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International Journal of Signal and Image Processing (Vol.1-2010/Iss.4) Gupta et al. / A Genetic Algorithm Based Sequential Hybrid Filter ... / pp. 242-248

A Genetic Algorithm Based Sequential Hybrid Filter for Image Smoothing

Siddharth Gupta , Rajesh Kumar , S. K. Panda Department of Computer Science and Engineering, Jaypee Institute of Information Technology, Noida, India

e-mail: [email protected]

Department of Electrical and Computer Engineering, National University of Singapore,Singapore

e-mail: {elerajes, eleskp}@nus.edu.sg Submitted: 11/07/2010 Accepted: 04/08/2010 Appeared:14/08/2010 c HyperSciences.Publisher

Abstract: Image smoothing is a useful and necessary part of image processing and its analysis. The quality of an image could be corrupted by different kind of noises, added due to the undesired conditions or during the transmission. The design of smoothing filters has become a real challenge for researchers because of diversity in the type of noises present in the images. Various smoothing filters have been developed with time to address these issues, but due to the lack of knowledge of types of noises, these methods are not efficient sometimes. A method is needed which can reduce noises in an image irrespective of its type. This paper presents an optimal tuned sequential approach to design hybrid filter for image denoising. The proposed method uses various smoothing filters in a sequence to develop a hybrid filter. The performance of hybrid filter totally depends upon the arrangement of filters in a sequence. The sequence of smoothing filters is evaluated with the help of Genetic Algorithm taking SNR or PSNR as the fitness function. Experimental and analytical results of hybrid filter to denoise the image shows better upshots than the other filters. Keywords: Genetic Algorithm, Hybrid Filter, SNR, PSNR, Smoothing Filters.

1. INTRODUCTION One of the most important task of image processing is noise filtering. It is frequently used as a pre-processing step in image processing (Min-Cheng pan et al. 1998). Analysis of images sometimes can be very critical. A slightest misinterpretation of the image may lead to disastrous conclusions. To analyze each and every minute detail in depth, it must be made sure that image quality is good and it contains neither an extra information nor any information is missing from it. One of the main concerns of image analysis is the quality of image. For detailed analysis of an image, it is important that its features should be easily recognizable and understandable. Image denoising is a key issue for all image processing researches. Image denoising refers to the methods of removing noise from the image through image enhancement techniques (Ashraf Aboshosha et al. 2009). A lot of care must be taken while applying a smoothing filter to an image because using a wrong filter results to some loss of information. A filter must remove maximum noise from the image without losing its important features. It is generally observed that an image signal is corrupted either due to unfavorable image capturing conditions or during transmission. The great challenge of image denoising is: how to preserve the edges and all fine details of an image when reducing the noise (Gonzalez et al. 2001). Reducing noise from the image is one of the most worked upon problems in the area of image processing. A lot of work has been done in past in the area of image smoothing. Noise reduction can be accomplished by blurring with linear filters (mean, median and mode) and nonlinear filters (circular, pyramidal and cone) (Niranjan DameraVenkata et al. 2000). (Min-Cheng Pan et al. 1998) proposed a spatial domain probability filter which achieves the advantages of median and mean filters. The aim of probability filter is to provide a compromise between the two more conventional filters (Min-Cheng Pan et al. 1998). It predicts the best possible image when original image is not available. (Michifumi Yoshioka et al. 1997) presented an approach based on genetic algorithm for minimizing noise from original image. Another concept of Modified Spatial Median Filter was introduced by (James C. Church et al. 2008). (Krishnan Nallaperumal et al. 2006) gave a new Median filter for removal of impulsive noise from a digital image. An algorithm to reduce gaussian noise from an image was given by (V. R. Vijaykumar et al. 2009). Probability filter operates in the spatial domain and focuses on processing images corrupted by either impulselike noise or random noise (Min-Cheng Pan et al. 1998). (Raman Maini et al. 2010) present an Image structure

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International Journal of Signal and Image Processing (Vol.1-2010/Iss.4) Gupta et al. / A Genetic Algorithm Based Sequential Hybrid Filter ... / pp. 242-248

preserving noise reduction technique. This method reduces Gaussian as well as Impulse noise whilst preserving image structure. (Krishnan M. Hari et al. 2010) gives a Fuzzy Filter for denoising an image which is corrupted by Gaussian noise. (James C. Church et al. 2008) and (Krishnan Nallaperumal et al. 2006) proposed an algorithm specifically for salt and pepper noise. (V. R. Vijaykumar et al. 2009) also proposes fast and efficient algorithm for removal of Gaussian noise. Most of algorithms proposed in literature are either noise dependent or threshold governed. In real time environment the type of noise in the image signal is unknown. So applying an algorithm specific to noise, will never be successful under these conditions. The above mentioned shortcomings can be eliminated by designing a filter which can remove noise irrespective of its type. The proposed method is not noise specific and does not use any assumptions and thresholds. This makes the hybrid filter a robust method for denoising. A hybrid filter is proposed, which uses various image smoothing filters in sequence on the corrupted image to reduce noise. The smoothing filters used are: 1-Mean, 2-Median, 3-Mode, 4-Circular, 5-Pyramid, 6-Cone, and 7-Gaussian. Genetic Algorithm (GA) is used as optimization tool to find the sequence of these filters. GA uses SNR or PSNR as its fitness function. Section 2 introduces a brief on some common type of noises normally appear in the images. The basic problem formulation is presented in section 3. Flow diagram and step wise detailed explanation of the proposed algorithm is also provided in this section. Section 4 discusses the details of genetic algorithm and its need for designing the Hybrid filter. The robustness and upshot of the proposed hybrid filter is presented and verified with experimental results in section 5. Section 6 concludes the paper. 2. TYPES OF NOISES Most of images suffer from unwanted elements nomenclature as noises. The noises can be classified depending upon their individual characteristics. They can be additive noises such as Gaussian noise, multiplicative noises such as Speckle noise etc. There are also some kind of noises which are neither multiplicative nor additive. For example - Poisson noise and Salt and Pepper noise are neither of the above mentioned types. A noise can be correlated or uncorrelated, signal dependent or signal independent etc. I. Gaussian Noise: This type of noise is the most common noise present in most of the images. Sometimes, it is also referred as white noise, but is confined to a narrower range of frequencies. This type of noises makes everything look soft and blurry. The noise has a probability density function of a Gaussian distribution. (x-µ)2 1 (1) × exp 22 G= 2 2

a noise sequence of integer numbers having a poisson probability distribution as follows (Gonzalez et al., 2001): n × exp- (2) P = n!

Where, is the expected number of occurrences that occur during a given interval and n is the number of occurrences of an event. III. Speckle Noise: This kind of noise is generally captured in a image signal during its transmission. This type of noise is known as data missing noise as it is caused due to loss of data during transmission of signal. The corrupted pixels are set to maximum value of intensity. It follows a gamma distribution. The mathematical model of speckle noise is given as follows:

-g g -1 × exp 2 ( - 1)!

(3)

where, g is the grayscale level and is the shape parameter. IV. Salt and Pepper Noise: Salt and pepper noise is one of the impulse noises, in which corrupted pixel has the intensity either very high or very low as compared to the intensities of the neighboring pixels. A pixel is said to be a salt pixel, if it has abnormally high values and pepper pixel, if it has abnormally low values. Due to which, it is represented by white and black pixels. The Probability Density Function of salt and pepper noise is given by: pa , for z=a; Pz = pb , for z=b; (4) 0, otherwise. If b > a, intensity b will appear as a light dot in the image. Conversely, level a will appear like a dark dot (Gonzalez et al, 2001). If neither probability is zero then it is termed as salt and pepper noise. 3. HYBRID FILTER: OPTIMIZATION PROBLEM FORMULATION Hybrid filter is a sequential filter where different filters are arranged in a sequence to obtain a noise free image. Signal to Noise Ratio (SNR) and Peak Signal to Noise Ratio (PSNR) are two performance indices which determines the quality of the image. SNR is the ratio of the average signal power to the average noise power. If x is the original non corrupted M*N image and y is the enhanced M*N image then for 1 i M and 1 j N, (Niranjan DameraVenkata et al. 2000), SNR is defined as follows: SN R = 10 × log10 ( x2 (i, j) ) (x(i, j) - y(i, j))2

(5)

PSNR can be defined as: P SN R = 10 × log10 ( 2552 × M × N ) (x(i, j) - y(i, j))2

Here µ is the mean, is the standard deviation and is the variance. II. Poisson Noise: Poisson noise is induced by nonlinear response of the image detectors and recorders. This type of noise is image data dependent. Poisson noise generates

2

(6)

The denominator of equations 5 and 6 gives the summation of pixel difference between the original image and denoised image. It is clear that smaller the denominator, better will be the quality of denoised image. Hence the output quality

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A Genetic Algorithm Based Sequential Hybrid Hybrid Filter ... / pp. 242-248 Gupta et al. / A Genetic Algorithm Based Sequential Filter for Image Smoothing is directly proportional to the value of SNR or PSNR. Better the value of SNR or PSNR, better is the quality of image. The problem objective function can be defined as follows: Objf n = M ax(f ) (7) here f can be SNR or PSNR. where y(i, j) in SNR and PSNR can be defined as: y(i, j) = I7 (W7 [...[I2 (W2 [I1 (W1 y1 )])]...]) (8)

International Journal of Signal and Image Processing (Vol.1-2010/Iss.4)

3

here y 1 is the initial corrupted image and * represents convolution. W k is the filters applied and I k is the boolean operators.Where k varies as 1 k 7. I k (Wk *yk ) = y k+1 , if Ik = 1; yk , if Ik = 0. (9)

In above equation, I k =0 will imply that no convolution will take place and I k =1 will imply that image y k will be convoluted with the filter W k to give a new image y k+1 . Constraints: Ik 0 and Wk 1 where 1 k 7 Ik {0, 1} Wk [1, 7] (10) (11) (12)

Fig. 1. Flow diagram of applied algorithm

Wk can be Mean, Median, Mode, Circular, Pyramid, Cone and gaussian filters (size 5×5) depending on the value Wk from 1 to 7. The above formulated problem is a nonlinear NP-Hard optimization problem. NP-Hard is a problem which can not be solved in polynomial time. It requires an exhaustive search of complete solution space. The search space and the complexity of the problem depends upon number of filters used in the sequence. As in this case 7 filters are used and hence it requires the evaluation of all 77 cases to find a optimal solution. A lot of classical methods have been developed and are being used for optimization problem. Golden section search, Newton's Method, Secant Method, Gradient Method and Neural Network are commonly used optimization algorithm but they suffer from trapping in local minima (David E. Goldberg 2005). Genetic algorithms are well known for finding global optimal solution to a NPHard problem without performing an exhaustive search. 4. GENETIC ALGORITHM BASED HYBRID FILTER GA has been used as the optimization tool to find the maximum value of SNR or PSNR. There are a few more reasons behind the use of GA: the first and most important point is that genetic algorithms are parallel in nature. Most of the other algorithms are serial and can only explore the solution space to a problem in one direction at a time. However, GAs can explore the solution space in multiple directions at once. If one path does not lead good results, they can easily eliminate it and continue work on more promising solutions, giving them a greater chance during each run of finding the optimal solution (David E. Goldberg 2005). Genetic algorithms are based on natural selection, discovered by Charles Darwin. It uses natural selection of fittest

individual as optimization problem solver (Mantas Paulins et al, 2007). It is a heuristic algorithm which tries to find the optimal results by decreasing the value of objective function (error function) continuously (Nurhan Karaboga et al. 2004). According to this theory only the fittest will survive and breed further, the others will eventually disappear with time. In computer application, genetic codes are replaced by string of bits and breeding is replaced by crossover and mutation. Crossover is an operation of producing new bit strings by the fusion old string bits.The mutation is random replacement of a bit in the string. Fig. 1 shows the flow control of the algorithm. Firstly, the original image, corrupted image and the smoothing filters are passed as an input to the GA function. Genetic algorithm analyzes the system quality by comparing the values of the fitness function obtained by various sequences. GA uses SNR or PSNR as the fitness function for evaluating the best sequence of smoothing filters. After the completion of the first iteration, new set of sequences are created by the process of crossover and mutation. Mutation operator is used to avoid the local minima trapping of the algorithm. The probability of selection of a sequence from the set is directly proportional to the value of its fitness function. The new set of sequences then replaces the previous set. The process continues until the stopping criterion is achieved. The sequence, that gives the maximum value of SNR or PSNR, is said to be the best sequence. This sequence is passed as input to the Sequence Application Function. Sequence Application Function applies the filters on the corrupted image in that sequence. The resultant image is the noise removed image. Genetic Algorithm finds the minimum value of the function. In order to find the maximum value, the fitness function has been negated, which provides the maximum value but with a negative sign.

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International Journal of Signal and Image Processing (Vol.1-2010/Iss.4) Gupta et al. / A Genetic Algorithm Based Sequential Hybrid Filter ... / pp. 242-248

Fig. 2. Elaine(512×512) (with gaussian noise (=50)) Fig. 4. Circuit(272×280) (with Salt and Pepper and Gaussian noise(=25 and mean=0))(image II)

Fig.

3. Circuit(272×280) noise)(image I)

(with

Salt

and

Pepper

Genetic Algorithm is used as an optimization tool in our algorithm which uses SNR or PSNR as its fitness function. The steps of GA is explained below: (1) Initial random population is selected (size=50). (2) Each sequence of population is used to calculate the Fitness function i.e. SNR or PSNR. (3) Parent sequence is selected from these sequences. The probability of a sequence to be selected a parent is directly proportional to the value of its fitness function. (4) Crossover(probability = 0.95) and Mutation(probability = 0.001) are the next step to form an offspring from parent. The probability of Mutation is generally taken very low. (5) After generating new population step (2), (3), (4) are repeated, until the stopping criteria is achieved. The stopping criteria taken is: optimum found or no increase in quality for 50 generations. 5. EXPERIMENTAL RESULTS AND ANALYSIS Hybrid filter has been tested on images belonging to different domains. Ankle and Skull images are of medical interest, Elaine and Lena are the images of the interest of the photographers and Liftingbody is an arial image taken during flight. These images are of different sizes and corrupted by different type of noises. Robustness of hybrid filter is also checked for the different intensity levels of noise present in the corrupted image. The experimental set-up ensures the possible combinations of different level of noises, different intensity of noises and different sizes of images are used to evaluate the performance of the filter for every possible situation. The superiority of the hybrid filter over other smoothing filters is clearly visible from the images in the Fig. 2 to Fig. 13. The values of PSNR and SNR provided in

Fig. 5. Circuit(272× 280) (with Poisson and Gaussian noise(=25 and mean=0))(image III)

Fig. 6. Liftingbody(256×256) (with Poisson and Gaussian noise(=25 and mean=0))(image IV)

Fig. 7. Liftingbody(512×512) (with Poisson and Gaussian noise(=25 and mean=0))(image V)

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Table 1. PSNR values and the filters used (in sequence) by the hybrid filter for ELAINE image

S.no 1 2 3 4 5 SD 10 20 30 40 50 Mean 26.25 25.6 24.45 23.19 20.65 Wiener 30.94 28.5 25.58 23.39 21.78 Alpha Trimmed 29.19 28.89 26.42 23.64 20.7 K-means 30.5 26.66 23.47 22.27 19.35 Bilateral Filter 30.4355 29.0547 27.9844 24.34 22.43 Trilateral Filters 29.4542 28.0619 26.1225 23.8076 21.6682 PA 32.53 30.56 28.07 26.85 25.83 Hybrid 31.884 29.8484 28.7328 27.5583 26.4893 Hybrid Sequence 6 5,2 5,2 5,2,2 6,2,2,2,2

Table 2. SNR (in dB) values and the filters used (in sequence) by the hybrid filter

S.no 1 2 3 4 5 6 7 8 9 10 11 Image I II III IV V VI VII VIII IX X XI Mean 17.6386 16.1302 18.8832 21.4078 24.2450 20.2630 18.3524 17.5967 18.1021 20.5828 17.3328 Median 20.3433 17.3032 18.5285 21.6814 23.9397 19.6656 20.3627 18.3245 17.7141 20.7352 17.3866 Mode 10.9587 7.0948 9.8486 13.9907 14.9026 7.7863 10.0010 7.0717 7.2097 12.5852 6.9179 Circular 17.8483 16.1933 19.3031 21.6643 24.3683 20.0487 18.1698 17.2911 18.0871 20.8228 17.4285 Pyramid 18.0436 16.2389 19.7079 22.1942 24.6321 19.8906 18.0112 17.0381 18.2719 21.5401 17.6596 Cone 17.2392 15.2547 19.2074 21.9670 23.6292 18.4476 17.0082 15.5751 17.3438 21.4360 16.9473 Gaussian 17.7080 15.7743 19.5916 22.1904 24.2085 19.1320 17.4784 16.2473 17.8569 21.6924 17.3630 Hybrid 20.3433 17.3032 19.7079 22.1942 25.0579 21.3564 22.6389 20.4773 18.7304 21.5401 18.0093 Hybrid Sequence 2 2 5 5 6,2 2,1,2,2 2,6,2,2,2,2,2 2,4,2,2,2,6,2 6,2 5 7,2

Fig. 8. Liftingbody(512×512) (with Salt and Pepper, Poisson, Speckle (SD=51) and Gaussian noise(=25 and mean=0))(image VI)

Fig. 10. Ankle(400×324) (with Salt and Pepper, Poisson, Speckle(SD=51) and Gaussian noise(=25 and mean=0))(image VIII)

Fig. 11. Lena(256×256) (with Poisson and Gaussian noise(=25 and mean=0))(image IX) Fig. 9. Skull(489×500) (with Salt and Pepper, Poisson, Speckle(SD=51) and Gaussian noise(=25 and mean=0))(image VII) Table 1 and Table 2 support the fact that image output is improved considerably with the application of hybrid filter. The algorithm performance has been tested on images of various sizes. The algorithm has successfully provided optimal output for each image, irrespective of the size of the image. It is clearly evident from the results that the PSNR and SNR values of hybrid filter are better or same as compared to other filters in majority of cases. Table 1 compares the PSNR values of various algorithms on same image at different noise levels. The compared values have Gaussian noise, added at various values of standard deviation. It can be observed that for standard deviation values of 10 and 20, hybrid filter has proved to be better than all methods, except the proposed algorithm of (V. R. Vijaykumar et al. 2009). It should be noted that the algorithm proposed by (V. R. Vijaykumar et al. 2009) is specific to Gaussian noise only. On the other hand, hybrid filter is a general filter which works irrespective of the type of noise. As the amount of noise increases with the increase of standard deviation, hybrid filter gains superiority over all the filters including the proposed algorithm of (V.

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Fig. 12. Lena(256×256)(with Gaussian noise(=25 and mean=0))(image X)

Fig. 15. Graphs of image III

Fig. 13. Pepper(256×256) (with Salt and Pepper, Poisson and Gaussian noise(=25 and mean=0))(image XI)

Fig. 16. Graphs for image IV

Fig. 14. Graphs of image I R. Vijaykumar et al. 2009). The table also provides the sequence of filter used to obtain this result. Table 2 compares the SNR values of proposed algorithms with some standard filters on various images and type of noises. It is evident that the proposed method has better performance as compared to the standard filters. The result of the images V, VI and VII have same set of noises applied to different images. The different sequence obtained for each of the three image shows that the filters used on a corrupted image, not only depends on the type of noises but also on the image characteristics such as the type of edges, intensity levels of the image etc. Each filter has its specific characteristics. One filter is not effective for

Fig. 17. Graphs for image V

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all noises. That is why, only some filters are a part of the optimal sequence for an image. Fig. 14 to Fig. 17 are the graphs between fitness values and the number of generations. They provide the best, mean and the worst fitness values for each generation. Fig. 14 and Fig. 15 provide result for circuit image, but corrupted with different noises. The best fitness value of both are nearly equal, but the convergence of mean value and best value of Fig. 15 is achieved at a very early stage as compared to Fig. 14. Fig. 16 and Fig. 17 provide the result for liftingbody image, but of different sizes and corrupted by same type of noises. It is evident that with the increase of size of the image, the best fitness value also increases. But the mean and best fitness values converge approximately around the same iteration. 6. CONCLUSION This paper develops hybrid filter which uses various smoothing filters (both linear and non linear) in a particular sequence to give an output as improved image with noise reduced to a large extent. Experimental results show that Hybrid filter is better than other smoothening filters. Hybrid filter is at advantage as compared to other smoothing filters, as it works satisfactorily with all images and noises. This filter considers no assumptions and no threshold which makes it a robust algorithm. Genetic Algorithm is used as an optimization tool to find the most optimal sequence of filters, which will give the best output. It has proved to be an efficient optimization tool. The result of hybrid filter is compared with other filters. The performance of hybrid filter is better than the other filters. SNR and PSNR have been used as fitness functions because they are mathematically simple to calculate as compared to other fitness functions. REFERENCES Ashraf Aboshosha, M. Hassan, M. Ashour, M. E. Mashade. Image Denoising based on Spatial Filters, an Analytical Study. International conference on Computer Engineering and systems 2009, ICCES 2009,pages 245-250, 2009. David E. Goldberg. Genetic Algorithms in search, Optimization and Machine Learning. Vol. 9th Edition, Pearson Education, 2005. Gonzalez and Woods. Digital Image Processing. Vol. 2nd Edition, pages 567-633, Prentice Hall, 2001 James C. Church, Yixin Chen, and Stephen V. Rice. A Spatial Median Filter for Noise Removal in Digital Images. IEEE Southeastcon, SECON, 2008, pages 618623, 2008. Krishnan M. Hari, Viswanathan R. An Innovative Method of Denoising the Gaussian Noise by Fuzzy Image Filter. International Journal of Computational Intelligence Research, volume 6, no. 1, 2010. Krishnan Nallaperumal, Justin Varghese, S. Saudia, R. K. Selvakumar, K. Krishnaveni, S. S. Vinsley. Selective Switching Median Filter for the Removal of Salt and Pepper Impulse Noise. International Conference on Wireless and Optical Communications Networks, WOCO, 2006, pages 5 pp. -5, 2006. Mantas Paulinas, Andrius Usinskas. A survey of Genetic Algorithm Applications for image Enhancement and

Application. ISSN 1392-124X Information Technology and Control, volume 36,no. 3, pages 278-285, 2007. Michifumi Yoshioka, Sigeru Omatu. Noise Reduction Method for Image Processing using Genetic Algorithm. International Conference on System, Man, Cybernetics, ICSMC, pages 2650-2655,1997. Min-Cheng Pan and Alan H. Lettington. Smoothing Images by a Probability Filter. International Joint Symposia on Intelligence and Systems, 1998, pages 343346, 1998. Niranjan Damera-Venkata, Thomas D. Kite, Wilson S. Geisler, Brian L. Evans, Alan C. Bovik. Image Quality Assessment Based on a Degradation Model. IEEE Transations on Image Proceessing, volume 9,no. 4, pages 636-650, 2000. Nurhan Karaboga and Bahadir Cetinkaya. Design of minimum phase digital IIR filters by using Genetic algorithm. Proceedings of the 6th Nordic Signal Processing Symposium, 2004, pages 29-32, 2004. Raman Maini and Himanshu Aggarwal. Image Structure Preserving Noise Reduction Technique. International Journal of Computational Intelligence Research, volume 6, no. 1, 2010. Tirimula Rao Benala, Sree Durga Jampala, Sathya Harish Villa, Bhargavi Konathala. A Novel Approach to Image Edge Enhancement Using Artificial Bee Colony Optimization Algorithm for Hybridized Smoothening Filters. World Congress on Nature and Biologically Inspired Computing (NaBIC 2009), pages 1071-1076, 2009. V. R. Vijaykumar, P. T. Vanathi, P. Kanagasabapathy. Fast and Efficient algorithm to remove Gaussian Noise in Digital Images. IAENG Internatinal Journal of Computer Science, 2009, volume 37, no. 1., 2009

AUTHORS PROFILE Siddharth Gupta is at present, a final year student of Computer Science and Engineering at Jaypee Institute of Information Technology University, Noida, India. His research interest includes image processing and analysis, Artificial Intelligence and robotics. Rajesh Kumar received the B.Tech. degree from National Institute of Technology (NIT), Kurukshetra, India in 1994, the M. E. from Malaviya National Institute of Technology (MNIT), Jaipur, India in 1997 and the Ph.D. degree from University of Rajasthan, India in 2005. Since 1995, he has been a Faculty Member in the Department of Electrical Engineering, MNIT, Jaipur, where he is serving as an Associate Professor. Presently, he is Post Doctorate Research Fellow in the Department of Electrical and Computer Engineering at the National University of Singapore (NUS), Singapore, on leave from MNIT. His field of interest includes theory and practice of intelligent systems, evolutionary algorithms, bio and nature inspired algorithms, fuzzy and neural methodologies, power electronics, electrical machines and drives, applications of AI to image processing and bioinformatics. S. K. Panda received the B.Eng. degree from REC, Surat, India in 1983, the M.Tech. degree from Institute of Technology, Banaras Hindu University, Varanasi, India in 1987, and the PhD. Degree from the University of Cambridge, U.K., in 1991, all in electrical engineering. Since 1992, he has been a Faculty Member in the Department of Electrical and Computer Engineering, National University of Singapore, where he is currently serving as an Associate Professor and Head of the Drives, Power and Control Research Group. His research interests are in control of electric drives and power electronic converters, energy harvesting, renewable energy, assistive technology and mechatronics.

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