Document Sample
40120130406008 Powered By Docstoc
					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

ISSN 0976 – 6464(Print)
ISSN 0976 – 6472(Online)                                                       IJECET
Volume 4, Issue 6, November - December, 2013, pp. 57-61
Journal Impact Factor (2013): 5.8896 (Calculated by GISI)


        Arvind Kumar                     A Bhattacharya                        D K Singh
      Department of ECE                Department of E&ECE                  Department of ECE
         BIT Sindri                       IIT Kharagpur                        NIT Patna


        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).


        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

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


        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:


                               (x,y)   I                                       (1)

where            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


The scattered field is given by

                                       AI                                       (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 permittivity . 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

              ×        ′        r AO                                           (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

                        ′    ′
                                     ′   ′      AI                             (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).

F(χ)=                                                                         (6)

       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.


     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
Step 3: Check the convergence of the cost function i.e. F(gbest)< .
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

        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.


       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.

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
                                                                                 1          25
         20                          0.8           20
                                                                                 0.8        20
         15                          0.6           15
                                                                                 0.6        15
         10                          0.4           10                            0.4        10                          0.4
                                     0.2           5                             0.2
          5                                                                                 5                           0.2
                                                   0                             0
          0                          0                  0    10        20   30              0                           0
              0     10     20   30                                                               0   10     20     30

                         (a)                                      (b)                                 (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.


        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.

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


 [1]    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 1856-
        1865, 2004.
 [2]    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.
 [3]    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.
 [4]    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.
 [5]    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.
 [6]    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.
 [7]    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.
 [8]    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.
 [9]    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.
 [10]   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.
 [11]   D. Coltonand R. Krees, “ Inverse Acoustics and Electromagnetic Scattering Theroy,” Berlin,
        Germany: Springer-Verlag, 1992.
 [12]   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.
 [13]   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.
 [14]   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,
 [15]   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.


Shared By: