCA) based denoising method, which uses the local pixel grouping and data selection. The primary idea behind this approach follows from earlier works on image denoising which make use of PCA transformation for filtering out noise by selecting and preserving the most significant principal components [31]. The first stage in their method yields an initial estimate of the image by removing most of the noise and the second stage further refines the output. However PCA based methods often result in reconstruction with missing fine details thus significantly effecting local structural similarity in complex pictures with several edges. Besides Pham and Wagner [32,33] have used punctual kriging along with fuzzy sets to enhance images corrupted by Gaussian white noise. They model soft-thresholding by fuzzy sets. In their approach, the pixel intensity in the processed image is a weighted sum of the original (noisy) and the estimated value through kriging. They have evaluated their results qualitatively in comparison with adaptive Wiener filter [34]. However, their study does not provide any quantitative performance analysis of their proposed technique [35,36]. In addition, they apply kriging to all pixels in the degraded image. Considering 3 × 3 neighborhood, inverse of a kriging matrix of size 9 × 9 is required, that can make the filtering process computationally expensive. In addition, due to a zero diagonal, inverse of the kriging matrix may not always be possible. The filter weights also suffer from the problem of negative values, which leads to an overall poor performance of the filter. It is also reported that separating noise and original signal from a single input image is under constrained, in theory it is very difficult to recover the original signal [37]. In this paper, we thus propose a hybrid technique based on fuzzy inference system, neural net and punctual kriging for image restoration. This paper makes the following contributions: we introduce an effective hybrid neuro-fuzzy based kriging methodology for image denoising. Both type-I and type-II fuzzy sets and NFC have been employed for decision making about the noisy and noise free pixels. We solve both the problems of matrix inversion failure and the negative weights in punctual kriging by exploiting learning capabilities of artificial neural network (ANN). A post processing phase is also employed to improve the noise decision map by reducing the wrong selected edge pixels. For clarity and understanding, in Table 1, first we present the abbreviations that have been used in the text. Rest of the paper is structured as follows: Section 2 introduces punctual kriging and variograms, fuzzy inference system, type-I and type-II fuzzy sets. It also presents some review of ANNs used for image restoration and few of the most commonly used image quality measures along with the proposed variogram based quality measure. Section 3 explains the proposed hybrid technique based on punctual kriging and the neuro-fuzzy approach of adaptive learning. Experimental results and discussion is presented in Section 4. Conclusions are made in Section 5.

A. Chaudhry et al. / Applied Soft Computing 13 (2013) 817–832

2. Related theory

zero and rearranging the system of equations, these can be written in matrix form as:

⎛

2.1. Punctual kriging and variogram Punctual kriging provides the best linear unbiased estimate of an unknown point on a surface [38]. The estimate is the weighted sum of the known neighboring values around the unknown point. The weights are determined to minimize the variance of the estimationerror. To achieve this, kriging uses a variogram model (a concept from geostatistics). Based on the variogram model chosen, known values are assigned optimal weights to calculate the unknown value. Variogram presents the variation of semi-variance with respect to distance from a point. Semi-variance provides a measure of spatial dependence between samples. Semi-variance [3] of the samples at lag ‘d’ can be calculated from Eq. (1). (d) =

Var(zi+d − zi ) 2

(1)

Different distance metrics can be used to identify a group of neighboring samples having the same lag. In the present investigations, however, we have considered the Euclidean metric as the distance measure. The experimental semi-variogram is obtained directly by using the sample values from the experimental data. For a given lag ‘d’, it is calculated from the available data as: 1  (zi − zi+d )2 2N(d) N(d)

(d) =

(2)

i=1

The above expression for experimental semi-variogram depends upon the spatial configuration of the available image data. One has to consider different cases, as to whether the data is aligned or not and whether it is regularly spaced along the alignments. However in the present case of digital images, the data is aligned and regularly spaced, which makes the estimation of the semi-variogram easy. Punctual kriging is a linear combination of the neighboring sample values, as given by Eq. (3). zˆ =



(3)

wi zi

i

where wi is the weights and zi is the neighboring values of z. It is an unbiased estimator if the weights add up to 1. This additional constraint on weights is given by:



wi = 1

(4)

i

Statistical variance is measure of how different the estimated value is from its neighboring sample values. It can be found using Eq. (5). Var(e) = Var(z − zˆ )

(5)

A number of such linear unbiased estimators are available, but we find the best one in the sense that it has the smallest estimation variance. Thus, the cost function is defined as:

ϕ(wi , ) = Var(e) − 2

819

 

 wi − 1

(d11 )

(d12 )

···

(d1n )

⎜ (d ) (d ) · · · (d ) ⎜ 21 22 2n ⎜ ⎜ . .. .. .. ⎜ .. . . . ⎜ ⎜ ⎝ (dn1 ) (dn2 ) · · · (dnn ) 1

1

1

1

1

⎞⎛

w1

⎞

⎛

(d1 )

⎞

⎟ ⎜ ⎟ ⎜ (d ) ⎟ ⎜ 2 ⎟ ⎟⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎟ .. ⎟ ⎜ . ⎟ = ⎜ .. ⎟ ⎜ ⎟ . ⎟ ⎜ .. ⎟ ⎜ . ⎟ ⎟⎜ ⎟ ⎜ ⎟ 1 ⎠ ⎝ wn ⎠ ⎝ (dn ) ⎠ 1 ⎟ ⎜ w2 ⎟

0



(7)

1

or in matrix–vector notations Aw = b

(8)

The A matrix is symmetric and has zero diagonal elements. The elements of the matrix are taken from the semi-variogram (defined in Eq. (1)) for the current point. Solving Eq. (8) gives us the optimal kriging weights {w1 , w2 , . . . , wn } for estimating the unknown value zˆ using its neighbors. However, if A is a singular matrix then punctual kriging fails to estimate pixel intensity. 2.2. Fuzzy inference system and fuzzy smoothing There are two types of FIS, that are commonly used i.e. Mamdani and Takagi-Sugeno type [39]. Both types of FIS are similar in many aspects; fuzzifying the inputs and applying the fuzzy operator. The Takagi-Sugeno output membership functions are either linear or constant and this aspect mainly differs from the Mamdani type [40]. Since classification of noisy pixels from an image is considered as a nonlinear process. In the proposed approach, nonlinear fuzzy output membership functions are employed to decide the fate of a pixel. Therefore, we have used Mamdani type FIS because the decision making of whether a pixel needs to be estimated or not, depending upon the local properties of the neighborhood, is a challenging problem [41]. Type-II fuzzy sets are considered as a generalization of the ordinary fuzzy sets, whereby fuzzy sets are characterized by a fuzzy membership function and consequently, the membership value for each member of the set is itself a fuzzy set in (0, 1) [42]. The main advantages of using a type-II framework are twofold; by using type-II fuzzy sets one can transform a vague pattern classification problem into a precise, well-defined, optimization problem, and secondly type-II fuzzy sets, unlike ordinary fuzzy sets, retain a controlled degree of uncertainty [43]. In the current work, in addition to type-I, we have also used type-II fuzzy sets for decision making about the pixel’s fate (generation of decision map). Fuzzy logic based smoothing filters have also been applied by many researchers in signal and image processing based applications. These include fuzzy rank selection filter, fuzzy weighted filter, switching fuzzy filter and fuzzy neural network filter [44,45]. However in the current work, we use a neuro-fuzzy filter in our approach. In the present work, we have used both fuzzy based intelligent decision-making and fuzzy smoothing to improve the performance of the proposed spatial neuro-fuzzy filter. The main use of the fuzzy inference system is to generate a fuzzy map from the degraded image, which is then employed by the neuro-fuzzy filter to enhance the degraded image. Further, fuzzy smoothing is used to smooth out the unselected pixels within the proposed filter. 2.3. Artificial neural networks

(6)

i

where  is the Lagrange multiplier. Differentiating the cost function ϕ(wi , ) with respect to wi and  and setting the differential equal to

The functional strength of ANN has already been demonstrated by many researchers in different areas such as pattern recognition and classification [46–50] image restoration [51], and machine vision [52,53]. Consequently, we use ANN to solve the set of

820

A. Chaudhry et al. / Applied Soft Computing 13 (2013) 817–832

equations obtained in punctual kriging. Section 3 explains the mechanism of exploiting backpropagation training algorithm for this purpose and thus avoiding the problem of matrix inversion failure and negative weights. 2.4. Image quality measures Besides MSE, PSNR, and SSIM [54], another image quality measure in terms of the experimental variograms of the original and degraded images is also used. 2.4.1. Mean square error (MSE) MSE is used to measure the average squared difference between reference and restored images. Its computation depends upon the pixel by pixel difference i.e., by adding up the squared differences of all pixels and divided by the total number of pixels. The property of MSE is a global measure of image quality.

n

MSE =

M,N

[I1 (m, n) − I2 (m, n)]2 M×N

(9)

where I1 and I2 represent original and restored images respectively. M and N represent rows and columns of given images. 2.4.2. Peak signal-to-noise ratio (PSNR) PSNR is ratio between the maximum possible power of a signal and power of noise level that corrupts the signal. It provides a measure of how much noise is present in the image, and is usually measured in logarithmic decibel (dB) scale. A higher value of PSNR represents better denoising performance. It is computed using the following expression.



PSNR = 10 log10

R2 MSE

(10)

where R represents maximum possible gray level present in the given image. 2.4.3. Structural similarity index measure (SSIM) SSIM is a method of measuring the structural similarity between two images. It measures the image quality based on the original noise free image as a reference. SSIM is considered as a more effective image quality measure compared to PSNR and MSE, which have been proved to be inconsistent with human vision perception [55]. SSIM depends upon three main factors; luminance, contrast and mask and it can be calculated by the following expression: SSIM(x, y) =

(2x y + C1 )(2xy + C2 ) (2x + 2y + C1 )(x2 + y2 + C2 )

(11)

where x , y , are average of x and y respectively, x2 , y2 are variances of x and y, xy is the covariance of x and y, and C1 and C2 are used to stabilize the division with weak denominator. Whereby, if o (d) and (d) represent the semi-variances at lag d of the original and degraded image respectively, then a variogram based image quality measure VMSE and VPSNR can be calculated as, 1  2 [o (d) − (d)] Md Md

VMSE =

(12)

point, and semi-variance provides a measure of spatial dependence between pixels. Variogram of two different images is different because both images have different distribution of data that can be verified from Fig. 5. Further, variogram of an image corrupted with white Gaussian noise shows the up-lifting of the variogram as the noise variance is increased. Furthermore, the general shape and structure of the variogram remains the same for low noise variances as shown in Fig. 6. The hypothesis in developing this image quality measure relies on the idea that if a technique which brings the variogram of the restored image very close to that of the original image, will perform better. Statistical meaning of VMSE is to measure the mean squared error of the variogram of the estimated and the original images. 3. The proposed hybrid approach The occurrence of singular matrix in kriging is inherently unpredictable as it depends on the variogram for a pixel in the degraded image. The variogram itself depends on neighboring values of a pixel. Such scenarios should be taken care of separately by replacing the processed pixel with a value given by fuzzy ‘averaging’ or ‘median’ filter, which ever makes the error variance ‘small’. Table 2 shows the statistics about the number of pixels selected for kriging through Fuzzy Decider. It is observed that for about 88% of the selected pixels, the punctual kriging procedure results in negative weights. To handle this problem, approximation has been used to reinitialize the weights i.e. negative weights have been set to zero and positive weights have been renormalized. Also, for some pixels, the kriging procedure fails due to the problem of matrix inversion failure. It can be observed from the results shown in Table 2 that the actual number of pixels where punctual kriging is applied successfully (less than 12%) is far less than the pixels where it is unsuccessful (88%). This leads us to introduce some methodology in order to apply successful estimation of the selected pixel. Fig. 1 shows the basic architecture of our proposed methodology. Firstly, we generate a map for pixels that needs kriging or not through Fuzzy Decider. These selected pixels are estimated using neural network based punctual kriging. The pixels that are not selected for kriging by the Fuzzy Decider are processed using the robust fuzzy weighted filter. Lastly, various image quality measures have been employed to analyze the quality of the processed image. 3.1. Details of different stages of proposed methodology In the proposed method, all pixels are not blindly kriged. Rather, based on the homogeneity and deviation of its local neighborhood, a pixel is selected for kriging by a fuzzy logic rule-based system. This fuzzy system is called the Fuzzy Decider in our work. The inputs to the Fuzzy Decider are a measure of homogeneity and DAMdistance which is based on the mean and deviation of the 3 × 3 window around the current pixel. The degree of homogeneity is estimated by Eq. (14) as proposed by Tizhoosh [56]. The numerator in Eq. (14) is the difference of the maximum and minimum gray values in the region comprising of the 3 × 3 window around a pixel where, the denominator is the difference of the maximum and minimum gray values in the whole image.



d=0

VPSNR = 10 log10

[max{o (d)}] VMSE

2

(13)

Here Md is the maximum lag for the images. VMSE and VPSNR are global quality measures; however, these do take into account the structural detail information present in the image. Variogram illustrate the variation of semi-variance with respect to distance from a

H =

local − g local gmax min global

global

gmax − gmin



(14)

The DAMdistance in the rules is simply the difference between the gray value of the current pixel and the mean gray value of its neighbors. The Fuzzy Decider is a basic Mamdani type-I fuzzy logic system consisting of the following rules:

A. Chaudhry et al. / Applied Soft Computing 13 (2013) 817–832

821

Table 2 Statistics of the pixels selected for kriging by the fuzzy type-I, type-II and NFC. The Boat image degraded with white Gaussian noise of different variances. Statistics of the data

White Gaussian noise of different variance 0.1

No. of pixels advised for kriging by type-II fuzzy No. of pixels advised for kriging by type-I fuzzy No. of pixels advised for kriginig by NFC Matrix inversion failure Parseval theorem violation

164,943 206,215 248,717 1080 206,441

0.08

0.06

155,123 190,083 240,786 1039 198,774

140,831 165,535 233,776 960 191,754

0.04 119,244 124,774 223,060 890 182,229

0.02 78,852 54,927 227,268 1112 184,561

0.01 39,846 13,857 223,135 1082 181,183

Fig. 1. Schematic flowchart of the proposed neuro-fuzzy kriging filter.

If (regionHomogenuity is HomoHigh) or (DAMdistance is acceptable) then (decision is KrigingNo) If (regionHomogenuity is HomoLow) or (DAMdistance is veryHigh) then (decision is KrigingYes) We have observed that spatial intensity variation is effectively represented with the two rules based on homogeneity and DAMdistance. The membership functions of homogeneity; HomoLow and HomoHigh, have been set as Gaussian. The effectiveness of High membership function is dominant as compared to Low membership function in a small range of [0–0.1]. While, the effectiveness of Low membership function is dominant in a relatively large range of [0.1–1]. Consequently, we make it sure that if the intensity of the pixel under consideration is close to that of the neighboring pixels (homogeneous region) then it is not a noisy pixel. Else, it is strictly considered as a noisy pixel and subsequently it is smoothed out. Similarly, the membership functions of DAMdistance; acceptable and veryHigh, have been set as Gaussian. In this case acceptable membership function is dominant in the range [0–87], while veryHigh remains dominant in the rage [88–255]. This means that if the difference in intensity of the current pixel with that of the mean intensity of the rest of 8 pixels is small (less than 87 in this case), the probability of the current pixel being noisy is less and vice versa. 3.1.1. Type-II fuzzy set The concept of type-II fuzzy logic is actually an extension of type-I fuzzy sets. Type-II fuzzy sets are capable to handle more uncertainties in spite of the fact that they are difficult to use and understand than type-I fuzzy sets. We have used type-II fuzzy set to enhance the fuzzification process for better decision making. In our approach based on type-II fuzzy sets, we have used the following nine rules to decide the pixel’s fate: If (regionHomogenuity is HomoMed) and (DAMdistance is Acceptable)

then (decision is KrigingNo) If (regionHomogenuity is HomoMed) and (DAMdistance is High) then (decision is KrigingYes) If (regionHomogenuity is HomoMed) and (DAMdistance is VeryHigh) then (decision is KrigingYes) If (regionHomogenuity is HomoLow) and (DAMdistance is Acceptable) then (decision is KrigingNo) If (regionHomogenuity is HomoLow) and (DAMdistance is High) then (decision is KrigingYes) If (regionHomogenuity is HomoLow) and (DAMdistance is VeryHigh) then (decision is KrigingYes) If (regionHomogenuity is HomoHigh) and (DAMdistance is Acceptable) then (decision is KrigingNo) If (regionHomogenuity is HomoHigh) and (DAMdistance is High) then (decision is KrigingNo) If (regionHomogenuity is HomoHigh) and (DAMdistance is VeryHigh) then (decision is KrigingYes) Figs. 2 and 3 show the graphical representations of type-II fuzzy membership functions. 3.1.2. Neuro fuzzy classier (NFC) In this paper, we have also employed neuro fuzzy classifier (NFC) in addition to fuzzy type-I and type-II for distinguishing the noisy and noise-free pixels, and its effectiveness on overall performance of the image restoration approach is analyzed. The basic purpose of fuzzy classification is to partition the feature space into fuzzy classes. When there is overlapping between classes, the partial membership exists in each class and fuzzy classification is thus one of the suitable approaches to be used in such case [57,58]. Like other fuzzy approaches, in NFC, fuzzy if then else rules are used to develop a classifier. Fig. 4 shows the general structure of NFC.

822

A. Chaudhry et al. / Applied Soft Computing 13 (2013) 817–832

using 2D-CWT. Eight different scale values (i.e. 1.0, 1.6, 2.6, 3.9, 4.0, 5.0, 5.4 and 6.5) are used for CWT features extraction [60]. These scale values are determined empirically. 3.1.2.3. Threshold adjacency statistics (TAS). Threshold adjacency statistics (TAS) has been proposed by Hamilton [61]. In our image restoration problem, 27 TAS features are extracted from a noisy image. These features are obtained by calculating three 9 bin histograms. It considers number of adjacent white pixels for each white pixel in the binary image. A global threshold is used for the whole image dataset which is empirically set. Homogeneity and DAMDistances are also calculated and added into the feature vector.

Fig. 2. Type-II fuzzy membership function for DAMdistance.

Fig. 3. Type-II fuzzy membership function for Homogeneity.

In our case, we have two-class classification problem i.e. noisy and noise-free pixels. As described earlier, images are corrupted by white Gaussian noise with different variances. Different types of features (as described below) are extracted from the corrupted image for classification of noisy and noise-free pixels. 3.1.2.1. Feature extraction strategy for NFC based image restoration. Three types of features are extracted from noisy image. (i) 2D-continous wavelet transform (2D-CWT). (ii) Threshold adjacency statistics (TAS). (iii) Homogeneity and DAMDistance. 3.1.2.2. 2D-continous wavelet transform. Continuous wavelet transform is convenient for analysis of non-stationary signals [59]. 2D-CWT (by Gaussian wavelet) is applied to the original image for eight different values of the scale parameter. This results in eight different filtered images, all corresponding to lower frequency bands. Scale is an important parameter in 2D-CWT because low frequency components (smooth areas) of image are present at high scale values, while high frequency components (edges) are present at lower scale values. A total of nine features are extracted

3.1.2.4. Feature selection strategy for NFC based image restoration. Feature selection is used to reduce the dimensionality of the feature space and improve the classification accuracy [62]. As we have a total of thirty-eight features, therefore, we select only those features which have better class discrimination capabilities. In this regard, we have used genetic algorithm based approach using WEKA software [63]. Selected features are then used by NFC to discriminate between noisy and noise-free pixels. 3.1.2.5. Training and testing of NFC. After selection of the optimum features, NFC training is performed. In this work, we have used 15 different images for training of NFC. Two-third images are used for training, while one-third is used for validation. Finally, NFC generates fuzzy inference system (FIS), which consists of fuzzy rules. One of the NFC generated FIS is represented in Fig. 5. The generated FIS is then used to classify the 450 test images corrupted with Gaussian noise of different variances. For this purpose, first the NFC generated FIS is employed to generate the fuzzy decision map for the pixels that need to be estimated. Similarly, fuzzy decision maps generated by fuzzy type-I and type-II are described below. 3.1.3. Generation of fuzzy decision map through fuzzy type-I and type-II In the first stage, the noisy image is presented to the Fuzzy Decider that generates a binary image called the fuzzy decision map. This decision map is generated through both type-I and type-II fuzzy sets and is provided to the BPNN based estimation stage, where the decision of whether to estimate or not is enforced. This helps to reduce the computational time. Effectiveness of fuzzy decision map generated through fuzzy type-I and type-II and NFC has been compared for image restoration. Fuzzy decision maps generated through NFC and fuzzy type-I and type-II for cameraman image are shown in Fig. 8. Neuro fuzzy classifier (NFC) is a supervised learning method. Its structure is similar to the other neural networks structures, the input, hidden and output layers. In our case, eight input features selected by Genetic Algorithm (GA) are presented to the classifier with a hidden layer. The output layer contains one neuron i.e. noisy and noise free pixels. The fuzzy inference system (FIS) is generated by the NFC and the classification will be performed based on the NFC generated FIS. The neural network used to learn the system behavior and accordingly generates the fuzzy rules and membership functions. Fig. 4 shows the graphical representation of the NFC. The structure of NFC is as under: Input layer: Hidden layer: Output layer:

Fig. 4. Neural networks based generation of membership functions and fuzzy rules.

Eight neurons Fifty neurons One neuron

The inputs to the NFC are the GA optimized features. The output of the NFC is the generated fuzzy inference system (FIS) containing fuzzy rules. The FIS is then used for classification of the input patterns.

A. Chaudhry et al. / Applied Soft Computing 13 (2013) 817–832

823

Fig. 5. FIS generated by neuro fuzzy classifier (NFC).

3.1.4. Employing BPN for estimation In the proposed approach, we have applied multilayer perceptron with backpropagation algorithm to estimate the pixels under consideration using the concept of punctual kriging. The BPN algorithm with modified cost function has been applied to train the neural net. 3.1.4.1. Architecture of the network. The network configuration used for estimation of the pixels is given below. Input layer: Hidden layer: Output layer: Activation function:

f (x) =



1 1 − exp(−ˇx)

Nine neurons Thirty-five neurons One neuron Binary sigmoidal function

 (15)

In our case, the slope parameter ˇ is set equal to 1. Noisy image sub-pattern of size 3 × 3 is fed as input to the input layer of the neural network; neurons in the hidden layer are empirically set to 35. Binary sigmoidal function is used as an activation function to keep the output of the network within range 0–1 because this is the required pixel intensity range of the estimated image. We have employed the binary sigmoidal activation function because input to the neural networks is a gray scale image (scaled between 0 and 1) and we need the output in the range of 0 and 1. Based on the output value, the system decides that the pixel needs estimation or not. Further, in literature, binary sigmoidal function is reported as advantageous for the use in neural networks trained through backpropagation algorithm [64]. And to train the neural network, 1000 epochs have been run. The initial conditions of the neural net have been set randomly to avoid its trapping in local minima.

Since there is only one neuron in the output layer, so we omit the subscript ‘k’ from Eq. (16)

⎛

L(w, v, , ) = Var(en ) +  ⎝

m 

⎞

wj − 1⎠ + 

j=1

m 

wj2

(17)

j=1

where ‘’ is the positive penalty factor. 3.1.4.3. Updating weights in our proposed methodology. Case-I: For output layer The correction in output layer weights wj is proportional to the instantaneous gradient ∂L/∂wj . By differentiating Eq. (17) with respect to output layer weights wj

 ∂L ∂Var(en ) = +  + 2 wj ∂wj ∂wj m

(18)

j=1

The correction term wj applied to the output layer weights wj is defined by wj = −˛

∂L ∂wj

(19)

where ˛ is learning rate parameter, negative sign in Eq. (19) accounts for gradient decent in weight space. Replacing the value of ∂L/∂wj (see Supplementary material Part-I for derivation) in Eq. (19),

⎡

wj = −˛ ⎣ıy · zj +  + 2

m 

⎤

wj ⎦

(20)

j=1

3.1.4.2. Cost function and updating weights. The standard backpropagation algorithm consists of two parts: forwardpropagation and error backpropagation. We modify the error backpropagation part to minimize a new cost function. The error signal is the variance of the output of neural net and the target as given in Eq. (5). The energy function or the Augmented Lagrangian is formed by incorporating the constraints and extra penalty terms. We modify the cost function by including the variance of estimation error, weights related constraint (the sum of weights should be equal to one) and extra penalty term.

⎛ L(w, v, , ) = Var(en ) +  ⎝

n m   j=1 k=1

⎞ wjk − 1⎠ + 

n m   j=1 k=1

Similarly, differentiating Eq. (17) with respect to , we obtain

 ∂L = wj − 1 ∂ m

(21)

j=1

Thus, weights and Lagrange multiplier updates will be wj (n + 1) = wj (n) + wj (n) (n + 1) = (n) + 

 m 



wj (n) − 1

1 2 wjk

(16)

where  is learning rate parameter for Lagrange multiplier. Case-II: For hidden layer

(22)

824

A. Chaudhry et al. / Applied Soft Computing 13 (2013) 817–832

Fig. 6. Experimental variograms of three different images.

Let us consider Neuron ‘j’ as a hidden node. In this case, we do not know what should be the desired response of the neuron, so we cannot calculate Var(e) directly. However, from Eq. (16), ∂Var(e) ∂L = ∂vij ∂vij

(23)

Thus, the correction term vij applied to the hidden layer weights is defined by vij = −˛

∂L ∂Var(e) = −˛ ∂vij ∂vij

4. Results and discussions (24) 4.1. Variograms of the original and degraded images

Replacing the value of ∂Var(e)/∂vij (see Supplementary material Part-II for derivation) in Eq. (24), vij = −˛[ıy · wj · f  (Zinj ) · xi ]

(25)

Thus, hidden layer weights update will be

vij (n + 1) = vij (n) + vij (n)

3.1.5. Fuzzy smoothing of pixels not selected for kriging In the third stage, the unselected pixels by the Fuzzy Decider are processed using the robust fuzzy weighted filter. After the second stage, the processed image contains two types of values based on the decision map: kriging estimate through neural net and original values (unselected pixels). In this stage, a fuzzy smoothing is applied on the unselected pixels.

(26)

3.1.4.4. Training and testing of the net. In the second stage, three images Cameraman, Lena and PCB are corrupted with white Gaussian noise of variance 0.1. The backpropagation neural network is trained through supervised learning on 3 × 3 image sub-patterns that constitute 10% of the flagged pixels of Cameraman, Lena and PCB images. However, these 10% 3 × 3 image sub-patterns are randomly picked from the degraded image, so that a general pattern of noise is learned by the BPN. To perform the image restoration simulation studies, we have used our Matlab based implementation of BPN. The developed BPN code is more general and enough to accept any number of neurons/layers [48,65]. Simulation study has been carried out on IBM compatible Intel P-IV, 2.6 GHz machine. During the training phase, in each epoch, we shuffle the order in which these sub-patterns are being fed as an input to the network to avoid the network being trapped in the local minima. After training, the neural net has been tested against various images corrupted with white Gaussian noise of different variances.

The experimental semi-variograms of three different types of images (Boat, Blood cells and Lena) have been computed and shown in Fig. 6. The shapes of the variograms for all three images near lag zero are continuous. This shows that the pixel values do not change abruptly at lags near zero. However, for Lena and Boat images, fluctuations start appearing for lags greater than 10. This shows that after a lag of 10 pixels, we enter into a new region. Further, in case of Blood cells image, the fluctuations appear after a lag of 20 pixels. The variograms show sharp changes for larger lags. Fig. 7 shows the changes in the experimental variogram when a zero mean Gaussian noise with various variances is added to a particular image. The most interesting aspect to note is the uplifting of the variogram as the noise variance is increased (see Fig. 7(d)). It is also important to note that the general shape and structure of the variogram stays the same for low noise variances. The abrupt changes in the variogram take place at the same lags. Even for high noise variance, the shape of the variogram remains similar to that of the original image; however, the abrupt changes become more discontinuous. Further, near zero lag, the variogram becomes highly discontinuous as the additive noise variance is increased. These observations have led us to introduce the variogram based image quality measure VMSE, as introduced in Section 4. Various image quality measures as explained in Section 2 are applied to find out the quality of the processed image as compared

A. Chaudhry et al. / Applied Soft Computing 13 (2013) 817–832

825

Fig. 7. (a)–(c) Gaussian noise corrupted images with zero mean and different variances. (d) Variograms of Blood cells image with additive Gaussian white noise.

Table 3 Comparison of the proposed NFC and fuzzy type-II approaches with other methods across 450 test images at 0.01 noise level. Denoising methods

Noisy image PWFK [32,33] AWF [34] SAFK [41] Neuro fuzzy-I [54] The proposed neuro fuzzy-II The proposed NFC

Qualitative measures MSE

PSNR (db)

SSIM

VMSE

VPSNR (db)

613.57 291.44 178.51 176.20 179.38 181.08 165.76

20.25 23.53 25.67 25.70 25.61 25.57 25.92

0.39 0.51 0.66 0.66 0.66 0.65 0.68

306043.95 201881.40 74228.07 70628.05 69740.33 62074.29 51096.97

16.37 18.18 22.52 22.74 22.79 23.30 24.14

to the original image. We have tested the performance of the proposed approach (both using fuzzy type-I and type-II fuzy sets and NFC) by considering three scenarios. Firstly, the performance of the proposed method has been tested for additive Gaussian white noise of different variances for a test image. Secondly, the performance is tested for different images corrupted with Gaussian white noise of same variance. This is because the effect of noise may change with the variance of noise as regards the visual distortion for the same image. On the other hand, same noise may affect different images differently as regards the visual distortion. Typical results from the Fuzzy Decider type-I and type-II

and NFC are shown in Fig. 8. The white pixels are the ones that need kriging.

4.2. Scenario 1: performance analysis by varying variance of Gaussian noise In the first case, we have considered Boat and Lena images as test images. The image is degraded with Gaussian white noise of variances ranging from 0.01 to 0.14. The results obtained from our approach have been compared with that of the AWF, PWFK,

Table 4 Qualitative comparison of the proposed fuzzy type-II and NFC approaches with other methods across 450 test images at 0.05 noise level. Denoising methods

Noisy image PWFK [32,33] AWF [34] SAFK [41] Neuro fuzzy-I [45] The proposed neuro fuzzy-II The proposed NFC

Qualitative measures MSE

PSNR (db)

SSIM

VMSE

VPSNR (db)

2640.50 913.38 592.70 592.63 505.00 503.00 557.20

13.92 18.50 20.28 20.41 21.00 21.10 20.20

0.18 0.29 0.40 0.37 0.42 0.43 0.47

5,734,243 267,462 68,699 67,441 65,697 65,349 97,567

−2.50 10.80 16.70 16.78 16.90 16.92 15.18

826

A. Chaudhry et al. / Applied Soft Computing 13 (2013) 817–832

Fig. 8. Result from (a) noisy cameraman image, (b) NFC, (c) fuzzy type-I and (d) fuzzy type-II. Decision map for Cameraman image degraded with variance 0.02.

Table 5 Qualitative comparison of the proposed fuzzy type-II and NFC approaches with other methods across 450 test images at 0.1 noise level. Denoising methods

Qualitative measures MSE

Noisy image PWFK [32,33] AWF [34] SAFK [41] Neuro fuzzy-I [54] The proposed neuro fuzzy-II The proposed NFC

4506.40 1559.15 996.51 926.88 800.73 797.77 828.74

PSNR (db)

SSIM

VMSE

VPSNR (db)

11.56 16.16 18.01 18.15 18.95 19.00 18.50

0.12 0.20 0.30 0.28 0.32 0.34 0.37

14,038,371 810,080 374,596 354,772 347,627 345,389 508,104

−6.40 5.99 9.70 9.57 9.66 9.70 8.02

Table 6 Qualitative comparison of the proposed fuzzy type-II and NFC approaches with other methods across 450 test images at 0.14 noise level. Denoising methods

Noisy image PWFK [32,33] AWF [34] SAFK [41] Neuro fuzzy-I [54] The proposed neuro fuzzy-II The proposed NFC

Qualitative measures MSE

PSNR (db)

SSIM

VMSE

4581.43 2005.13 1249.85 1273.80 1042.13 1032.00 1057.43

10.59 15.11 17.10 17.08 17.95 18.00 17.44

0.09 0.17 0.26 0.24 0.29 0.30 0.32

21,563,370 1,381,501 450,682 454,841 437,249 433,079 605,773

VPSNR (db) −8.26 3.67 8.53 8.50 8.67 8.71 7.30

A. Chaudhry et al. / Applied Soft Computing 13 (2013) 817–832

SAFK, and fuzzy type-I approaches. The effect of the additive Gaussian noise and its removal by various approaches is shown in Figs. 9 and 10. Table 3 gives a quantitative comparison among different methods in terms of MSE, PSNR, SSIM, VMSE and VPSNR at 450 test images. It can be observed from Table 3 that the proposed NFC based punctual kriging offers superior performance at 0.01 noise level compared to the rest of the methods. The experimental variograms of the original, noisy, and restored images through AWF, PWFK, SAFK, fuzzy type-I and proposed fuzzy

827

type-II and NFC are plotted in Fig. 11. The image is corrupted with Gaussian noise of variance 0.08. From Fig. 11, it is clear that variograms of both the original as well as noisy image retain the structural information about the image and differ only in the semivariance at different lags depending upon the strength of the noise variance. Further, in comparison to the variograms produced by other methods, our approach produces a variogram that is very close to the variogram of the original image. This is also clear from Table 3, where NFC, outperforms at all quality measures compared

Fig. 9. Original, noisy and estimated Boat images obtained through AWF, SAFK, PWFK, neuro fuzzy type-I, neuro fuzzy type-II and NFC method.

828

A. Chaudhry et al. / Applied Soft Computing 13 (2013) 817–832

Fig. 9. Continued

to AWF, PWFK, SAFK, and fuzzy type-I and type-II image restoration techniques.

4.3. Scenario 2: performance analysis using 450 test images In the second case, we consider 450 different images as the test data. These images have been corrupted with white Gaussian noise of variance 0.01. Performance analysis of the above-mentioned methods is carried out in terms of average values of MSE, PSNR, SSIM, VMSE and VPSNR across 450 test images as shown in Table 3. The graphical representation of various performance measures is shown in Fig. 12. The results of neuro fuzzy type-II and NFC based punctual kriging are compared with the existing techniques. It can be observed from Table 3 that performance of the proposed NFC based punctual kriging approach is better compared to that of PWFK, SAFK, fuzzy type-I and type-II and AWF at 0.01 noise level.

4.4. Scenario 3: performance analysis of NFC using 450 test images In the third scenario, the proposed approach of NFC based punctual kriging is tested on the 450 images. Images are corrupted using Gaussian noise with different level of noise variances. Performance of the proposed approaches has been compared with existing techniques. At lower noise levels i.e. 0.01–0.03, the proposed NFC based punctual kriging outperforms all the other techniques as it is shown in Table 3. While, at higher noise levels 0.04–0.14, the performance of the proposed fuzzy type-II based punctual kriging is higher. However, SSIM measure for the NFC based punctual kriging is still better than the fuzzy type-II based punctual kriging (see Tables 4–6).

NFC based punctual kriging thus offers better SSIM at all noise levels. SSIM is a method of measuring the similarity between two images. It measures the image quality based on the original noise free image as a reference. SSIM is considered as a more effective image quality measure compared to PSNR and MSE, which have been proved to be inconsistent with human vision perception [55]. Thus improvement in SSIM shows the effectiveness of the NFC based punctual kriging approach.

4.5. Performance comparison using type-I and type-II fuzzy sets, and neuro fuzzy classifier (NFC) The results of fuzzy type-I, type-II, and NFC based punctual kriging approaches are compared using various image quality measures. Number of pixels selected for kriging by the Fuzzy Decider using fuzzy type-I and type-II, and NFC are shown in Table 2. From Table 2, it is clear that Fuzzy Decider using fuzzy type-II selects less number of noisy pixels for high variance compared to that of type-I fuzzy set. The reason for the selection of less number of noisy pixels by type-II fuzzy set might be that it avoids over smoothing and preserves edges more efficiently for a noise variance range [0.04–0.1]. Whereas for low level of noise, it selects more pixels compared to type-I fuzzy set. This might be because it also selects pixels for noise removal that are corrupted but close to homogenous or textured gray level. Further, Table 2 also shows that NFC selects more pixels for kriging than type-I and type-II because it uses 8 optimum features extracted from three different approaches. Tables 4–6 show comparison of various techniques in terms of MSE, PSNR, SSIM, VMSE and VPSNR at different noise levels. The performance of the proposed neuro fuzzy type-II is better at higher noise levels in terms of MSE, PSNR, VMSE and VPSNR. In Fig. 11, variograms of the proposed fuzzy type-II and

Table 7 Comparison of the proposed NFC and fuzzy type-II approaches with and without BPNN modified cost function for LENA image. Denoising methods

Noisy image PWFK [32,33] AWF [34] SAFK [41] Neuro fuzzy-I [54] The proposed neuro fuzzy-II The proposed NFC ANN without modified cost function

Qualitative measures at 0.01 Gaussian noise level MSE

PSNR (db)

SSIM

643.52 276.02 252.05 184.57 159.85 167.28 149.08 204.12

20.04 23.72 23.48 25.11 25.56 25.37 26.13 24.75

0.36 0.49 0.66 0.61 0.66 0.65 0.68 0.64

VMSE 423,998 2758 2755 3865 7040 4201 1920 2755

VPSNR (db) 10.41 32.28 32.28 30.81 28.12 30.50 34.04 31.98

A. Chaudhry et al. / Applied Soft Computing 13 (2013) 817–832

NFC approaches are compared with existing approaches using boat image. It can be observed from Fig. 11 that the variogram curve of the proposed methods are close to the original image and thus shows its effectiveness. When the proposed NFC based punctual kriging approach is compared to other image restoration approaches,it is observed that NFC based punctual kriging, outperforms the rest of the methods in terms of all quality measures at low noise levels range of

829

0.01–0.03. But as the noise level increases from 0.04 to 0.14, NFC still outperforms the rest of the methods in terms of SSIM while, neuro fuzzy type-II provides superior performance in terms of MSE, PSNR, VMSE and VPSNR. This fact can be observed from Tables 3–6 respectively. Performance analysis of the proposed technique is also carried out for Lena image by employing BPNN with and without modified cost function. Table 7, shows the performance comparison of

Fig. 10. Original, noisy and estimated Lena images obtained through AWF, PWFK, SAFK, neuro fuzzy type-I, neuro fuzzy type-II and NFC method.

830

A. Chaudhry et al. / Applied Soft Computing 13 (2013) 817–832

Fig. 10. Continued

5. Conclusions

3000

2500

Semi Variance

2000

1500 OriginalImage PhamWagFuzzy AdaptiveWiener BPN Estimated Image Fuzzy-I BPN Estimated Image Fuzzy-II SAFK NFC

1000

500

0

0

20

40

60

80

100

120

140

Lag 'd' Fig. 11. Comparison of the variograms of the original, degraded and processed Boat image.

An effective hybrid image denoising method based on the concept of punctual kriging is analyzed. Fuzzy IF THEN rules based on region homogeneity and deviations, are used to intelligently decide the importance of a pixel in view of edge preservation. The performance of both type-I and type-II fuzzy sets has been analyzed for this purpose. The method further solves the kriging matrix inversion and negative filter weights problems due to the learning capabilities of the neural net. The overall kriging procedure is coupled with a fuzzy smoothing filter. Due to the use of Fuzzy Decider, neural net is employed to estimate pixels along region boundaries and isolated discontinuities. However, for pixels inside the regions, away from the region boundaries, fuzzy smoothing is used. The results show a marked improvement in the performance of image restoration scheme as compared to the existing fuzzy kriging and adaptive Wiener filter approaches. Using NFC based punctual kriging for image restoration; thirty-eight different types of features are extracted. Further to reduce the features dimensionality, we have employed GA to select the important features for classification of noisy and noise-free pixels. A decision map is then generated based on the NFC FIS. A total of 450 images are used to test the effectiveness of the proposed NFC and fuzzy type-II based punctual kriging image restoration approaches. The proposed NFC technique outperforms at all determined image quality measures with small noise levels. While, at higher noise level neuro fuzzy type-II outperforms onalmost all of the quality measures, which shows the effectiveness of the proposed approaches. In future work, we intend to use evolutionary algorithms in addition to fuzzy sets for developing a majority voting based composite predictor. The composite predictor thus formed would decide the fate of pixel under consideration for the better exploitation of the intensity variation on the edges and lines in the image. Acknowledgements

Fig. 12. Comparison of 450 images test data with different methods. Average values of various qualitative measures. (Note: the different image quality parameters are rescaled for elaboration purpose.)

This work is supported by the Higher Education Commission of Pakistan under the indigenous PhD scholarship program (17-54(Ps4-078)/HEC/Sch/2008/) and BK21, program of South Korea. Appendix A. Supplementary data

different techniques using Lena image. It is observed that BPNN with modified cost function outperforms the rest of approaches in terms of the image quality measures.

Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.asoc.2012.10.017.

A. Chaudhry et al. / Applied Soft Computing 13 (2013) 817–832

References [1] H.H. Tsai, X.P. Lin, B.-M. Chang, An image filter with a hybrid impulse detector based on decision tree and particle swarm optimization, in: International Conference on Machine Learning and Cybernetics, China, 2009. [2] D. Krige, A statistical approach to some basic mine valuation problems on the Witwatersrand, Journal of the Chemical, Metallurgical and Mining Society of South Africa 52 (1951) 119–139. [3] S. Voloshynovskiy, O. Koval, T. Pun, Image denoising based on the edge-process model, Signal Processing 85 (2005) 1950–1969. [4] C. Young Sik, R. Krishnapuram, A robust approach to image enhancement based on fuzzy logic, IEEE Transactions on Image Processing 6 (1997) 808–825. [5] M. Doroodchi, A.M. Reza, Implementation of fuzzy cluster filter for nonlinear signal and image processing, in: Proceedings of the Fifth IEEE International Conference on Fuzzy Systems, 1996, pp. 2117–2122. [6] A. Hussain, M. Jaffar, A. Mirza, A hybrid image restoration approach: fuzzy logic and directional weighted median based uniform impulse noise removal, Knowledge and Information Systems 24 (2010) 77–90. [7] A. Majid, C.-H. Lee, M. Mahmood, T.-S. Choi, Impulse noise filtering based on noise-free pixels using genetic programming, Knowledge and Information Systems (2011) 1–22. [8] F. Farbiz, M.B. Menhaj, A fuzzy logic control based approach for image filtering, in: Fuzzy Techniques in Image Process, 2000, pp. 194–221. [9] L.R. Liang, C.G. Looney, Competitive fuzzy edge detection, Applied Soft Computing 3 (2003) 123–137. [10] L. Khriji, M. Gabbouj, Rational-based adaptive fuzzy filters, International Journal of Computational Cognition 2 (2004) 113–132. [11] L.O. Chua, L. Yang, Cellular neural networks: theory, IEEE Transactions on Circuits and Systems 35 (1988) 1257–1272. [12] L.O. Chua, L. Yang, Cellular neural networks: applications, IEEE Transactions on Circuits and Systems 35 (1988) 1273–1290. [13] M. Zamparelli, Genetically trained cellular neural networks, Neural Networks 10 (1997) 1143–1151. [14] N. Ansari, Z.Z. Zhang, Generalised adaptive neural filters, Electronics Letters 29 (1993) 342–343. [15] Z.Z. Zhang, N. Ansari, Structure and properties of generalized adaptive neural filters for signal enhancement, IEEE Transactions on Neural Networks 7 (1996) 857–868. [16] W. Qian, M. Kallergi, L.P. Clarke, Order statistic-neural network hybrid filters for gamma camera-bremsstrahlung image restoration, IEEE Transactions on Medical Imaging 12 (1993) 58–64. [17] N. Suetake, E. Uchino, An RBFN-Wiener hybrid filter using higher order signal statistics, Applied Soft Computing 7 (2007) 915–922. [18] K. Sivakumar, U.B. Desai, Image restoration using a multilayer perceptron with a multilevel sigmoidal function, in: IEEE International Symposium on Circuits and Systems, ISCAS’92, 1992, pp. 2917–2920. [19] M.R. Widyanto, H. Nobuhara, K. Kawamoto, K. Hirota, B. Kusumoputro, Improving recognition and generalization capability of back-propagation NN using a self-organized network inspired by immune algorithm (SONIA), Applied Soft Computing 6 (2005) 72–84. [20] A.S. Palmer, M. Razaz, D.P. Mandic, Spatially adaptive image restoration by neural network filtering, in: Proceedings of VII Brazilian Symposium on Neural Networks SBRN’02, 2002, pp. 184–189. [21] J. Gwanggil, A. Marco, B. Valerio, D. Ernesto, J. Jechang, Designing of a type-2 fuzzy logic filter for improving edge-preserving restoration of interlaced-to-progressive conversion, Information Sciences 179 (2009) 2194–2207. [22] L. Zhang, B. Paul, X. Wu, Hybrid inter and intra wavelet scale image restoration, Pattern Recognition 36 (8) (2003) 1737–1746. [23] L. Zhang, X.W.P. Bao, Multiscale LMMSE-based image denoising with optimal wavelet selection, IEEE Transaction on Circuits and Systems for Video Technology 15 (4) (2005) 469–481. [24] S.G. Chang, M.V.B. Yu, Spatially adaptive wavelet thresholding with context modeling for image denoising, IEEE Transaction on Image Processing 9 (2000) 1522–1531. [25] H. Zujun, Adaptive singular value decomposition in wavelet domain for image denoising, Pattern Recognition 36 (2003) 1747–1763. [26] S. Jean-Luc, E.J. Candes, D.L. Donoho, The curvelet transform for image denoising, IEEE Transactions on Image Processing 11 (2002) 670–684. [27] G.Y. Chen, K.B. gl, Image denoising with complex ridgelets, Pattern Recognition 40 (2007) 578–585. [28] J. Portilla, V. Strela, M.J. Wainwright, E.P. Simoncelli, Image denoising using scale mixtures of Gaussians in the wavelet domain, IEEE Transactions on Image Processing 12 (2003) 1338–1351. [29] V. Laparra, J. Gutierrez, G. Malo, Image denoising with Kernels based on natural image relations, Journal of Machine Learning Research 11 (2010) 873–903. [30] Z. Lei, D. Weisheng, Z. David, S. Guangming, Two-stage image denoising by principal component analysis with local pixel grouping, Pattern Recognition 43 (2010) 1531–1549. [31] D.D. Muresan, T.W. Parks, Adaptive principal components and image denoising, in: International Conference on Image Processing, vol. 101, 2003, pp. I-101–I104. [32] T.D. Pham, M. Wagner, Filtering noisy images using kriging, in: Proceedings of the Fifth International Symposium on Signal Processing and Its Applications, ISSPA’99, vol. 421, 1999, pp. 427–430.

831

[33] T.D. Pham, M. Wagner, Image enhancement by kriging and fuzzy sets, International Journal of Pattern Recognition and Artificial Intelligence 14 (2000) 1025–1038. [34] J.S. Lim, Two-Dimensional Signal and Image Processing, Prentice Hall, Englewood Cliffs, NJ, 1990. [35] A.M. Mirza, B. Munir, Combining fuzzy logic and kriging for image enhancement, in: 8th International Conference on Computational Intelligence, Theory and Applications, Fuzzy Days, 2004. [36] C. Asmatullah, Image restoration using machine learning, Ph.D. Thesis, Faculty of Computer Sciences and Engineering, GIK, Institute, Pakistan, 2007. [37] L. Ce, S. Richard, K. Sing Bing, C.L. Zitnick, T.F. William, Automatic estimation and removal of noise from a single image, IEEE Transactions on Pattern Analysis and Machine Intelligence 30 (2008) 299–314. [38] N. El-Sheimy, C. Valeo, A. Habib, Digital Terrain Modeling; Acquisition, Manipulation and Applications, Artech House, London, UK and Boston, USA, 2005. [39] D. Driankov, H. Hellendorn, M. Reinfrank, An Introduction to Fuzzy Control, Springer Verlag, NY, 1993. [40] M. Sugeno, Industrial Applications of Fuzzy Control, Elsevier Science Inc., New York, NY, USA, 1985. [41] M.M. Anwar, C. Asmatullah, M. Badre, Spatially adaptive image restoration using fuzzy punctual kriging, Journal of Computer Science and Technology 22 (2007) 580–589. [42] L.A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning, Information Sciences 8 (1975) 199–249. [43] H.B. Mitchell, Pattern recognition using type-II fuzzy sets, Information Sciences 170 (2005) 409–418. [44] M. Nachtegeal, Fuzzy Techniques in Image Processing, Springer Verlag LII, Heidelberg, New York, USA, 2000. [45] P. Liu, H. Li, Fuzzy techniques in image restoration research—a survey, International Journal of Computational Cognition 2 (2004) 131–149. [46] L. Rudasi, S.A. Zahorian, Pattern recognition using neural networks with a binary partitioning approach, in: IEEE Proceedings of Southeastcon’91, vol. 722, 1991, pp. 726–730. [47] M.S. El Sherif, M.S. Abdel Samee, Pattern recognition using neural networks that learn from fuzzy rules, in: Proceedings of the 37th Midwest Symposium on Circuits and Systems, vol. 591, 1994, pp. 599–602. [48] H. Takahashi, N. Pecharanin, Y. Akima, M. Sone, The reliability of neural networks on pattern recognition, in: IEEE World Congress on Computational Intelligence, 1994, pp. 3067–3070. [49] A. Khan, A. Majid, T.-S. Choi, Predicting protein subcellular location: exploiting amino acid based sequence of feature spaces and fusion of diverse classifiers, Amino Acids 38 (2010) 347–350. [50] K. Asifullah, T. Syed Fahad, M. Abdul, C. Tae-Sun, Machine learning based adaptive watermark decoding in view of anticipated attack, Pattern Recognition 41 (2008) 2594–2610. [51] D. Greenhil, E.R. Dvvies, Relative effectiveness of neural networks for image noise suppression, in: Proceedings of the Pattern Recognition in Practice, 1994, pp. 367–378. [52] T.M. Jochem, D.A. Pomerleau, C.E. Thorpe, Vision-based neural network road and intersection detection and traversal, in: Human Robot Interaction and Cooperative Robots, Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems 95, 1995, pp. 344–349. [53] D.A. Pomerleau, Neural Network Perception for Mobile Robot Guidance, Carnegie Mellon University, 1992. [54] C. Asmatullah, K. Asifullah, A. Asad, M.M. Anwar, A hybrid image restoration approach: using fuzzy punctual kriging and genetic programming, International Journal of Imaging Systems and Technology 17 (2007) 224–231. [55] W. Zhou, A.C. Bovik, H.R. Sheikh, E.P. Simoncelli, Image quality assessment: from error visibility to structural similarity, IEEE Transactions on Image Processing 13 (2004) 600–612. [56] H. Tizhoosh, Fuzzy image enhancement: an overview, in: Fuzzy Techniques in Image Processing, Springer Verlag LII, New York, 2000, pp. 137–171. [57] S. Ovchinnikov, Similarity relations, fuzzy partitions and fuzzy ordering, Fuzzy Sets and Systems 40 (1991) 107–126. [58] L.A. Zadeh, Fuzzy sets and their application to pattern classification and clustering analysis, in: J.K. George, Y. Bo (Eds.), Fuzzy Sets, Fuzzy Logic, and Fuzzy Systems, World Scientific Publishing Co. Inc., River Edge, NJ, USA, 1996, pp. 355–393. [59] R. Polikar, Fundamental Concepts & An Overview of the Wavelet Theory: Tutorial, 1996, http://users.rowan.edu/∼polikar/WAVELETS/WTpart1.html [60] I. Zafer, Y. Ayhan, Z. Dokur, K. Mehmet, O. Tamer, Medical image segmentation with transform and moment based features and incremental supervised neural network, Digital Signal Processing 19 (2009) 890–901. [61] N. Hamilton, R. Pantelic, K. Hanson, R. Teasdale, Fast automated cell phenotype image classification, BMC Bioinformatics 8 (2007) 110. [62] D.V.S.B.M. Vasantha, T. Dhamodharan, Medical image features, extraction, selection and classification, International Journal of Engineering Sciences and Technology 2 (26) (2010) 2071–2076. [63] G. Holmes, A. Donkin, I.H. Witten, WEKA: a machine learning workbench, in: Proceedings of the 1994 Second Australian and New Zealand Conference on Intelligent Information Systems, 1994, pp. 357–361. [64] E. Maduko, Development and testing of a neuro-fuzzy classification system for IOS data in asthmatic children, ETD Collection for University of Texas, El Paso, Paper AAI1449744, 2007.

832

A. Chaudhry et al. / Applied Soft Computing 13 (2013) 817–832

[65] C. Asmatullah, A.M. Mirza, A. Khan, Blind image restoration using multilayer backpropagator, in: 7th International Multi Topic Conference, INMIC, 2003, pp. 55–58. Asmatullah Chaudhry received his M.Sc. degree in Physics from Islamia University Bahawalpur, Pakistan in 1993 and his M.S. degree in Nuclear Engineering from Pakistan Institute of Engineering and Applied Sciences (PIEAS), Islamabad, Pakistan, in 1998. He received his M.S. and Ph.D. degrees in Computer Systems Engineering from GIK Institute, Topi, Pakistan, in 2003 and 2007, respectively. He has more than 13 years of research experience and is working as Principal Scientist in HRD Division at PINSTECH. Currently, he is postdoc fellow at Chonnam National University, Gwangju, South Korea. His research areas include Image Processing, Pattern Recognition, and Machine Learning. Asifullah Khan received his M.Sc. degree in Physics from University of Peshawar, Pakistan in 1996 and his M.S. degree in Nuclear Engineering from PIEAS, Islamabad, Pakistan, in 1998. He received his M.S. and Ph.D. degrees in Computer Systems Engineering from GIK Institute, Topi, Pakistan, in 2003 and 2006, respectively. He has carried out two-years postdoc Research at Signal and Image Processing Lab, Department of Mechatronics, GIST, South Korea. He has more than 13 years of research experience and is working as Associate Professor in DCIS at PIEAS. His research areas include Digital Watermarking, Pattern Recognition, Image Processing, Evolutionary Algorithms, Bioinformatics, Machine Learning, and Computational Materials Science. Anwar Majid Mirza received his M.Sc. degree in Physics, Quaid-e-Azam University (QAU), Islamabad in 1987 and he received his M.Sc. degree Nuclear Engineering, CNS, QAU, Islamabad in 1989. He received DIC and Ph.D. in Computational Physics, from Imperial College, UK in 1995. He has research interests in the areas of Machine Intelligence, Soft-Computing, Computer Vision and Modeling & Simulation. He has supervised more than 40 MS/MPhil thesis projects. He has been ranked at number 4 in the list of the most productive scientists of Pakistan in engineering sciences category by Pakistan Council for Science & Technology (PCST) in year 2003.

Asad Ali received the B.E. degree in Software Engineering from Army Public College of Management & Science (APCOMS), Rawalpindi, Pakistan in 2004 and the MS degree in Computer System Engineering from GIK Institute, Topi, Pakistan in 2006. He is currently a Ph.D. candidate at the Sato Lab in University of Tokyo. He was a recipient of Government scholarship for M.S. studies and MEXT scholarship for Ph.D. studies. His areas of interest include Material Recognition, Reflectance Analysis, Invariant Features, Intelligent Transportation Systems, Reversible Watermarking and Machine Cognition.

Mehdi Hassan received his M.Sc. degree in Computer Science from Gomal University, D.I.Khan in 2004. He is M.S. leading to Ph.D. scholar of Higher Education Commission (HEC), Pakistan. He received his M.S. degree in Computer System Engineering from GIK Institute, Topi, Pakistan, in 2010 and he is currently continuing his Ph.D. studies at PIEAS, Islamabad, Pakistan. His research interests are Image Processing, Data Mining and Machine Learning, Medical Image Processing and Classification.

Jin Young Kim received his B.S. degree in Electrical Engineering in 1986. He did his M.S. and Ph.D. in Electrical Engineering from same institute in 1988 and 1994 respectively from Department of Electrical Engineering, Seoul National University, S. Korea. Currently he is working as a Professor in Department of Electronics and Computer Engineering, Chonnam National Univerity, South Korea. His research interests are Audio Visual signal processing and embedded systems.