Journal of Experimental & Theoretical Artificial

1 downloads 0 Views 1MB Size Report
Mar 16, 2015 - To cite this article: Ashish Kumar Bhandari, Anil Kumar, Girish Kumar .... has been given (Mittal, Moorthy, & Bovik, 2012), which is based on natural scene statistics ... For minimisation of the above drawback, several class of thresholding ..... Each egg in CS algorithm represents a solution and Cuckoo egg.
This article was downloaded by: [Inst of Info Tech Design & Manufacturing] On: 23 August 2015, At: 00:25 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: 5 Howick Place, London, SW1P 1WG

Journal of Experimental & Theoretical Artificial Intelligence Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/teta20

Performance study of evolutionary algorithm for different wavelet filters for satellite image denoising using subband adaptive threshold a

a

b

Ashish Kumar Bhandari , Anil Kumar , Girish Kumar Singh & Vivek a

Soni a

PDPM Indian Institute of Information Technology Design and Manufacturing, Jabalpur 482005, Madhya Pradesh, India

Click for updates

b

Department of Electrical Engineering, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand 247667, India Published online: 16 Mar 2015.

To cite this article: Ashish Kumar Bhandari, Anil Kumar, Girish Kumar Singh & Vivek Soni (2015): Performance study of evolutionary algorithm for different wavelet filters for satellite image denoising using sub-band adaptive threshold, Journal of Experimental & Theoretical Artificial Intelligence, DOI: 10.1080/0952813X.2015.1020518 To link to this article: http://dx.doi.org/10.1080/0952813X.2015.1020518

PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing,

Downloaded by [Inst of Info Tech Design & Manufacturing] at 00:25 23 August 2015

systematic supply, or distribution in any form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http://www.tandfonline.com/page/termsand-conditions

Journal of Experimental & Theoretical Artificial Intelligence, 2015 http://dx.doi.org/10.1080/0952813X.2015.1020518

Performance study of evolutionary algorithm for different wavelet filters for satellite image denoising using sub-band adaptive threshold

Downloaded by [Inst of Info Tech Design & Manufacturing] at 00:25 23 August 2015

Ashish Kumar Bhandaria*, Anil Kumara1, Girish Kumar Singhb2 and Vivek Sonia3 a

PDPM Indian Institute of Information Technology Design and Manufacturing, Jabalpur 482005, Madhya Pradesh, India; bDepartment of Electrical Engineering, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand 247667, India (Received 28 January 2014; accepted 2 November 2014) In this paper, a comparative study of different wavelet filters using improved sub-band adaptive thresholding function for denoising of satellite images, based on evolutionary algorithms, has been performed. In this approach, the stochastic global optimisation techniques such as Cuckoo Search (CS) algorithm, artificial bee colony (ABC) and particle swarm optimisation (PSO) are used for obtaining the parameters of adaptive thresholding function required for optimum performance. The visual and quantitative results clearly show the increased efficiency and flexibility of the proposed CS algorithm based on Meyer wavelet filter over various other wavelet filters for image denoising. From the comparative study of different wavelet filters, it is found that the proposed Meyer wavelet-based CS algorithm denoising approach gives better performance in terms of signal-to-noise ratio (SNR), peak signal-to-noise ratio (PSNR), mean square error (MSE) and mean as compared to ABC- and PSO-based denoising approach. The proposed technique has been tested on several satellite images. The quantitative (EKI or EPI, mean, MSE, SNR and PSNR) and visual (denoised images) results show the superiority of the proposed technique over conventional and state-of-art image denoising techniques. Keywords: adaptive learning; satellite image denoising; Cuckoo search algorithm; particle swarm optimisation; artificial bee colony; wavelet analysis; wavelet thresholding; wavelet transform

1.

Introduction

During image acquisition or transmission process, bad visual effects arise due to many factors such as illumination, equipments and noise, etc. Data-sets collected by image sensors are generally contaminated by noise. In general, noise is an inevitable factor which has an enormous effect upon performance of various approaches. The objective of image denoising is to eliminate the noise while preserving as much as possible the significant signal information. Therefore, it is typically observed as an essential preprocessing step that is expected to mitigate distortion or blur of the desired signal. The multispectral remote sensing images are very efficient for obtaining better understanding of the earth environment. In the case of satellite images, the distinct types of noise and artefact in different imaging modalities degrade the image quality. In practice, most ordinary degradations arise due to the effect of additive noise (Gaussian), multiplicative noise (speckle) and so on.

*Corresponding author. Email: [email protected] q 2015 Taylor & Francis

Downloaded by [Inst of Info Tech Design & Manufacturing] at 00:25 23 August 2015

2

A.K. Bhandari et al.

These kinds of degradations can have an extensive impact on the image quality, and as a result it influences the human interpretation as well as accuracy of the computer-assisted methods in various imaging systems. Furthermore, feature extraction, analysis, recognition and quantitative measurements become difficult and unpredictable due to the poor quality of images (Kumar, Bhandari, & Padhy, 2012). Thus, image denoising and enhancement (Bhandari, Kumar, & Padhy, 2011) have become the foremost necessities for many practical applications. Image denoising still remains a challenge for researchers because noise removal introduces artefacts and blurring of the image, causing a very drastic reduction in information. The image denoising research can be broadly divided into two domains: spatial and transform domains. Among these two domains, in last two decades, intensive research has been done in wavelet transform (WT) domain. Wavelet thresholding denoising technique is very useful and an important research field (Gonzalez & Woods, 2002). Normally, images are having different type of artefacts, and they often have a Gaussian noise due to various acquisitions, transmission storage and display devices. To avoid such kind of artefacts, an appropriate noise removal phase is often compulsory before any relevant information could be extracted from the analysed images. Recently, wavelet thresholding-based denoising approaches have become popular and have drawn much attention. Over the last decade, there has been broad interest for noise removal in signals and images based on wavelet methods. Wavelet coefficients at numerous scales can be achieved by applying the discrete wavelet transform (DWT) of the image. The small coefficients in sub-bands are dominated by noise, whereas coefficients having large absolute value contain more signal information in comparison with noise. Replacing noisy coefficients with zero and an inverse discrete wavelet transform may lead to reconstruction that has lesser noise (Bhadauria & Dewal, 2014). For such kind of denoising practice, usually hard and soft thresholding methods are used, but they have some drawbacks. In the case of hard thresholding method, the wavelet coefficients are not continuous at the preset threshold and it may lead to oscillation of the reconstructed signal, whereas in the case of soft thresholding method, the wavelet coefficients have better continuity, but it may cause constant deviations between the estimated wavelet coefficients and original wavelet coefficients. Therefore, accuracy of the reconstructed image might suffer. Numerous works have been reported which are either based on wavelet-based thresholding or some other criteria for signal and image denoising (Donoho, 2000; Donoho & Johnstone, 1995; Jain & Tyagi, 2014; Om & Biswas, 2014). The 2-D wavelet decomposition of an image is performed by applying 1-D DWT along the row of the image first, and then the results are decomposed along the columns. This action results into four decomposed sub-band images referred to low –low (LL) image, low – high (LH) image, high –low (HL) image and high – high (HH) image. The frequency components of those sub-bands cover the full frequency spectrum of the original image (Demirel & Anbarjafari, 2010a, 2010b). Theoretically, a filter bank shown in Figure 1(a) should operate on the image in order to generate various level sub-band frequency images. Figure 1(b) shows the different subbands of a satellite image where the top left image is LL sub-band, and the bottom right image is HH sub-band. Satellite image processing and resolution enhancement using wavelets is a relatively new subject, and recently many new algorithms have been proposed (Ashish, Kumar, & Padhy, 2011; Bhandari, Kumar, & Singh, 2012a, 2012b; Demirel & Anbarjafari, 2011). Wavelet shrinkage methodology has been proposed by Donoho(2000) and Donoho and Johnstone (1994, 1995) for classifying the wavelet coefficients of real-world noisy data, which have been further modified to increase signal-to-noise ratio (SNR). Intensive research (Chang, Yu, & Vetterli, 2000b; Donoho, 2000; Gao, 1998; Gao & Bruce, 1997) was carried out for improving the performance of thresholding, based on these domain. Consequently, a vast research has emerged recently on image denoising using wavelet thresholding or shrinkage (Donoho &

Journal of Experimental & Theoretical Artificial Intelligence (a)

Lowpass

2

Input Image

2

LL

Highpass

2

LH

2

HL

2

HH

Lowpass Highpass

Downloaded by [Inst of Info Tech Design & Manufacturing] at 00:25 23 August 2015

Lowpass

2

Highpass

3

(b)

Figure 1. (a) Block diagram of DWT filter banks of level 1 and (b) LL, LH, HL and HH sub-bands of a satellite image obtained by DWT.

Johnstone, 1994). There has been continuos focus on developing and implementing the thresholding function. The Bayes Shrink and Sure Shrink give good performance (Fodor & Kamath, 2003) on denoising by wavelet shrinkage such as soft, hard, garrote and semi-soft. Statistical approach such as the Bayesian approach for denoising the images has been proposed by researchers (Achim, Bezerianos, & Tsakalides, 2001; Achim & Kuruoglu, 2005). Various noise models for distribution of noisy wavelet coefficients such as hidden Markov models (Crouse, Nowak, & Baraniuk, 1998), Gaussian (Chang, Yu, & Vetterli, 2000a), Rayleigh (Gupta, Chauhan, & Saxena, 2005), Fisher-Tippet (Michailovich & Tannenbaum, 2006) and Maxwell (Bhuiyan, Ahmad, & Swamy, 2007) were analysed. These methods are dependent on a specific noise model, and thus reduce their flexibility. Further, some researchers (Pizurica & Philips, 2006; Portilla, Strela, Wainwright, & Simoncelli, 2003; Rabbani, 2009; Rabbani, Vafadust, Abolmaesumi, & Gazor, 2008) have proposed a mixture of statistical models, which are more computationally complex. Rabbani (2009) has proposed a mixture of Laplacian and Gaussian model for estimating the noise-free wavelet coefficient and a mixture of Gaussian and Rayleigh model for additive noise, but it is complex in computation. Joint bilateral filter in spatial domain and trivariate shrinkages filter in wavelet domain is proposed by Yu, Zhao, and Wang (2009). Generally, the conventional approaches utilise single threshold to apply on wavelet coefficients in each decomposed sub-bands. To select different thresholds for each resolution level was introduced by Jansen and Bultheel (1999). The benefit of multithresholding method is presented in Binh and Khare (2010) and Chen and Han (2005). Further improvement in perceptual quality of an image can also be achieved by proper shrinkages using an optimum threshold value determined in sub-band adaptive method, which are based on either wavelet transform or wavelet packets or adaptive thresholding function (Bhutada, Anand, & Saxena, 2011b; Soni, Bhandari, Kumar, & Singh, 2013; Nasri & Nezamabadi-Pour, 2009; Yang, Wang, Niu, & Liu, 2014; Zhang, 2001; Zhang & Desai, 1998). In 1997, Beghdadi and Khellaf (1997) proposed a noise-filtering method using local information measure, which identifies the noise through local contrast entropy. This method outperformed the well-known image denoising techique such as median filter and centreweighted median filter. In 2007, another approach for image denoising has been proposed using sparse 3-D transform-domain collaborative filtering (Dabov, Foi, Katkovnik, & Egiazarian, 2007), which is based on an enhanced sparse representation in transform domain. In this approach, the enhancement of the sparsity is obtained by grouping similar 2-D image fragments (e.g. blocks) into 3-D data arrays which is known as ‘groups’, and collaborative filtering is a special procedure that is developed to deal with these 3-D groups. Furthermore, recently an automatic parameter prediction for image denoising algorithms using perceptual quality features has been given (Mittal, Moorthy, & Bovik, 2012), which is based on natural scene statistics

Downloaded by [Inst of Info Tech Design & Manufacturing] at 00:25 23 August 2015

4

A.K. Bhandari et al.

technique. In this technique, denoising is performed without the knowledge of noise variance present in the image. In this paper, a wavelet coefficient is compared to a given threshold, if obtained magnitude is less than the threshold then it is set to zero; otherwise, it is kept or modified on the basis of thresholding rule. The threshold performs as an oracle that is used to differentiate among the irrelevant coefficients added because of noise, and the valuable coefficients containing useful signal information. Basically, thresholding criteria generate a region near to zero, in which the coefficients are assumed to be negligible. Outside of this region, thresholded coefficients are considered with full accuracy. For image denoising, the most popular thresholding approach consists of VisuShrink (Donoho & Johnstone, 1994) and SureShrink (Donoho & Johnstone, 1995). The paper is organised as follows: Section 2 gives an overview of the optimisation-based denoising process and DWT. In Section 3, different wavelet filters used for image denoising approach is discussed. Section 4 introduces particle swarm optimisation (PSO), artificial bee colony (ABC) and the proposed Cuckoo Search (CS) algorithm based on different wavelet analysis for image denoising. In Section 5, experimentation and analysis of the results with qualitative and quantitative outputs of the proposed method using different wavelet filters and supported by SNR, peak signal-to-noise ratio (PSNR), mean and mean square error (MSE) are presented. Finally, in last section, conclusions are drawn. 2.

Brief explanation of optimisation-based denoising process and DWT

The basic idea of denoising of an image using wavelet transform is as follows: first, the wavelet transform of a noisy image is taken. Then the wavelet coefficient is modified by a suitable thresholding function. Finally, after modification of the wavelet coefficient, an inverse wavelet transform is applied to obtain the reconstructed image. In the wavelet-based thresholding technique, thresholding function has a major effect on the quality of image. Therefore, many types of thresholding function were introduced having the properties of hard, soft, semi-soft and garrote. The garrote and semi-soft thresholding functions are an improved way of thresholding. These thresholding functions have property and advantage of both hard and soft thresholding. There is no flexibility exhibit due to fixed structure and dependency of these functions on a fixed threshold value. For minimisation of the above drawback, several class of thresholding functions, with several shape tuning parameters that make it more flexible in usage, have been proposed. Some researchers (Bhutada et al., 2011b; Nasri & Nezamabadi-Pour, 2009) have proposed a form of soft thresholding function. For better flexibility and capability, researchers (Bhutada, Anand, & Saxena, 2012; Soni et al., 2013) have extended Zhang’s proposed functions by adding three shape tuning factors that are given by Equation (1). 8 kl m > > Y ij 2 0:5 m21 þ ðk 2 1Þl Y ij . l > > Y ij > > > > > mþð22k=kÞ < kjY ij j signðY ij Þ Y ij # l ; ð1Þ h Nasri ðY ij ; l; k; mÞ ¼ 0:5 > l mþð22kÞ=k > > > > kð2lÞm > > Y þ 0:5 2 ðk 2 1Þl Y ij , 2l > ij > : Y m21 ij where, h is the thresholded wavelet coefficient, Yij is the wavelet coefficient of input, l is threshold, l, k and m are jointly tunning parameters, sign represents negative or positive sign of Yi,j, and 0.5 and 2.0 are constants. In this paper, the range of l, k, m are selected as [1, 0.1, 1] to [150, 1, 4] respectively.

Downloaded by [Inst of Info Tech Design & Manufacturing] at 00:25 23 August 2015

Journal of Experimental & Theoretical Artificial Intelligence

5

The thresholding function h varies from hard to soft thresholding by adjusting the parameter k [0, 1] in the given expression. The flexibility in adjustment of thresholding from hard to soft because of the variation of k is shown in Figure 2(a). The shape of the thresholding function is decided by the parameter m, which adds more flexibility to the thresholding function as shown in Figure 2(b). l is the threshold value, which has a major role in the thresholding operation. In the thresholding function, the desired optimum value of threshold is obtained by optimum value of l, k and m. To obtain the optimum value parameters, researchers (Bhutada et al., 2012; Nasri & Nezamabadi-Pour, 2009) have proposed the TNN methodolgy based on the neural networks concept. In this type of neural network, activation function has been replaced by the wavelet thresholding function. Instead of learning weights of the classical networks, learning process focuses on learning threshold value of the thresholding function. It is extended for each sub-band of the wavelet domain as shown in Figure 3. In this approach, an adaptive least mean square algorithm has been used with an adjustment of learning parameter with the help of steepest descent gradient of MSE risk or Steins unbiased risk estimation depending on availability/unavailability of the original (noise free) image, respectively. 2.1

Overview of discrete wavelet transform

Wavelet analysis allows the use of long time intervals where more precise low-frequency information is needed, and shorter regions where high-frequency information is needed. One major advantage afforded by wavelets is the ability to perform local analysis, which is to analyse a localised area of a larger signal. A wavelet is a waveform of effectively limited duration that has an average value of zero. The 2-D wavelet decomposition of an image is performed by applying 1-D DWT along the rows of the image first, and then the results are decomposed along the columns (Bhandari, Gadde, Kumar, & Singh, 2012). This action results into four decomposed sub-band images referred to LL, LH, HL and HH image as shown in Figure 4. The frequency components of those sub-bands cover the full frequency spectrum of the original image. Let the signal be ( fi,j) where, i, j ¼ 1, . . . , N and N is some integer power of 2. Assume that the signal fi,j is distorted due to additive noise and it is expressed as: gi;j ¼ f i;j þ 1i;j ;

i; j ¼ 1; . . . ; N;

ð2Þ

Figure 2. Behaviour of thresholding function with respect to variation in thresholding parameters. (a) Effect of variation of k between 0 and 1 with m ¼ 2, l ¼ 5 and (b) effect of variation of m between 2 and 10 with k ¼ 1, l ¼ 5 (Nasri & Nezamabadi-Pour, 2009).

6

A.K. Bhandari et al.

Low Contrast Image

Adaptive Thresholding Function (λ, k, m)

Different Wavelet Filters (DWT)

Optimization Technique (CS, ABC and PSO)

Inverse DWT

Denoised Image

Downloaded by [Inst of Info Tech Design & Manufacturing] at 00:25 23 August 2015

Figure 3. Wavelet domain thresholding approach.

where 1i,j is the noisy signal and is identically distributed and independent of signal ( fi,j). The aim is to eliminate the noise or denoised (gi,j), and to achieve an estimate f^i;j of f i;j , which minimises the MSE as given in Equation (3). Let g ¼ (gi,j)i,j, f ¼ ( fi,j)i,j and 1 ¼ (1i,j)i,j. The boldfaced letters represent matrix illustration of the signals under consideration. Let Y ¼ Wg, which represents the matrix of wavelet coefficients of g, where W is the 2-D DWT operator, and similarly Z ¼ Wf and V ¼ W1. The sub-bands HHk, HLk, LHk, where k ¼ 1, 2, . . . , J are called the detailed coefficients of DWT and k is the scale, with J being higher scale in the decomposition. The wavelet thresholding-based denoising method filters each coefficient Yi,j from the detail sub-bands using objective function given in Equation (1) to achieve X^ i;j . The denoised estimate ^ where W 21 is the inverse wavelet transform. is then f^ ¼ W 21 ðXÞ, 3. Overview of different wavelet filters Wavelets were first used in 1909 in a thesis by Alfred Haar. The present theoretical form was first proposed by Jean Morlet et al. in the Marseille Theoretical Physics Center. Wavelet analyses have been developed mainly by Y. Meyer. The main algorithm developed by Stephane Mallat in 1988 (Mallat, 1989). Haar wavelet is a sequence of rescaled ‘square-shaped’ functions, which jointly develop a wavelet family or basis. It is same as Fourier analysis in which it allows a target function over an interval to be denoted in terms of an orthonormal function basis. The Haar sequence is now recognised as the first known wavelet basis. Haar, the first and simplest wavelet, is a step function. The drawback of Haar wavelet is that it is not continuous and due to that it is not LL3

HL3

LH3 HH3

HL2 HL1

LH2

HH2

LH1

Figure 4. Sub-bands of the 2-D discrete wavelet transform.

HH1

Downloaded by [Inst of Info Tech Design & Manufacturing] at 00:25 23 August 2015

Journal of Experimental & Theoretical Artificial Intelligence

7

differentiable, although this property can be beneficial for the analysis of signals or images with immediate transitions, such as monitoring of tool failure in machines. Daubechies wavelets are widely used in solving a broad range of problems, for example selfsimilarity properties of a signal or fractal problems, signal discontinuities, etc. Ingrid Daubechies invented the compactly supported orthonormal wavelets making DWT practicable. It is characterised by a maximal number of vanishing moments for some given support. With each wavelet type of this category, there is a scaling function (known as father wavelet) that is used to generate an orthogonal multi-resolution analysis. Name of the Daubechies family wavelets is written as dbN, where N is the order, and db the ‘surname’ of the wavelet. The db1 wavelet, as mentioned above, is the same as Haar (Gonzalez & Woods, 2007). These wavelets have no explicit expression except for db1, which is the Haar wavelet. However, the square modulus of transfer function of h is explicit and fairly simple. More details of each wavelet filters such as Haar wavelet, Daubechies wavelets, Symlets wavelets, Coiflets wavelets, Biorthogonal wavelets, reverse biorthogonal wavelets and discrete approximation of Meyer wavelet are given in Bhandari, Gadde, et al. (2012). 4. Different wavelet filters-based proposed satellite image denoising using evolutionary techniques 4.1

PSO technique

PSO (Kennedy & Eberhart, 1995) algorithm is inspired by social behaviour patterns of organisms that live and interact within the large groups. In particular, it incorporates swarming behaviours observed in flocks of birds, schools of fish or swarms of bees, and even human social behaviour from which the swarm intelligence (SI) paradigm has emerged (Clerc & Kennedy, 2002; Poli, Kennedy, & Blackwell, 2007; Vandenbergh & Engelbrecht, 2004). PSO technique for image denoising was proposed by Bhutada et al. (2012). PSO is used for tuning the thresholding function parameters l, k and m 9 (Bhutada, Anand, & Saxena, 2011a). Here, fitness function is taken as MSE, which can be minimised using Equation (3). f ¼ MSEðy; y^ Þ ¼

N 1X ½yðnÞ 2 y^ ðnÞ2 ; N n¼1

ð3Þ

where N is the is the size of sub-band, y (n) is the WT coefficients of noise free image and y^ ðnÞ is the thresholded WT coefficients of noisy image. In order to show the connection of phases of the PSO algorithm, a flowchart is presented in Figure 5. 4.1.1

PSO based denosing

In PSO, possible solution and collection of possible solutions (search space) are known as particle position and swarm correspondingly. The PSO is dominated by two basic updating equations for particle position i, first is velocity updating equation, which is formulated as V i ðk þ 1Þ ¼ w £ V i ðkÞ þ c1 f1 ðPibest ðkÞ 2 Pi ðkÞÞ þ c2 f2 ðGbest ðkÞ 2 Pi ðkÞÞ;

ð4Þ

and second is position updating equation defined as Pi ðk þ 1Þ ¼ Pi ðkÞ þ V i ðk þ 1Þ;

ð5Þ

where w represents the inertia weight factor, which varies linearly from 0 to 1, while c1 and c2 are cognitive and social acceleration factors, respectively, and u1 and u2 indicate uniformly

8

A.K. Bhandari et al. Initialization of PSO

Determine gbest of the PSO

Calculate the fitness values of the particles

Downloaded by [Inst of Info Tech Design & Manufacturing] at 00:25 23 August 2015

Update the velocities of the particles using Eq. (4)

Update the positions of the particles using Eq. (5)

Determine personal bests of the particles

Determine the gbest of the population

Is a termination criteria fulfilled?

No

Yes Obtain the best solution

Figure 5. Flowchart of PSO algorithm.

distributed random numbers in the range of 0 – 1. The next velocity Vi (k þ 1) of particle i can be computed by Equation (4) and the next position Pi (k þ 1) is tracked by Equation (5). Fundamentally, particle position Pi indicates one possible solution of optimisation problem, and at each iteration, the objective function (fitness function) is measured by position vector Pi (k). The position vector corresponding to best fitness is called ‘pbest’ and the overall best solution of all the particles in population is known as ‘gbest’. In PSO algorithm, the success in finding the global optimum depends exceptionally on initial values of the control parameters such as w, c1, c2, u1, u2, swarm size (s) and the maximum iteration number. 4.2 ABC algorithm based denosing SI is briefly defined as the collective behaviour of decentralised and self-organised swarms. The well-known examples for these swarms are bird flocks, fish schools and the colony of social insects such as termites, ants and bees (Karaboga, Gorkemli, Ozturk, & Karaboga, 2012). ABC optimisation is developed by Karaboga (2005). In order to show the connection of phases of the ABC algorithm, a complete flowchart routine is shown in Figure 6. In addition, a detailed discussion on ABC optimisation algorithm is given in Bhandari, Kumar, and Singh (2014), Bhandari, Soni, Kumar, and Singh (2014a) and Karaboga and Akay (2009). In ABC, each food source position stands for a set of possible solutions to the particular optimisation problem. After random generation of food source, the honey bees are divided

Journal of Experimental & Theoretical Artificial Intelligence

9

Initialization of ABC

Employed Bee Phase

Onlooker Bee Phase

Downloaded by [Inst of Info Tech Design & Manufacturing] at 00:25 23 August 2015

Store the best food source position using Eq. (6)

Yes Scout Bee Phase

Is there a scout bee in the colony? No

Is a termination criteria fulfilled?

No

Yes Obtain the best solution

Figure 6. General flowchart of the ABC algorithm.

into three types: employed bees, onlooker bees and scout bees. Initially, overall bees in the hive are equally divided into employed and onlooker bees. Employed bees and onlooker bees are positioned to search food sources and to measure the amount of nectar (fitness value or objective function) of those sources, respectively, whereas scout bees walk around the entire colony without any guidance. The neighbour food position is formulated as SPi ðc þ 1Þ ¼ SPi ðcÞ þ xi ðSPi ðcÞ 2 SPk ðcÞÞ;

ð6Þ

where xi is randomly generated in the range of [ – 1, þ 1], c denotes number of cycle and k stands for a randomly created index, which is different from i. If the nectar amount or fitness value F (SPi (c þ 1)) is superior in comparison with F (SPi (c)), then the employed bee stores SPi (c þ 1) and shares her information with the onlooker bees, and the position SPi (c) of food source i is updated by SPi (c þ 1), or else SPi (c) remains same. Each food source has single employed bee that means employed bees are equal to food sources. After some predefined trials or ‘limit’, if the position SPi (c) of food source i does not improve, the food source i is abandoned and the corresponding bees are declared as scout bee. Random food sources are assigned to scout bees to search for a new food source and after finding a fit one, the new position is accepted to be SPi (c þ 1).

10

A.K. Bhandari et al.

Downloaded by [Inst of Info Tech Design & Manufacturing] at 00:25 23 August 2015

4.3 Proposed CS algorithm-based denoising CS is a metaheuristic search algorithm, which has been proposed recently by Yang and Deb (2009). The algorithm is based on the obligate brood parasitic behaviour of some cuckoo species in combination with Le´vy flight behaviour of fruit flies and some of the birds (Bhandari, Soni, Kumar, & Singh, 2014b). Each egg in CS algorithm represents a solution and Cuckoo egg represents a new solution. A detailed conceptual comparison of these optimisation algorithms are given in Civicioglu and Besdok (2013). A detailed description of CS is given in Bhandari, Singh, Kumar, and Singh (2014). The CS is based on three idealised rules: (i) Each Cuckoo lays one egg at a time, and dumps it in a randomly chosen nest. (ii) The best nests with high quality of eggs (solutions) will carry over to the next generations. (iii) The number of available host nests is fixed, and a host can discover an alien egg with probability pa [ [0 1]. In this case, the host bird can either throw the egg away or abandon the nest to build a completely new nest in a new location. The steps involved in the CS are then derived from these rules and are shown in Figure 7. Based on afore mentioned rules, the basic steps of Cuckoo algorithm are as follows: Step 1: Set the number of nest. Nest is nothing but different solutions. In this problem, it is taken as 20. Set the probability with a discovery rate (probability). Set the stopping criteria, which is either a fixed number of iteration or tolerance value. Set the dimension of the problem, number of dimension is 3. Also, set the boundaries of parameters. Step 2: Randomly initialise the solution by generating n different nests for obtaining n different solutions using Equation (1). Step 3: Evaluate fitness for each of the obtained solution using Equation (3). Find best nest corresponding to minimum value of fitness. Step 4: Start iteration, generate new nest by Le´vy flight but keep the current best. A Le´vy flight can be formed as Cuckoo i, and a Le´vy flight is performed by the equation: xi ðt þ 1Þ ¼ xðtÞi þ a % LevyðlÞ;

ð7Þ

where a is the step size. It essentially provides a random walk while the random step length is drawn from Le´vy distribution, which has an infinite variance with an infinite mean. Le´vy distribution is given by: Levy , u ¼ t 2l ;

ð1 , l # 3Þ:

ð8Þ

Le´vy function can be changed according to the application. Mantegna’s algorithm is one of the Le´vy functions. Step 5: Evaluate this set of solutions and obtain the new fitness. Compare old fitness with this new fitness. Replace old fitness if the new fitness is better than the old one. Update best nest corresponding to fitness. Step 6: Repeat the above process until some stopping criteria is achieved giving the best fitness and corresponding best nest. In addition, a complete flowchart routine of optimisationbased methodology for image denoising is shown in Figure 8 which describes detailed steps of the overall algorithm. 5. Experimentation and analysis of results In this section, different evolutionary algorithms, based on the proposed denoising scheme, are exploited for satellite images. Performance of the proposed scheme is computed by determining the

Journal of Experimental & Theoretical Artificial Intelligence

11

Initialization the population of ‘n’ hostnest, set iteration=1 Yes Is Iteration > Max-Iteration No

Downloaded by [Inst of Info Tech Design & Manufacturing] at 00:25 23 August 2015

Set a cuckoo ‘i' randomly using Lévy flights Eq. (7)

Evaluate the quality of egg ‘fi’

Choose a nest ‘j’ randomly from ‘n’ nests

Evaluate the quality of egg ‘fi’ No fi > fj Yes Replace the egg ‘j’ with ‘i’

Abandon a fraction (pa) of worse nest

Build new nests at new locations via Lévy flights to replace nests lost

Evaluate fitness of new nests to find the current best and rank all solutions

Report the best solution

Figure 7. Flowchart of Cuckoo search algorithm.

different fidelity parameters such as mean, MSE, SNR and PSNR given by Equations (9)–(12), respectively. Different satellite images are included to demonstrate the usefulness of this algorithm. Performance of this method is measured in terms of the following significant parameters: MeanðmÞ ¼

21 X N 21 X 1 M Iðx; yÞ; MN x¼1 y¼1

ð9Þ

where the mean (m) is the average of all intensity value. It denotes average brightness of the image. Here, I (x, y) is the intensity value of pixel (x, y), and M and N) are the dimensions of the image. Any pixel of an image can be considered as a random variable with a distribution function.

12

A.K. Bhandari et al. Noisy Image

DWT of Noisy Image

Downloaded by [Inst of Info Tech Design & Manufacturing] at 00:25 23 August 2015

Used Different Wavelet Filters

LL1

LH1

HL1

HH1

DWT of LL1

Thresholding function η(λ , k, m)

LL2

LH2

HL2

HH2

Optimization algorithm

Minimum MSE

Thresholding for each sub-band

IDWT of LL2, thresholded LH2, HL2, HH2

IDWT of HL1, HH2, thresholded LL1, LH1

Denoised Image

Figure 8. Flowchart of the optimization-based methodology for image denoising.

PSNR block computes the PSNR in decibels between two images. This ratio is often used as a quality measurement between the original and denoised images. Higher PSNR signifies better quality of the denoised or reconstructed image. MSE and PSNR are the two error metrics used to compare the enhanced or denoised quality of the images. MSE represents the cumulative squared error between the enhanced and original image, whereas PSNR represents a measure of the peak error. Lower value of MSE represents lower error (Tables 1 – 3).

Journal of Experimental & Theoretical Artificial Intelligence

13

Table 1. Parameters used for PSO.

Downloaded by [Inst of Info Tech Design & Manufacturing] at 00:25 23 August 2015

Parameters

Value

Swam size Number of time steps Cognitive and social ACCELERATION Constant (C1, C2) Inertia weight (w) Lower bound (LB) (Xmin) for (l, k, m) Upper bound (UB) (Xmax) for (l, k, m) Scalar minimum for particle velocity (vMin) Scalar maximum for particle velocity (vMax (i)) Number of dimensions (Nd)

50 200 2, 2 0.9 [1, 0.1, 1] [150, 2, 4] [0, 0.001, 0.01] [10, 0.4, 0.4] 3

Table 2. Parameters used for ABC. Parameters

Value

The number of colony size (Np) The number of food sources Limit trials The number of cycles for foraging {a stopping criteria} The number of parameters of the problem to be optimised (D1) Lower bound (LB) (Xmin) for (l, k, m) Upper bound (UB) (Xmax) for (l, k, m)

50 (Np/2) 100 10 3 [1, 0.1, 1] [150, 1, 4]

To compute PSNR, block first calculates the mean-squared error using the following equation: 1 X MSEðsÞ ¼ ½I 1 ðm; nÞ 2 I 2 ðm; nÞ2 ; ð10Þ MN M;N Here, M and N are the number of rows and columns in the input images, respectively. Block computes the SNR and PSNR in dB using the following equations: 

 signal power ; noise power  2  R PSNR ðbÞ ¼ 10 log 10 ; MSE

SNRðaÞ ¼ 10 log 10

ð11Þ ð12Þ

where R is the maximum fluctuation in input image data type. Table 3. Parameters used for CS algorithm. Parameters Number of nests Number of iterations Mutation probability value ( pa) Lower bound (LB) (Xmin) for (l, k, m) Upper bound (UB) (Xmax) for (l, k, m)

Value 30 100 0.25 [1, 0.1, 1] [150, 1, 4]

14

A.K. Bhandari et al. Calculation of Edge Keeping Index (EKI) or Edge Preservation Index (EPI).

Downloaded by [Inst of Info Tech Design & Manufacturing] at 00:25 23 August 2015

PN i¼1 ðDgi 2 Dmg ÞðDf i 2 Dmf Þ ffi; EKI ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi PN PN 2 2 ðDg 2 D m Þ ðDf 2 D m Þ i g i f i¼1 i¼1

ð13Þ

where gi and fi are the original and reconstructed images, respectively. Dgi and Dfi are found by filtering g and f through high-pass Laplacian filter with mean values as mg and mf, respectively. The EKI calculates that how much the edges are preserved for reconstructed image compared with the original image. More the value of EKI or EPI, more is the edge details that are conserved as referred in Table 7. To analyse robustness of the proposed approach, two INSAT images having three bands and one LANDSAT image having seven bands are taken for better interpretation of results. In order to show effectiveness of the proposed method, various wavelet filters are used for comparison purpose. Table 4 indicates the comparison of mean, MSE, SNR and PSNR performance indices of the proposed CS algorithm technique using different wavelet filters. It was found that Meyer wavelet filter-based CS algorithm gives best denoised images in comparison with PSO- and ABC-based approach. Table 5 depicts the comparison of mean, MSE, SNR and PSNR performance indices of the ABC technique using different wavelet filters, whereas Tables 6 signifies the comparison of mean, MSE, SNR and PSNR performance indices of the PSO technique using different wavelet filters. Visual results of the proposed technique are shown in Figure 9 (l1, l2 and l3) supported by the quantitative results given in Table 4. Results in Table 4 clearly indicate superiority of the proposed technique over ABC- and PSO-based image denoising techniques (Table 7). The comparative performances of all the three individual sets of results using different wavelet based approaches are depicted in Tables 4– 6, respectively. Table 4 shows that the Meyer wavelet filter-based CS algorithm approach gives the best result. Performance of Meyer wavelet filter-based ABC algorithm was also found to be better. Further testing of the performance of other applied algorithm is elaborated in Tables 5 and 6. From Table 4, it is evident that the proposed CS algorithm approach with ‘dmey’ wavelet filter yields best results when compared to the results of ‘haar’, ‘sym4’, ‘coif5’, ‘rbior3.9’, ‘rbior4.4’, ‘bior3.3’, ‘bior6.8’, ‘db8’ and ‘db10’ wavelet filters. Among all the performance indices, particularly MSE gets much decreased and PSNR gets increased when the proposed approach is used with ‘dmey’ wavelet filter instead of ‘haar’, ‘sym4’, ‘coif5’, ‘rbior3.9’, ‘rbior4.4’, ‘bior3.3’, ‘bior6.8’, ‘db8’ and ‘db10’ wavelet filters. This subjective visualisation indicates consistency with the quantitative results of better edge preserved denoising. In addition, convergence graph has been calculated for Meyer wavelet filter-based denoised images using CS algorithm for satellite images first, second and third, respectively which is shown in Figure 10 (a1), (b1), (a2), (b2), and (a3), (b3), respectively. From the Table 5, it can be observed that ABC algorithm-based approach with ‘dmey’ wavelet filter yields better results when compared to the results of ‘haar’, ‘sym4’, ‘coif5’, ‘rbior3.9’, ‘rbior4.4’, ‘bior3.3’,‘ bior6.8’, ‘db8’ and ‘db10’ wavelet filters. Each algorithm is tested for different number of iterations, and it was found that all the included methods are giving best results for almost 300 iterations. The time taken to complete the process of denoising is considered for multiband data or input original satellite image. Satellite image is a multiband data (3 bands or 7 bands) (Bhandari, Gadde, et al., 2012), so the time required to complete the process of denoising is thrice (in case of 3 band satellite image) as compared to the time required for single band or grey-scale image. Due to complexity in application of ABC algorithm and CS

a ¼ 18.5843; b ¼ 34.1425 a ¼ 19.9462; b ¼ 34.8943 a ¼ 20.1639; b ¼ 35.1427 a ¼ 20.7584; b ¼ 36.1274 a ¼ 20.3657; b ¼ 35.0289 a ¼ 21.6692; b ¼ 36.8265

m ¼ 122.0814; s ¼ 25.0513

Biorthogonal (bior3.3) m ¼ 119.3462; s ¼ 21.0693

Biorthogonal (bior6.8) m ¼ 120.3458; s ¼ 19.8980

m ¼ 122.3873; s ¼ 15.8614

m ¼ 120.0134; s ¼ 20.4263

m ¼ 124.5432; s ¼ 13.5030

Daubechies (db8)

Daubechies (db10)

Meyer (dmey)

6

7

8

9

10

Reverse biorthogonal (rbior4.4)

5

a ¼ 19.1424; b ¼ 33.5689

Reverse biorthogonal (rbior3.9)

4

m ¼ 121.2454; s ¼ 28.5884

Coiflets (coif5)

3

a ¼ 19.7234; b ¼ 33.1924

Symlets (sym4)

2

m ¼ 129.3465; s ¼ 31.1774

Haar (haar)

1

a ¼ 18.9365; b ¼ 34.0986

SNR (a); PSNR (b) in dB

m ¼ 129.3612; s ¼ 25.3058

Mean (m); MSE (s)

a ¼ 16.2431; b ¼ 32.4127

Different wavelet filters

m ¼ 118.2342; s ¼ 17.1104

m ¼ 117.0465; s ¼ 26.2416

m ¼ 117.3942; s ¼ 22.4497

m ¼ 116.3215; s ¼ 26.6662

m ¼ 121.4970; s ¼ 39.0409

m ¼ 117.2439; s ¼ 30.8014

m ¼ 116.0397; s ¼ 25.3356

m ¼ 121.3492; s ¼ 27.1425

m ¼ 115.3619; s ¼ 32.3140

m ¼ 114.2049; s ¼ 48.5971

Mean (m); MSE (s)

a ¼ 20.8457; b ¼ 35.7982

a ¼ 18.9365; b ¼ 33.9409

a ¼ 19.8246; b ¼ 34.6187

a ¼ 19.8792; b ¼ 33.8712

a ¼ 18.9340; b ¼ 32.2156

a ¼ 18.2354; b ¼ 33.2451

a ¼ 19.5368; b ¼ 34.0935

a ¼ 19.0694; b ¼ 33.7943

a ¼ 18.4643; b ¼ 33.0369

a ¼ 16.5983; b ¼ 31.2647

SNR (a); PSNR (b) in dB

Denoised image 2

Denoised image 1

m ¼ 121.7154; s ¼ 37.3087

Sr. no.

Data-set

Input image 2: mean (m ¼ 114.8540); Noisy image 2: MSE (s ¼ 86.8708)

Input image 1: mean (m ¼ 124.0820); Noisy image 1: MSE (s ¼ 86.7657)

Table 4. Comparison of denoised images using various wavelets filters based on proposed CS algorithm.

m ¼ 116.3689; s ¼ 16.4987

m ¼ 110.3542; s ¼ 24.6264

m ¼ 113.8924; s ¼ 19.6485

m ¼ 110.3791; s ¼ 17.8103

m ¼ 115.9731; s ¼ 33.0195

m ¼ 114.5324; s ¼ 31.5377

m ¼ 117.4221; s ¼ 26.1481

m ¼ 118.3429; s ¼ 24.7372

m ¼ 119.6432; s ¼ 25.7719

m ¼ 114.3495; s ¼ 42.3312

Mean (m); MSE (s)

a ¼ 22.0936; b ¼ 35.9563

a ¼ 19.8634; b ¼ 34.2168

a ¼ 21.8436; b ¼ 35.1975

a ¼ 21.2465; b ¼ 35.6241

a ¼ 20.1038; b ¼ 32.9431

a ¼ 20.2412; b ¼ 33.1425

a ¼ 19.4830; b ¼ 33.9564

a ¼ 19.9401; b ¼ 34.1973

a ¼ 19.9032; b ¼ 34.01934

a ¼ 17.2935; b ¼ 31.8642

SNR (a); PSNR (b) in dB

Denoised image 3

Input image 3: mean (m ¼ 108.4103); Noisy image 3: MSE (s ¼ 85.7345)

Downloaded by [Inst of Info Tech Design & Manufacturing] at 00:25 23 August 2015

Journal of Experimental & Theoretical Artificial Intelligence 15

a ¼ 18.0192; b ¼ 33.7928 a ¼ 18.9725; b ¼ 33.7204 a ¼ 19.4762; b ¼ 34.8346 a ¼ 19.6402; b ¼ 35.6925 a ¼ 19.0245; b ¼ 34.8501 a ¼ 16.0548; b ¼ 36.0748

m ¼ 121.2658; s ¼ 27.1519

Biorthogonal (bior3.3) m ¼ 118.4392; s ¼ 27.6083

Biorthogonal (bior6.8) m ¼ 122.4935; s ¼ 21.3609

m ¼ 124.8013; s ¼ 17.5320

m ¼ 121.469; s ¼ 21.2848

m ¼ 125.7932; s ¼ 16.4682

Daubechies (db8)

Daubechies (db10)

Meyer (dmey)

6

7

8

9

10

Reverse biorthogonal (rbior4.4)

5

a ¼ 18.4972; b ¼ 33.8291

Reverse biorthogonal (rbior3.9)

4

m ¼ 123.8926; s ¼ 26.9259

Coiflets (coif5)

3

a ¼ 19.1572; b ¼ 32.8261

Symlets (sym4)

2

m ¼ 128.1852; s ¼ 33.9211

Haar (haar)

1

a ¼ 18.2014; b ¼ 33.7652

SNR (a); PSNR (b) in dB

m ¼ 128.4652; s ¼ 27.3250

Mean (m); MSE (s)

m ¼ 119.4762; s ¼ 19.9370

m ¼ 118.0392; s ¼ 31.8010

m ¼ 119.4265; s ¼ 25.3140

m ¼ 117.3469; s ¼ 31.7936

m ¼ 118.2431; s ¼ 33.3703

m ¼ 118.9432; s ¼ 33.8408

m ¼ 118.4943; s ¼ 26.1018

m ¼ 122.4098; s ¼ 32.2798

m ¼ 116.243; s ¼ 34.1885

m ¼ 122.2342; s ¼ 61.4993

Mean (m); MSE (s)

a ¼ 11.2072; b ¼ 37.6359

a ¼ 18.0439; b ¼ 33.1064

a ¼ 19.1087; b ¼ 34.0972

a ¼ 19.0238; b ¼ 33.1074

a ¼ 18.0124; b ¼ 32.8972

a ¼ 18.1034; b ¼ 32.8364

a ¼ 19.0132; b ¼ 33.9641

a ¼ 18.7492; b ¼ 33.0415

a ¼ 18.1203; b ¼ 32.7920

a ¼ 15.2431; b ¼ 30.2421

SNR (a); PSNR (b) in dB

Denoised image 2

Denoised image 1

a ¼ 15.2392; b ¼ 29.9542

Different wavelet filters

Noisy image 2: MSE (s ¼ 86.8708)

Noisy image1: MSE (s ¼ 86.7657)

m ¼ 124.1395; s ¼ 65.7144

Sr. no.

Data-set

Input image 2: mean (m ¼ 114.8540)

Input image 1: mean (m ¼ 124.0820)

Table 5. Comparison of denoised images using various wavelets filters based on ABC technique.

m ¼ 118.2419; s ¼ 20.9765

m ¼ 112.7942; s ¼ 27.1438

m ¼ 115.2976; s ¼ 21.5675

m ¼ 116.4928; s ¼ 21.0785

m ¼ 117.2495; s ¼ 40.9110

m ¼ 115.5625; s ¼ 33.6597

m ¼ 118.2435; s ¼ 31.5400

m ¼ 119.2853; s ¼ 27.3691

m ¼ 118.0146; s ¼ 27.6796

m ¼ 117.2436; s ¼ 51.9470

Mean (m); MSE (s)

a ¼ 21.8346; b ¼ 34.91348

a ¼ 19.0432; b ¼ 33.7941

a ¼ 20.9640; b ¼ 34.7928

a ¼ 20.9390; b ¼ 34.8924

a ¼ 19.2342; b ¼ 32.0124

a ¼ 19.5203; b ¼ 32.8597

a ¼ 18.8752; b ¼ 33.1419

a ¼ 19.0421; b ¼ 33.7582

a ¼ 19.1032; b ¼ 33.7092

a ¼ 16.2406; b ¼ 30.9752

SNR (a); PSNR (b) in dB

Denoised image 3

Noisy image 3: MSE (s ¼ 85.7345)

Input image 3: mean (m ¼ 108.4103)

Downloaded by [Inst of Info Tech Design & Manufacturing] at 00:25 23 August 2015

16 A.K. Bhandari et al.

a ¼ 17.9824; b ¼ 32.6493 a ¼ 18.1034; b ¼ 32.1459 a ¼ 19.0964; b ¼ 34.3716 a ¼ 19.1286; b ¼ 35.1754 a ¼ 18.7630; b ¼ 34.1082 a ¼ 20.4391; b ¼ 35.0139

m ¼ 125.2431; s ¼ 35.3305

Biorthogonal (bior3.3) m ¼ 117.2431; s ¼ 39.6726

Biorthogonal (bior6.8) m ¼ 121.4352; s ¼ 23.7640

m ¼ 124.5682; s ¼ 19.7488

m ¼ 122.2151; s ¼ 25.2499

m ¼ 131.2431; s ¼ 20.4970

Daubechies (db8)

Daubechies (db10)

Meyer (dmey)

6

7

8

9

10

Reverse biorthogonal (rbior4.4)

5

a ¼ 17.8903; b ¼ 32.1064

Reverse biorthogonal (rbior3.9)

4

m ¼ 126.4850; s ¼ 40.0350

Coiflets (coif5)

3

a ¼ 18.8034; b ¼ 32.1940

Symlets (sym4)

2

m ¼ 125.2895; s ¼ 39.2356

Haar (haar)

1

a ¼ 17.9204; b ¼ 32.1420

SNR (a); PSNR (b) in dB

m ¼ 129.234; s ¼ 39.7082

Mean (m); MSE (s)

a ¼ 15.0147; b ¼ 29.1091

Different wavelet filters

Denoised image 1

m ¼ 119.2146; s ¼ 21.7155

m ¼ 118.2462; s ¼ 33.6249

m ¼ 119.4328; s ¼ 27.6592

m ¼ 119.1438; s ¼ 33.2139

m ¼ 124.6589; s ¼ 50.7178

m ¼ 126.4583; s ¼ 34.8450

m ¼ 120.4930; s ¼ 32.4586

m ¼ 128.9342; s ¼ 34.7240

m ¼ 117.5620; s ¼ 40.8536

m ¼ 118.3421; s ¼ 62.9391

Mean (m); MSE (s)

a ¼ 20.0193; b ¼ 34.7631

a ¼ 17.9243; b ¼ 32.8642

a ¼ 18.2094; b ¼ 33.7124

a ¼ 19.0137; b ¼ 32.9176

a ¼ 17.9832; b ¼ 31.0792

a ¼ 17.8623; b ¼ 32.7094

a ¼ 18.4520; b ¼ 33.0175

a ¼ 18.1356; b ¼ 32.7245

a ¼ 18.2234; b ¼ 32.0185

a ¼ 14.8920; b ¼ 30.1416

SNR (a); PSNR (b) in dB

Denoised image 2

Noisy image 2: MSE (s ¼ 86.8708)

Noisy image 1: MSE (s ¼ 86.7657)

m ¼ 124.2491; s ¼ 79.8308

Sr. no.

Data-set

Input image 2: mean (m ¼ 114.8540)

Input image 1: mean (m ¼ 124.0820)

Table 6. Comparison of denoised images using various wavelets filters based on PSO technique.

m ¼ 119.4365; s ¼ 23.4920

m ¼ 113.249; s ¼ 32.4534

m ¼ 116.2430; s ¼ 25.1791

m ¼ 112.4672; s ¼ 25.1137

m ¼ 119.2461; s ¼ 47.0815

m ¼ 116.0238; s ¼ 39.2772

m ¼ 117.2904; s ¼ 33.1719

m ¼ 117.5456; s ¼ 33.0271

m ¼ 119.4520; s ¼ 31.1430

m ¼ 115.2934; s ¼ 64.7531

Mean (m); MSE (s)

a ¼ 20.9937; b ¼ 34.4216

a ¼ 18.7034; b ¼ 33.0182

a ¼ 20.09537; b ¼ 25.1791

a ¼ 20.0926; b ¼ 34.1317

a ¼ 18.9452; b ¼ 31.4023

a ¼ 19.0485; b ¼ 32.1894

a ¼ 18.2401; b ¼ 32.9231

a ¼ 18.7620; b ¼ 32.9421

a ¼ 18.7304; b ¼ 33.1972

a ¼ 16.4263; b ¼ 30.0182

SNR (a); PSNR (b) in dB

Denoised image 3

Noisy image 3: MSE (s ¼ 85.7345)

Input image 3: mean (m ¼ 108.4103)

Downloaded by [Inst of Info Tech Design & Manufacturing] at 00:25 23 August 2015

Journal of Experimental & Theoretical Artificial Intelligence 17

18

A.K. Bhandari et al.

Downloaded by [Inst of Info Tech Design & Manufacturing] at 00:25 23 August 2015

Input Images

(a1)

(a2)

(a3)

(b1) Haar Wavelet (haar)

(b2)

(b3)

(c1) Symlets Wavelet (sym4)

(c2)

(c3)

(d1)

(d2)

(d3)

Noisy Images

Figure 9. (a1 – a3) show low contrast satellite images, (b1– b3) represent noisy image, (c1– c3) indicate Haar wavelet filter-based denoised images using CS algorithm, (d1 – d3) show Symlets4 wavelet filterbased denoised image using CS algorithm, (e1– e3) show Coiflets5 wavelet filter-based denoised image using CS algorithm, (f1 – f3) show Reverse Biorthogonal3.9 wavelet filter-based denoised image using CS algorithm, (g1 – g3) show Reverse Biorthogonal4.4 wavelet filter-based denoised image using CS algorithm, (h1– h3) show Biorthogonal3.3 wavelet filter-based denoised image using CS algorithm, (i1 – i3) show Biorthogonal6.8 wavelet filter-based denoised image using CS algorithm, (j1 –j3) show Daubechies8 wavelet filter-based denoised image using CS algorithm, (k1 –k3) show Daubechies10 wavelet filter-based denoised image using CS algorithm and (l1– l3) show Meyer wavelet filter-based denoised image using CS algorithm.

Journal of Experimental & Theoretical Artificial Intelligence

19

Downloaded by [Inst of Info Tech Design & Manufacturing] at 00:25 23 August 2015

Coiflets Wavelet (coif5)

(e1) Reverse Biorthogonal Wavelet (rbior3.9)

(e2)

(f1) Reverse Biorthogonal Wavelet (rbior4.4)

(f2)

(f3)

(g1) Biorthogonal Wavelet (bior3.3)

(g2)

(g3)

(h2)

(h3)

(h1)

(e3)

Figure 9. (Continued)

algorithm in image denoising, the time taken is more as compared to PSO but fidelity parameter mean, MSE, SNR and PSNR values are better. From Table 6, it can be observed that PSO-based approach with ‘dmey’ wavelet filter yields better results as compared to ‘haar’, ‘sym4’, ‘coif5’, ‘rbior3.9’, ‘rbior4.4’, ‘bior3.3’, ‘bior6.8’, ‘db8’ and ‘db10’ wavelet filters. Analysis of the results, depicted in Table 4 –6, reveals that dmey’ wavelet filter yields better results in the case of all the approaches such as CS algorithm, ABC- and PSO-based methods, but it is found that the proposed CS algorithm approach with ‘dmey’ wavelet filter yields best results.

20

A.K. Bhandari et al.

Downloaded by [Inst of Info Tech Design & Manufacturing] at 00:25 23 August 2015

Biorthogonal Wavelet (bior6.8)

(i1) Daubechies Wavelets (db8)

(i2)

(i3)

(j1) Daubechies Wavelets (db10)

(j2)

(j3)

(k1) Discrete approximation of Meyer Wavelet (dmey)

(k2)

(l1)

(l2)

(k3)

(l3)

Figure 9. (Continued)

6.

Conclusion

In this paper, a comparative study of the performance of wavelet based denoising schemes is presented for satellite images using different evolutionary algorithms such as CS algorithm, ABC algorithm and PSO for learning of parameters of adaptive thresholding function required for optimum performance. In most of the image-processing applications, a suitable noise removal phase is often required before any relevant information could be extracted from the

Journal of Experimental & Theoretical Artificial Intelligence

21

Table 7. EKI or EPI. Method (100 iterations)

Downloaded by [Inst of Info Tech Design & Manufacturing] at 00:25 23 August 2015

PSO Meyer wavelet ABC using Meyer wavelet CS algorithm Meyer wavelet

(EPI) sample image 1

(EPI) sample image 2

(EPI) sample image 3

0.3343 0.6645 0.6878

0.3324 0.6792 0.6947

0.5499 0.4287 0.6289

analysed images. The performance and accuracy of the proposed method were examined on benchmark functions. A relative study of different evolutionary algorithms has also been made. The proposed wavelet based technique was tested on several satellite images, where their EKI or

Figure 10. (a1), (b1), (a2), (b2) and (a3), (b3) shows the convergence graph of Meyer wavelet filter based denoised images using CS Algorithm for satellite images 1st, 2nd and 3rd respectively.

22

A.K. Bhandari et al.

EPI, mean, MSE, SNR, PSNR and visual results show the superiority of proposed technique over other denoising approach such as ABC and PSO techniques. Finally, it is concluded that Meyer wavelet filter-based CS algorithm denoising method outperforms all other wavelet filter-based methods not only for noise suppression but also for edge preservation. Disclosure statement

Downloaded by [Inst of Info Tech Design & Manufacturing] at 00:25 23 August 2015

No potential conflict of interest was reported by the authors.

Notes 1. Email: [email protected] 2. Email: [email protected] 3. Email: [email protected]

References Achim, A., Bezerianos, A., & Tsakalides, P. (2001). Novel Bayesian multiscale method for speckle removal in medical ultrasound images. IEEE Transaction on Medical Imaging, 20, 772– 783. doi:10. 1109/42.938245 Achim, A., & Kuruoglu, E. (2005). Image denoising using bivariate-stable distributions in the complex wavelet domain. IEEE Signal Processing Letters, 12, 17 – 20. doi:10.1109/LSP.2004.839692 Ashish, B. K., Kumar, A., & Padhy, P. K. (2011). Satellite image processing using discrete cosine transform and singular value decomposition. In Proceedings Advances in Digital Image Processing and Information Technology (pp. 277– 290). Springer Berlin Heidelberg. Beghdadi, A., & Khellaf, A. (1997). A noise-filtering method using a local information measure. IEEE Transactions on Image Processing, 6, 879– 882. doi:10.1109/83.585237 Bhadauria, H. S., & Dewal, M. L. (2014). Analysis of effect of cycle spinning on wavelet- and curveletbased denoising methods on brain CT images. Journal of the Chinese Institute of Engineers, 37, 939– 945. doi:10.1080/02533839.2014.912771 Bhandari, A. K., Gadde, M., Kumar, A., & Singh, G. K. (2012). Comparative analysis of different wavelet filters for low contrast and brightness enhancement of multispectral remote sensing images. In Proceedings IEEE international conference on machine vision and image processing (MVIP) (pp. 81 –86). Taipei: IEEE. doi:10.1109/MVIP.2012.6428766. Bhandari, A. K., Kumar, A., & Padhy, P. K. (2011). Enhancement of low contrast satellite images using discrete cosine transform and singular value decomposition. World Academy of Science, Engineering and Technology, 55, 35– 41. Bhandari, A. K., Kumar, A., & Singh, G. K. (2012a). Feature extraction using Normalized Difference Vegetation Index (NDVI): A case study of Jabalpur city. Procedia Technology, 6, 612– 621. doi:10. 1016/j.protcy.2012.10.074 Bhandari, A. K., Kumar, A., & Singh, G. K. (2012b). SVD based poor contrast improvement of blurred multispectral remote sensing satellite images. In Proceeding IEEE 3rd international conference on computer and communication technology (ICCCT) (pp. 156– 159). Allahabad: IEEE. doi:10.1109/ ICCCT.2012.81. Bhandari, A. K., Kumar, A., & Singh, G. K. (2014). Modified artificial bee colony based computationally efficient multilevel thresholding for satellite image segmentation using Kapur’s, Otsu and Tsallis functions. Expert Systems with Applications, 42, 1573 –1601. Retrieved from http://dx.doi.org/10. 1016/j.eswa.2014.09.049 Bhandari, A. K., Singh, V. K., Kumar, A., & Singh, G. K. (2014b). Cuckoo search algorithm and wind driven optimization based study of satellite image segmentation for multilevel thresholding using Kapur’s entropy. Expert Systems with Applications, 41, 3538– 3560. doi:10.1016/j.eswa.2013.10. 059

Downloaded by [Inst of Info Tech Design & Manufacturing] at 00:25 23 August 2015

Journal of Experimental & Theoretical Artificial Intelligence

23

Bhandari, A. K., Soni, V., Kumar, A., & Singh, G. K. (2014a). Artificial bee colony-based satellite image contrast and brightness enhancement technique using DWT-SVD. International Journal of Remote Sensing, 35, 1601– 1624. doi:10.1080/01431161.2013.876518 Bhandari, A. K., Soni, V., Kumar, A., & Singh, G. K. (2014b). Cuckoo search algorithm based satellite image contrast and brightness enhancement using DWT – SVD. ISA Transaction, 53, 1286– 1296. doi:10.1016/j.isatra.2014.04.007 Bhuiyan, M. I. H., Ahmad, M. O., & Swamy, M. N. S. (2007). New spatial adaptive wavelet based method for the despeckling of medical ultrasound image. In Proceedings IEEE international conference on symposium on circuits and system (pp. 2347– 2350). New Orleans, LA: IEEE. doi:10.1109/ISCAS. 2007.378859. Bhutada, G. G., Anand, R. S., & Saxena, S. C. (2011a). Edge preserved image enhancement using adaptive fusion of images denoised by wavelet and curvelet transform. Digital Signal Processing, 21, 118– 130. doi:10.1016/j.dsp.2010.09.002 Bhutada, G. G., Anand, R. S., & Saxena, S. C. (2011b). Image enhancement by wavelet-based thresholding neural network with adaptive learning rate. IET Image Processing, 5, 573 –582. doi:10.1049/iet-ipr. 2010.0014 Bhutada, G. G., Anand, R. S., & Saxena, S. C. (2012). PSO-based learning of sub-band adaptive thresholding function for image denoising. Springer on Signal, Image and Video Processing (SIViP), 6(1), 1 – 7. doi:10.1007/s11760-010-0167-7 Binh, N. T., & Khare, A. (2010). Multilevel threshold based image denoising in curvelet domain. Journal of Computer Science and Technology, 25, 632– 640. doi:10.1007/s11390-010-9352-y Chang, S. G., Yu, B., & Vetterli, M. (2000a). Adaptive wavelet thresholding for image denoising and compression. IEEE Transactions on Image Processing, 9, 1532– 1546. doi:10.1109/83.862633 Chang, S. G., Yu, B., & Vetterli, M. (2000b). Wavelet thresholding for multiple noisy image copies. IEEE Transaction Image Processing, 9, 1631– 1635. doi:10.1109/83.862646 Chen, Y., & Han, C. (2005). Adaptive wavelet threshold for image denoising. Electronics Letters, 41, 586– 587. doi:10.1049/el:20050103 Civicioglu, P., & Besdok, E. (2013). A conceptual comparison of the Cuckoo-search, particle swarm optimization, differential evolution and artificial bee colony algorithms. Artificial Intelligence Review, 39, 315– 346. doi:10.1007/s10462-011-9276-0 Clerc, M., & Kennedy, J. (2002). The particle swarm – Explosion, stability, and convergence in a multidimensional complex space. IEEE Transaction on Evolutionary Computation, 6, 58– 73. doi:10.1109/4235.985692 Crouse, M. S., Nowak, R. D., & Baraniuk, R. G. (1998). Wavelet-based statistical signal processing using hidden Markov models. IEEE Transaction on Signal Processing, 46, 886– 902. doi:10.1109/78. 668544 Dabov, K., Foi, A., Katkovnik, V., & Egiazarian, K. (2007). Image denoising by sparse 3-D transformdomain collaborative filtering. IEEE Transactions on Image Processing, 16, 2080– 2095. doi:10. 1109/TIP.2007.901238 Demirel, H., & Anbarjafari, G. (2010a). Discrete wavelet transform-based satellite image resolution enhancement. IEEE Transaction on Geoscience and Remote Sensing, 49, 1997– 2004. doi:10.1109/ TGRS.2010.2100401 Demirel, H., & Anbarjafari, G. (2010b). Satellite image resolution enhancement using complex wavelet transform. IEEE Geoscience and Remote Sensing Letters, 7, 123– 126. doi:10.1109/LGRS.2009. 2028440 Demirel, H., & Anbarjafari, G. (2011). Image resolution enhancement by using discrete and stationary wavelet decomposition. IEEE Transaction on Image Processing, 20, 1458–1460. doi:10.1109/TIP. 2010.2087767 Donoho, D. L. (2000). De-noising by soft-thresholding. IEEE Transaction on Information Theory, 41, 613– 627. doi:10.1109/18.382009 Donoho, D. L., & Johnstone, I. M. (1994). Ideal spatial adaptation by wavelet shrinkage. Biometrika, 81, 425– 455. doi:10.1093/biomet/81.3.425

Downloaded by [Inst of Info Tech Design & Manufacturing] at 00:25 23 August 2015

24

A.K. Bhandari et al.

Donoho, D. L., & Johnstone, I. M. (1995). Adapting to unknown smoothness via wavelet shrinkage. Journal of American Statistical Association, 90, 1200– 1224. doi:10.1080/01621459.1995.10476626 Fodor, I. K., & Kamath, C. (2003). Denoising through wavelet shrinkage: An empirical study. Journal of Electronic Imaging, 12, 151–160. doi:10.1117/1.1525793 Gao, H. (1998). Wavelet shrinkage denoising using the nonnegative garrote. Journal of Computational and Graphical Statistics, 7, 469– 488. Gao, H., & Bruce, A. G. (1997). Wave shrink with firm shrinkage. Statistica Sinica, 7, 855– 874. Gonzalez, R. C., & Woods, R. E. (2002). Digital image processing (Vol. 2, 2nd ed.). Singapore: PrenticeHall. Gonzalez, R. C., & Woods, R. E. (2007). Digital image processing. Englewood Cliffs, NJ: Prentice-Hall. Retrieved from http://earthobservatory.nasa.gov/IOTD/view.php?id¼39125 Gupta, S., Chauhan, R. C., & Saxena, S. C. (2005). Locally adaptive wavelet domain Bayesian processor for denoising medical ultrasound images using Speckle modelling based on Rayleigh distribution. Proceedings IEEE International Conference on Visual Image Signal Processing, 152, 129– 135. doi:10.1049/ip-vis:20050975 Jain, P., & Tyagi, V. (2014). LAPB: Locally adaptive patch-based wavelet domain edge-preserving image denoising. Information Sciences, 294, 164– 181. Retrieved from http://dx.doi.org/10.1016/j.ins. 2014.09.060 Jansen, M., & Bultheel, A. (1999). Multiple wavelet threshold estimation by generalized cross validation for images with correlated noise. IEEE Transactions on Image Processing, 8, 947– 953. doi:10. 1109/83.772237 Karaboga, D. (2005). An idea based on honey bee swarm for numerical optimization. Technical ReportTR06, Erciyes University, Engineering Faculty, Computer Engineering Department. Karaboga, D., & Akay, B. (2009). A comparative study of artificial bee colony algorithm. Applied Mathematics and Computation, 214, 108 –132. doi:10.1016/j.amc.2009.03.090 Karaboga, D., Gorkemli, B., Ozturk, C., & Karaboga, N. (2012). A comprehensive survey: Artificial bee colony (ABC) algorithm and applications. Artificial Intelligence Review, 42(1), 1 – 37. Kennedy, J., & Eberhart, R. C. (1995). Particle swarm optimization. In Proceedings IEEE international conference on neural network, Perth, Australia, 4, 1942– 1948. Kumar, A., Bhandari, A. K., & Padhy, P. (2012). Improved normalised difference vegetation index method based on discrete cosine transform and singular value decomposition for satellite image processing. IET Signal Processing, 6, 617– 625. doi:10.1049/iet-spr.2011.0298 Mallat, S. G. (1989). A theory for multiresolution signal decomposition: the wavelet representation. IEEE Transaction on Pattern Analysis and Machine Intelligence, 11, 674– 693. doi:10.1109/34.192463 Michailovich, O. V., & Tannenbaum, A. (2006). Despeckling of medical ultrasound images. IEEE Transactions on Ultrasonics, Ferroelectronics, and Frequency Control, 53, 64 –78. doi:10.1109/ TUFFC.2006.1588392 Mittal, A., Moorthy, A. K., & Bovik, A. C. (2012). Automatic parameter prediction for image denoising algorithms using perceptual quality features. In SPIE Proceedings on Human Vision and Electronic Imaging XVII, 8291 (pp. 1– 7). San Francisco, CA: SPIE. doi:10.1117/12.912243. Nasri, M., & Nezamabadi-Pour, H. N. (2009). Image denoising in the wavelet domain using a new adaptive thresholding function. Elsevier Journal of Neurocomputing, 72, 1012– 1025. doi:10.1016/j.neucom. 2008.04.016 Om, H., & Biswas, M. (2014). MMSE based map estimation for image denoising. Optics & Laser Technology, 57, 252– 264. doi:10.1016/j.optlastec.2013.07.018 Pizurica, A., & Philips, W. (2006). Estimating the probability of the presence of a signal of interest in multiresolution single- and multiband image denoising. IEEE Transaction on Image Processing, 15, 654– 665. doi:10.1109/TIP.2005.863698 Poli, R., Kennedy, J., & Blackwell, T. (2007). Particle swarm optimization. Swarm Intelligence, 1, 33 –57. doi:10.1007/s11721-007-0002-0

Downloaded by [Inst of Info Tech Design & Manufacturing] at 00:25 23 August 2015

Journal of Experimental & Theoretical Artificial Intelligence

25

Portilla, J., Strela, V., Wainwright, M. J., & Simoncelli, E. P. (2003). Image denoising using scale mixtures of Gaussians in the wavelet domain. IEEE Transaction on Image Processing, 12, 1338– 1351. doi:10.1109/TIP.2003.818640 Rabbani, H. (2009). Image denoising in steerable pyramid domain based on a local Laplace prior. Elsevier Journal of Pattern Recognition, 42, 2181– 2193. doi:10.1016/j.patcog.2009.01.005 Rabbani, H., Vafadust, V., Abolmaesumi, A., & Gazor, G. (2008). Speckle noise reduction of medical ultrasound images in complex wavelet domain using mixture priors. IEEE Transaction on Biomedical Engineering, 55, 2152 –2160. doi:10.1109/TBME.2008.923140 Soni, V., Bhandari, A. K., Kumar, A., & Singh, G. K. (2013). Improved sub-band adaptive thresholding function for denoising of satellite image based on evolutionary algorithms. IET Signal Processing, 7, 720– 730. doi:10.1049/iet-spr.2013.0139. Vandenbergh, F. V. D., & Engelbrecht, A. P. (2004). A cooperative approach to particle swarm optimization. IEEE Transaction on Evolutionary Computation, 8, 225– 239. doi:10.1109/TEVC. 2004.826069 Yang, X. S., & Deb, S. (2009). Cuckoo search via Le´vy flights. In Proceedings IEEE World Congress on Nature & biologically inspired computing (NaBIC) (pp. 210– 214). Coimbatore: IEEE. doi:10.1109/ NABIC.2009.5393690. Yang, H. Y., Wang, X. Y., Niu, P. P., & Liu, Y. C. (2014). Image denoising using nonsubsampled shearlet transform and twin support vector machines. Neural Networks, 57, 152– 165. doi:10.1016/j.neunet. 2014.06.007 Yu, H., Zhao, L., & Wang, H. (2009). Image denoising using trivariate shrinkage filter in the wavelet domain and joint bilateral filter in the spatial domain. IEEE Transaction on Image Processing, 18, 2364– 2369. doi:10.1109/TIP.2009.2026685 Zhang, X. P. (2001). Thresholding neural network for adaptive noise reduction. IEEE Transactions on Neural Network, 12, 567– 584. doi:10.1109/72.925559 Zhang, X. P., & Desai, M. D. (1998). Adaptive denoising based on SURE risk. IEEE Signal Processing Letters, 5, 265–267. doi:10.1109/97.720560