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  1. 1. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – INTERNATIONAL JOURNAL OF ELECTRONICS AND 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 6, November - December (2013), © IAEME COMMUNICATION ENGINEERING & TECHNOLOGY (IJECET) ISSN 0976 – 6464(Print) ISSN 0976 – 6472(Online) Volume 4, Issue 6, November - December, 2013, pp. 57-61 © IAEME: www.iaeme.com/ijecet.asp Journal Impact Factor (2013): 5.8896 (Calculated by GISI) www.jifactor.com IJECET ©IAEME MICROWAVE IMAGE RECONSTRUCTION OF TWO DIMENSION DIELECTRIC SCATTERERS USING SWARM PARTICLE OPTIMIZATION Arvind Kumar Department of ECE BIT Sindri A Bhattacharya Department of E&ECE IIT Kharagpur D K Singh Department of ECE NIT Patna ABSTRACT In this paper multi-view approach to microwave imaging is proposed which is based on stochastic optimization algorithm, particle swarm optimization (PSO). The inverse problem is recast in an optimization problem. This paper is aimed at assessing the effectiveness of proposed approach in reconstructing the dielectric parameter of known two dimensional scatterers. Such an analysis is carried out by comparing performance of PSO based approach with genetics algorithm (GA). Index term: Inverse Scattering, Microwave Imaging, Particle Swarm Optimization (PSO), Genetics Algorithm (GA). I. INTRODUCTION In recent years microwave imaging techniques have found considerable attention by researcher since these techniques can be used for a number of engineering applications such as biomedical diagnosis of human physiologies [1], [2] non-destructive evaluation [3], [4] subsurface detection [5] and dielectric properties of scaterers [6]. It is well known that traditional deterministic techniques [7], [8] used for fast reconstruction of microwave images suffers from major drawback, where the final image is highly dependent upon the initial trial solution. In addition, the use of the iterative procedures often the reconstruction process computationally expensive. To overcome this obstacle, population based stochastic methods such as genetics algorithm (GA) [9] and particle swarm optimization have immersed as alternative to reconstruct microwave image. Kennedy and Eberhart [10] proposed particle swarm optimization (PSO) technique in 1995, which is a robust stochastic search procedure inspired by the social behavior of insects swarm. In this technique the original inverse microwave imaging problem is recast as a global optimization problem and successively solved by means of a minimization technique. 57
  2. 2. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 6, November - December (2013), © IAEME II. MATHEMATICAL FORMULATION Let us consider an investigating domain as square AI with side a x a shown in fig.1 containing a cylindrical dielectric scatterer of circular cross-section an modeled by following object functions: Fig.1 ߯ሺ‫ݕ ,ݔ‬ሻ ൌ ሾߝ௥ ሺ‫ݕ ,ݔ‬ሻ െ 1ሿ (x,y)‫ א‬I (1) where ߝ௥ ሺ‫ݕ ,ݔ‬ሻ is the relative dielectric permittivity. The investigating domain is successfully illuminated by set of V-incident TM wave characterized by z-directed electric field given by ௏ ௏ ‫ܧ‬௜௡௖ ሺ‫ݎ‬ሻ ൌ ‫ܧ‬௜௡௖ ሺ‫ݕ ,ݔ‬ሻࢠ (2) The scattered field is given by ௏ ௏ ‫ܧ‬௦௖௔௧ ሺ‫ݎ‬ሻ ൌ ‫ܧ‬௦௖௔௧ ሺ‫ ,ݔ‬ሻ ሺ‫ݕ ,ݔ‬ሻ ‫א‬AI (3) where v= 1,……V The scattered field is arising from multiple-scattering interaction between incident wave and the unknown object and is measured at V-different measuring points. V measurement points are located in area called the observation domain AO, external to the investigating domain AI. The background medium is assumed to be homogeneous and lossless with dielectric permittivityߝ଴ . The imaging process is aimed at retrieving the distribution of object function given by equation (1) and of electric Etot starting from the knowledge of scattering data Escatt and Einc. By modeling the nonlinear electromagnetic interaction through well known Lippmann-Schwinger integral equations ௏ ଶ ‫ܧ‬௦௖௔௧ ሺ‫ݎ‬ሻ ൌ ݇଴ ‫׬‬஺ ‫ܩ‬଴ ሺ‫ ′ ݎ ,ݎ‬ሻ߯ሺ‫′ݎ ,ݎ‬ሻ బ ௏ × ‫ܧ‬௧௢௧ ሺ‫′ݎ‬ሻ݀‫ ݎ‬r‫א‬AO (4) 58
  3. 3. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 6, November - December (2013), © IAEME ௏ ௏ ‫ܧ‬௧௢௧ ሺ‫ݎ‬ሻ ൌ ‫ܧ‬௜௡௖ ଶ ௏ ൅݇଴ ‫׬‬஺ ‫ܩ‬଴ ሺ‫ ′ ݎ ,ݎ‬ሻ߯ሺ‫ ′ ݎ‬ሻ‫ܧ‬௧௢௧ ሺ‫′ݎ‬ሻ݀‫ א ݎ ′ݎ‬AI బ (5) where G0 is the two dimensional free space Green function. The forward scattering in (4) and (5) has been solved using Richmond’s method [12]. The inverse problem is then recast as the global minimization problem. The cost function is given in (6). మ F(χ)= ೔ ೔ ∑ೇ ∑ಿ ቛாೞ೎ೌ೟ ሺ௣ೕ ሻି ீ ೄ ఞா೔೙೎ ሺ௣ೕ ሻቛ ೔సభ ೕ (6) మ ೔ ∑ೇ ∑ಿ ฮாೞ೎ೌ೟ ฮ ೔ ೕ Where χ is the unknown parameter, GS is radiation operator which relates internal source to the scattered field, N is the total number of discretization cells and V is the measuring points. III. PARTICLE SWARM OPTIMIZATION The swarm particle optimization technique is global search technique proposed by Kennedy and Eberhart in 1995. The steps of algorithm are as: Step 1: Initialize swarm (particle) with random position and velocity. Step 2: Evaluate the fitness of each particle and select the best position (pbest) and global best (gbest). Step 3: Check the convergence of the cost function i.e. F(gbest)< ϵ. Step 4: If function does not converse, update the velocity and position of the particle. Step 5: Repeat the steps from 2 to 4 until the function converses or maximum number of iteration is reached. In the initialization process N x D swarm has been generated randomly for χ(x, y). Here N is the population of the swarm and D is the number of unknowns in the investigating domain i.e. the dimension the inverse of the problem. Prior knowledge of χ can be used in selecting the range of χ(x, y).Fitness of cost function is evaluated for each value of χ(x,y) and Fmin{χ(x,y)}is obtained . The value of χ(x, y) for which cost function is minimum is considered as pbest for that fitness. The value of χ(x, y) for which cost function has least value among Fmin {χ(x,y)}of all iteration has been considered best .Convergence of F(gbest) is checked and iteration is either stopped (depending upon convergence limit) or velocity and position of the particle is updated. IV. NUMERICAL RESULTS In the experiment a homogeneous circular cylinder has been taken as the scattering object. The assumed parameters are followings: diameter d= λ0/4 (λ0 wavelength in free space); χ =1.0; a= λ0; D=625(discretization cell) ; V=18 (measurement points) and b= 3λ0.The other PSO parameter are (chosen according to suggestions in the literature) N=30; c1=c2=1.49,wmax=0.9 and wmin=0.4. 59
  4. 4. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 6, November - December (2013), © IAEME In the table 1 the quantitative reconstruction errors, in different optimization techniques, are expressed through the followings parameters: the percentage errors on the reconstruction of the object (∑o), the percentage errors on the reconstruction of the back ground (∑b), maximum value the χ. The percentage errors in the reconstruction of back ground are better in the case of PSO based procedure while the reconstruction of object profile is good in the case of GA based procedure. The shape of the scatterer (homogeneous cylinder) has been retrieved better in PSO because of the better reconstruction of the back ground. The reconstruction the dielectric scatter has be shown in fig 2. 25 1 25 20 0.8 20 1 15 0.6 10 0.4 5 0.2 5 0 0 0 10 20 10 0.4 5 0.2 1 0.8 0.2 0.6 0 0 0 30 15 0.4 10 20 0.6 15 25 0.8 10 20 0 0 30 0 (a) (b) 10 20 30 (c) Fig.2 Reconstructed image of test area (a) Ideal reconstruction for reference, (b) reconstruction using PSO (χ=1), (c) reconstruction using GA Table 1 Optimization process ∑b ∑o χmax GA 1.51% 34.48% 1.1 PSO 0.84% 41.37% 1.1 ∑b = Percentage error on the reconstruction of the back ground ∑o = Percentage error on the reconstruction of the object χmax= Maximum value of χ reconstructed In fig 2. (a) Shows the original dielectric scatterer for reference while in (b) it has been reconstructed using PSO procedure. The reconstructed image of the dielectric scatterer in (b) part give very clear information when sharp change in the dielectric value at the boundary of the background and the cylindrical scatterer. The maximum value of the χ is 1.1 while in the reference it is 1.0. From equation(2) maximum value of the relative dielectric constant is 2.1 instead of 2.0. So the error is 5% in retrieving the relative dielectric constant using PSO technique for inverse imaging. V. CONCLUSION In this paper particle swarm optimization (PSO) technique has been presented for high dimensional microwave imaging problem. It has been found that PSO based optimization technique is suitable for reconstruction of dielectric profile of the scatterer. This technique has been found more efficient than GA based technique because of its capability of escaping from local minima and convergence speed. It has the capability to include the priori information in the computational technique which enhances the rate of convergence. The computational cost increases with number of particle and dimensionality of the inverse imaging problem. Because of the simplicity and ease of implementation of its algorithm this optimization technique can further be integrated with some procedures to reduce the cost of computation. 60
  5. 5. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 6, November - December (2013), © IAEME REFERENCES [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] X. Li, S . K . Davis, S . C . Hagness, D . W . Van der Weide, and B . D . Van Veen,“ Microwave Imaging via. Space-time beam forming: Experimental investigation of tumor detection in multilayer breast phantoms” IEEE Trans. Micro. Theory Tech., vol. 52, pp 18561865, 2004. A.E.Bulyshev, S.Y. Semenov, A.E. Souvorov, R. H. Sevenov, A.G. Nazarov, Y.E.Sizov and G.P. Tatsis, “ Computaional modeling of three dimensional microwavetomography of breat cancer” IEEE Trans. Biomed. Eng., Vol. 48,pp. 1053-1056,2001. J.C. Bolomey , A Izadnegahdar, LJofre, C.Pchot, G. Peronnet and M. Soaimani ,“Microwave diffraction tomography for biomedical applications,” IEEE trans.Microwave Theory Tech.,vol. MTT-82 no. 11 , pp. 1998-2000, Nov. 1982. J.C. Bolomey, “ Recent Europian developments in active microwave imaging for industrial, scientific and medical applications,” IEEE Trans. Microw. Theory Tech.,vol. 37, no.12, pp. 2109-2117, Dec. 1989. A.C. Dubey, I. Cindrich, M. Ralston, and K.A. Rigano, “ Ditection technology for mines and mine like targets,” in proc. SPIE, vol. 2496, Ornaldo, FL, pp. 568-569, Jun. 1995. T. M.Habashy, M.L. Oristaglio, and A.T. de Hoop, “Simultaneous nonlinear reconstruction of two- dimensional permittivity and conductivity,” Radio Sci., vol. 29, pp. 1101-1118. 1994. A.E. Souvorov, A.E.Bulyshev, S.Y. Semenov, R. H. Sevenov, A.G. Nazarov, Y.E. Sizov and G.P. Tatsis, “ Microwave tomography: A two-dimenssional Newton iterative scheme,” IEEE Trans.Mocrow. Theory Tech., vol. 16, pp. 1654-1659, 1998. W.C. Chew and Y. M. Wang. “ Reconstruction of two dimensional permittivity distribution using the distorted Born iterative method,” IEEE Trans. Med. Img., vol. 9, pp. 218-225, jun. 1990. Salvatore Caorsi and Matteo Pastorino, “Two- dimensional Microwave imaging approach based on genetic algorithm,” IEEE Trans. on antennas and prop., vol. 48 ,no.3, pp. 370-373, Mar. 2000. J. Kennedy and R. C. Eberhart, “ Particle swarm optimization,” in Proc. IEEE Int. Neural Networks Conf., vol. IV, perth , Austrelia, pp. 1942-1948, Nov./Dec. 1995. D. Coltonand R. Krees, “ Inverse Acoustics and Electromagnetic Scattering Theroy,” Berlin, Germany: Springer-Verlag, 1992. J.H. Richmond, “ Scattering by a dielectric cylinder of arbitrary cross section shape,” IEEE Trans. Antenna propag., vol. AP-13, no. 5, pp 334-341, May 1965. A.Sri Rama Chandra Murty and M. Surendra Prasad Babu, “Implementation of Particle Swarm Optimization (PSO) Algorithm on Potato Expert System”, International Journal of Computer Engineering & Technology (IJCET), Volume 4, Issue 4, 2013, pp. 82 - 90, ISSN Print: 0976 – 6367, ISSN Online: 0976 – 6375. R. Arivoli and Dr. I. A. Chidambaram, “Multi-Objective Particle Swarm Optimization Based Load-Frequency Control of a Two-Area Power System with SMES Inter Connected using AC-DC Tie-Lines” International Journal of Electrical Engineering & Technology (IJEET), Volume 3, Issue 1, 2012, pp. 1 - 20, ISSN Print : 0976-6545, ISSN Online: 0976-6553, Anuradha L. Borkar, “Self Accelerated Smart Particle Swarm Optimization for Non Linear Programming Problems”, International Journal of Electronics and Communication Engineering & Technology (IJECET), Volume 4, Issue 5, 2013, pp. 218 - 224, ISSN Print: 0976- 6464, ISSN Online: 0976 –6472. 61