Abstract

An assessment is presented of the integrated genetic-algorithm strategy based on a numerically computed Green’s function for subsurface inverse scattering problems arising in nondestructive evaluation/testing industrial applications. To show the effectiveness and current limitations of such a microwave technique in dealing with various scenarios characterized by lossless and lossy host media as well as in noisy environments, several numerical experiments are considered. The results obtained confirm the effectiveness of the approach in fully exploiting the available a priori information through a suitable scattering model, which allows a nonnegligible enhancement of the reconstruction accuracy as well as a reduction of the overall computational burden with respect to standard imaging approaches.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. E. Nyfors, "Industrial microwave sensors—a review," Subsurf. Sens. Technol. Appl. 1, 23-43 (2000).
    [CrossRef]
  2. M. Moghaddam and W. C. Chew, "Study of some practical issues in inversion with the Born iterative method using time-domain data," IEEE Trans. Antennas Propag. 41, 177-184 (1993).
    [CrossRef]
  3. W. C. Chew and Y. M. Wang, "Reconstruction of two-dimensional permittivity using the distorted Born iterative method," IEEE Trans. Med. Imaging 9, 218-225 (1990).
    [CrossRef] [PubMed]
  4. A. Franchois and Ch. Pichot, "Microwave imaging - Complex permittivity reconstruction with a Levenberg-Marquardt method," IEEE Trans. Antennas Propag. 45, 203-215 (1997).
    [CrossRef]
  5. N. Joachimowicz, J. J. Mallorqui, J.-C. Bolomey, and A. Broquetas, "Convergence and stability assessment of Newton-Kantorovich reconstruction algorithms for microwave tomography," IEEE Trans. Med. Imaging 17, 562-570 (1998).
    [CrossRef] [PubMed]
  6. R. E. Kleinman and P. M. van den Berg, "A modified gradient method for two-dimensional problems in tomography," J. Comput. Appl. Math. 42, 17-35 (1992).
    [CrossRef]
  7. H. Harada, D. J. N. Wall, T. Takenaka, and M. Tanaka, "Conjugate gradient method applied to inverse scattering problem," IEEE Trans. Antennas Propag. 43, 784-792 (1995).
    [CrossRef]
  8. T. Isernia, V. Pascazio, and R. Pierri, "A nonlinear estimation method in tomographic imaging," IEEE Trans. Geosci. Remote Sens. 35, 910-923 (1997).
    [CrossRef]
  9. P. M. van den Berg and A. Abubakar, "Contrast source inversion: state of art," Prog. Electromagn. Res. 34, 189-218 (2001).
    [CrossRef]
  10. Z. Q. Meng, T. Takenaka, and T. Tanaka, "Image reconstruction of two-dimensional impenetrable objects using genetic algorithms," J. Electromagn. Waves Appl. 13, 95-118 (1999).
    [CrossRef]
  11. S. Caorsi, A. Massa, and M. Pastorino, "A computational technique based on a real-coded genetic algorithm for microwave imaging purposes," IEEE Trans. Geosci. Remote Sens. 38, 1679-1708 (2000).
    [CrossRef]
  12. A. Massa, "Genetic algorithm (GA) based techniques for 2D microwave inverse scattering," in Recent Research Developments in Microwave Theory and Techniques (Special issue on Microwave Non-Destructive Evaluation and Imaging), S. G. Pandalai, ed. (Transworld Research Network Press, Trivandrum, India, 2002), pp. 193-218.
  13. J. W. Ra, H. K. Choi, and J. S. Kim, "Two-and-half dimensional reconstruction of buried tunnel and pipes from cross-borehole and reflection measurements by using a genetic and Levenburg-Marquardt hybrid algorithm," Inverse Probl. 17, 233-252 (2003).
  14. R. de Oliveira, D. Lesselier, and B. Duchene, "Mapping defects in a conductive half-space by simulated annealing with connectivity and size as constraints," J. Electromagn. Waves Appl. 10, 983-1004 (1996).
  15. A. A. Arkadan, Y. Chen, S. Subramaniam, and S. R. H. Hoole, "NDT identification of a crack using ANNs with stochastic gradient descent," IEEE Trans. Magn. 31, 1984-1987 (1995).
    [CrossRef]
  16. S. Norton and J. Bowler, "Theory of eddy current inversion," J. Appl. Phys. 73, 501-512 (1993).
    [CrossRef]
  17. R. Zorgati, B. Duchene, D. Lesselier, and F. Pons, "Eddy current testing of anomalies in conductive materials, Part I: Qualitative imaging via diffraction tomography technique," IEEE Trans. Magn. 27, 4416-4437 (1991).
    [CrossRef]
  18. R. Zorgati, B. Duchene, D. Lesselier, and F. Pons, "Eddy current testing of anomalies in conductive materials, Part II: Quantitative imaging via generalized inverse techniques," IEEE Trans. Magn. 28, 1850-1862 (1992).
    [CrossRef]
  19. S. Caorsi, A. Massa, and M. Pastorino, "A crack identification microwave procedure based on a genetic algorithm for non-destructive testing," IEEE Trans. Antennas Propag. 49, 1812-1820 (2001).
    [CrossRef]
  20. S. Caorsi, A. Massa, M. Pastorino, and M. Donelli, "Improved microwave imaging procedure for non-destructive evaluations of two-dimensional structures," IEEE Trans. Antennas Propag. 52, 1386-1396 (2004).
    [CrossRef]
  21. A. Ishimaru, Electromagnetic Wave, Propagation, Radiation and Scattering (Prentice Hall, 1991).
  22. J. H. Richmond, "Scattering by a dielectric cylinder of arbitrary cross section shape," IEEE Trans. Antennas Propag. 13, 334-341 (1965).
    [CrossRef]
  23. S. Caorsi, G. L. Gragnani, M. Pastorino, and M. Rebagliati, "A model-driven approach to microwave diagnostics in biomedical applications," IEEE Trans. Microwave Theory Tech. 44, 1910-1920 (1996).
    [CrossRef]
  24. D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning (Addison-Wesley, 1989).
  25. J. H. Holland, Adaption in Natural and Artificial Systems (U. Michigan Press, 1975).
  26. D. E. Goldberg, "Real-coded genetic algorithms, virtual alphabets, and blocking," Complex Syst. 5, 139-167 (1991).
  27. Z. Michalewicz, Genetic Algorithms + Data Structures = Evolution Programs (Springer-Verlag, 1996).

2004 (1)

S. Caorsi, A. Massa, M. Pastorino, and M. Donelli, "Improved microwave imaging procedure for non-destructive evaluations of two-dimensional structures," IEEE Trans. Antennas Propag. 52, 1386-1396 (2004).
[CrossRef]

2003 (1)

J. W. Ra, H. K. Choi, and J. S. Kim, "Two-and-half dimensional reconstruction of buried tunnel and pipes from cross-borehole and reflection measurements by using a genetic and Levenburg-Marquardt hybrid algorithm," Inverse Probl. 17, 233-252 (2003).

2001 (2)

S. Caorsi, A. Massa, and M. Pastorino, "A crack identification microwave procedure based on a genetic algorithm for non-destructive testing," IEEE Trans. Antennas Propag. 49, 1812-1820 (2001).
[CrossRef]

P. M. van den Berg and A. Abubakar, "Contrast source inversion: state of art," Prog. Electromagn. Res. 34, 189-218 (2001).
[CrossRef]

2000 (2)

E. Nyfors, "Industrial microwave sensors—a review," Subsurf. Sens. Technol. Appl. 1, 23-43 (2000).
[CrossRef]

S. Caorsi, A. Massa, and M. Pastorino, "A computational technique based on a real-coded genetic algorithm for microwave imaging purposes," IEEE Trans. Geosci. Remote Sens. 38, 1679-1708 (2000).
[CrossRef]

1999 (1)

Z. Q. Meng, T. Takenaka, and T. Tanaka, "Image reconstruction of two-dimensional impenetrable objects using genetic algorithms," J. Electromagn. Waves Appl. 13, 95-118 (1999).
[CrossRef]

1998 (1)

N. Joachimowicz, J. J. Mallorqui, J.-C. Bolomey, and A. Broquetas, "Convergence and stability assessment of Newton-Kantorovich reconstruction algorithms for microwave tomography," IEEE Trans. Med. Imaging 17, 562-570 (1998).
[CrossRef] [PubMed]

1997 (2)

A. Franchois and Ch. Pichot, "Microwave imaging - Complex permittivity reconstruction with a Levenberg-Marquardt method," IEEE Trans. Antennas Propag. 45, 203-215 (1997).
[CrossRef]

T. Isernia, V. Pascazio, and R. Pierri, "A nonlinear estimation method in tomographic imaging," IEEE Trans. Geosci. Remote Sens. 35, 910-923 (1997).
[CrossRef]

1996 (2)

R. de Oliveira, D. Lesselier, and B. Duchene, "Mapping defects in a conductive half-space by simulated annealing with connectivity and size as constraints," J. Electromagn. Waves Appl. 10, 983-1004 (1996).

S. Caorsi, G. L. Gragnani, M. Pastorino, and M. Rebagliati, "A model-driven approach to microwave diagnostics in biomedical applications," IEEE Trans. Microwave Theory Tech. 44, 1910-1920 (1996).
[CrossRef]

1995 (2)

A. A. Arkadan, Y. Chen, S. Subramaniam, and S. R. H. Hoole, "NDT identification of a crack using ANNs with stochastic gradient descent," IEEE Trans. Magn. 31, 1984-1987 (1995).
[CrossRef]

H. Harada, D. J. N. Wall, T. Takenaka, and M. Tanaka, "Conjugate gradient method applied to inverse scattering problem," IEEE Trans. Antennas Propag. 43, 784-792 (1995).
[CrossRef]

1993 (2)

M. Moghaddam and W. C. Chew, "Study of some practical issues in inversion with the Born iterative method using time-domain data," IEEE Trans. Antennas Propag. 41, 177-184 (1993).
[CrossRef]

S. Norton and J. Bowler, "Theory of eddy current inversion," J. Appl. Phys. 73, 501-512 (1993).
[CrossRef]

1992 (2)

R. Zorgati, B. Duchene, D. Lesselier, and F. Pons, "Eddy current testing of anomalies in conductive materials, Part II: Quantitative imaging via generalized inverse techniques," IEEE Trans. Magn. 28, 1850-1862 (1992).
[CrossRef]

R. E. Kleinman and P. M. van den Berg, "A modified gradient method for two-dimensional problems in tomography," J. Comput. Appl. Math. 42, 17-35 (1992).
[CrossRef]

1991 (2)

R. Zorgati, B. Duchene, D. Lesselier, and F. Pons, "Eddy current testing of anomalies in conductive materials, Part I: Qualitative imaging via diffraction tomography technique," IEEE Trans. Magn. 27, 4416-4437 (1991).
[CrossRef]

D. E. Goldberg, "Real-coded genetic algorithms, virtual alphabets, and blocking," Complex Syst. 5, 139-167 (1991).

1990 (1)

W. C. Chew and Y. M. Wang, "Reconstruction of two-dimensional permittivity using the distorted Born iterative method," IEEE Trans. Med. Imaging 9, 218-225 (1990).
[CrossRef] [PubMed]

1965 (1)

J. H. Richmond, "Scattering by a dielectric cylinder of arbitrary cross section shape," IEEE Trans. Antennas Propag. 13, 334-341 (1965).
[CrossRef]

Abubakar, A.

P. M. van den Berg and A. Abubakar, "Contrast source inversion: state of art," Prog. Electromagn. Res. 34, 189-218 (2001).
[CrossRef]

Arkadan, A. A.

A. A. Arkadan, Y. Chen, S. Subramaniam, and S. R. H. Hoole, "NDT identification of a crack using ANNs with stochastic gradient descent," IEEE Trans. Magn. 31, 1984-1987 (1995).
[CrossRef]

Bolomey, J.-C.

N. Joachimowicz, J. J. Mallorqui, J.-C. Bolomey, and A. Broquetas, "Convergence and stability assessment of Newton-Kantorovich reconstruction algorithms for microwave tomography," IEEE Trans. Med. Imaging 17, 562-570 (1998).
[CrossRef] [PubMed]

Bowler, J.

S. Norton and J. Bowler, "Theory of eddy current inversion," J. Appl. Phys. 73, 501-512 (1993).
[CrossRef]

Broquetas, A.

N. Joachimowicz, J. J. Mallorqui, J.-C. Bolomey, and A. Broquetas, "Convergence and stability assessment of Newton-Kantorovich reconstruction algorithms for microwave tomography," IEEE Trans. Med. Imaging 17, 562-570 (1998).
[CrossRef] [PubMed]

Caorsi, S.

S. Caorsi, A. Massa, M. Pastorino, and M. Donelli, "Improved microwave imaging procedure for non-destructive evaluations of two-dimensional structures," IEEE Trans. Antennas Propag. 52, 1386-1396 (2004).
[CrossRef]

S. Caorsi, A. Massa, and M. Pastorino, "A crack identification microwave procedure based on a genetic algorithm for non-destructive testing," IEEE Trans. Antennas Propag. 49, 1812-1820 (2001).
[CrossRef]

S. Caorsi, A. Massa, and M. Pastorino, "A computational technique based on a real-coded genetic algorithm for microwave imaging purposes," IEEE Trans. Geosci. Remote Sens. 38, 1679-1708 (2000).
[CrossRef]

S. Caorsi, G. L. Gragnani, M. Pastorino, and M. Rebagliati, "A model-driven approach to microwave diagnostics in biomedical applications," IEEE Trans. Microwave Theory Tech. 44, 1910-1920 (1996).
[CrossRef]

Chen, Y.

A. A. Arkadan, Y. Chen, S. Subramaniam, and S. R. H. Hoole, "NDT identification of a crack using ANNs with stochastic gradient descent," IEEE Trans. Magn. 31, 1984-1987 (1995).
[CrossRef]

Chew, W. C.

M. Moghaddam and W. C. Chew, "Study of some practical issues in inversion with the Born iterative method using time-domain data," IEEE Trans. Antennas Propag. 41, 177-184 (1993).
[CrossRef]

W. C. Chew and Y. M. Wang, "Reconstruction of two-dimensional permittivity using the distorted Born iterative method," IEEE Trans. Med. Imaging 9, 218-225 (1990).
[CrossRef] [PubMed]

Choi, H. K.

J. W. Ra, H. K. Choi, and J. S. Kim, "Two-and-half dimensional reconstruction of buried tunnel and pipes from cross-borehole and reflection measurements by using a genetic and Levenburg-Marquardt hybrid algorithm," Inverse Probl. 17, 233-252 (2003).

de Oliveira, R.

R. de Oliveira, D. Lesselier, and B. Duchene, "Mapping defects in a conductive half-space by simulated annealing with connectivity and size as constraints," J. Electromagn. Waves Appl. 10, 983-1004 (1996).

Donelli, M.

S. Caorsi, A. Massa, M. Pastorino, and M. Donelli, "Improved microwave imaging procedure for non-destructive evaluations of two-dimensional structures," IEEE Trans. Antennas Propag. 52, 1386-1396 (2004).
[CrossRef]

Duchene, B.

R. de Oliveira, D. Lesselier, and B. Duchene, "Mapping defects in a conductive half-space by simulated annealing with connectivity and size as constraints," J. Electromagn. Waves Appl. 10, 983-1004 (1996).

R. Zorgati, B. Duchene, D. Lesselier, and F. Pons, "Eddy current testing of anomalies in conductive materials, Part II: Quantitative imaging via generalized inverse techniques," IEEE Trans. Magn. 28, 1850-1862 (1992).
[CrossRef]

R. Zorgati, B. Duchene, D. Lesselier, and F. Pons, "Eddy current testing of anomalies in conductive materials, Part I: Qualitative imaging via diffraction tomography technique," IEEE Trans. Magn. 27, 4416-4437 (1991).
[CrossRef]

Franchois, A.

A. Franchois and Ch. Pichot, "Microwave imaging - Complex permittivity reconstruction with a Levenberg-Marquardt method," IEEE Trans. Antennas Propag. 45, 203-215 (1997).
[CrossRef]

Goldberg, D. E.

D. E. Goldberg, "Real-coded genetic algorithms, virtual alphabets, and blocking," Complex Syst. 5, 139-167 (1991).

D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning (Addison-Wesley, 1989).

Gragnani, G. L.

S. Caorsi, G. L. Gragnani, M. Pastorino, and M. Rebagliati, "A model-driven approach to microwave diagnostics in biomedical applications," IEEE Trans. Microwave Theory Tech. 44, 1910-1920 (1996).
[CrossRef]

Harada, H.

H. Harada, D. J. N. Wall, T. Takenaka, and M. Tanaka, "Conjugate gradient method applied to inverse scattering problem," IEEE Trans. Antennas Propag. 43, 784-792 (1995).
[CrossRef]

Holland, J. H.

J. H. Holland, Adaption in Natural and Artificial Systems (U. Michigan Press, 1975).

Hoole, S. R. H.

A. A. Arkadan, Y. Chen, S. Subramaniam, and S. R. H. Hoole, "NDT identification of a crack using ANNs with stochastic gradient descent," IEEE Trans. Magn. 31, 1984-1987 (1995).
[CrossRef]

Isernia, T.

T. Isernia, V. Pascazio, and R. Pierri, "A nonlinear estimation method in tomographic imaging," IEEE Trans. Geosci. Remote Sens. 35, 910-923 (1997).
[CrossRef]

Ishimaru, A.

A. Ishimaru, Electromagnetic Wave, Propagation, Radiation and Scattering (Prentice Hall, 1991).

Joachimowicz, N.

N. Joachimowicz, J. J. Mallorqui, J.-C. Bolomey, and A. Broquetas, "Convergence and stability assessment of Newton-Kantorovich reconstruction algorithms for microwave tomography," IEEE Trans. Med. Imaging 17, 562-570 (1998).
[CrossRef] [PubMed]

Kim, J. S.

J. W. Ra, H. K. Choi, and J. S. Kim, "Two-and-half dimensional reconstruction of buried tunnel and pipes from cross-borehole and reflection measurements by using a genetic and Levenburg-Marquardt hybrid algorithm," Inverse Probl. 17, 233-252 (2003).

Kleinman, R. E.

R. E. Kleinman and P. M. van den Berg, "A modified gradient method for two-dimensional problems in tomography," J. Comput. Appl. Math. 42, 17-35 (1992).
[CrossRef]

Lesselier, D.

R. de Oliveira, D. Lesselier, and B. Duchene, "Mapping defects in a conductive half-space by simulated annealing with connectivity and size as constraints," J. Electromagn. Waves Appl. 10, 983-1004 (1996).

R. Zorgati, B. Duchene, D. Lesselier, and F. Pons, "Eddy current testing of anomalies in conductive materials, Part II: Quantitative imaging via generalized inverse techniques," IEEE Trans. Magn. 28, 1850-1862 (1992).
[CrossRef]

R. Zorgati, B. Duchene, D. Lesselier, and F. Pons, "Eddy current testing of anomalies in conductive materials, Part I: Qualitative imaging via diffraction tomography technique," IEEE Trans. Magn. 27, 4416-4437 (1991).
[CrossRef]

Mallorqui, J. J.

N. Joachimowicz, J. J. Mallorqui, J.-C. Bolomey, and A. Broquetas, "Convergence and stability assessment of Newton-Kantorovich reconstruction algorithms for microwave tomography," IEEE Trans. Med. Imaging 17, 562-570 (1998).
[CrossRef] [PubMed]

Massa, A.

S. Caorsi, A. Massa, M. Pastorino, and M. Donelli, "Improved microwave imaging procedure for non-destructive evaluations of two-dimensional structures," IEEE Trans. Antennas Propag. 52, 1386-1396 (2004).
[CrossRef]

S. Caorsi, A. Massa, and M. Pastorino, "A crack identification microwave procedure based on a genetic algorithm for non-destructive testing," IEEE Trans. Antennas Propag. 49, 1812-1820 (2001).
[CrossRef]

S. Caorsi, A. Massa, and M. Pastorino, "A computational technique based on a real-coded genetic algorithm for microwave imaging purposes," IEEE Trans. Geosci. Remote Sens. 38, 1679-1708 (2000).
[CrossRef]

A. Massa, "Genetic algorithm (GA) based techniques for 2D microwave inverse scattering," in Recent Research Developments in Microwave Theory and Techniques (Special issue on Microwave Non-Destructive Evaluation and Imaging), S. G. Pandalai, ed. (Transworld Research Network Press, Trivandrum, India, 2002), pp. 193-218.

Meng, Z. Q.

Z. Q. Meng, T. Takenaka, and T. Tanaka, "Image reconstruction of two-dimensional impenetrable objects using genetic algorithms," J. Electromagn. Waves Appl. 13, 95-118 (1999).
[CrossRef]

Michalewicz, Z.

Z. Michalewicz, Genetic Algorithms + Data Structures = Evolution Programs (Springer-Verlag, 1996).

Moghaddam, M.

M. Moghaddam and W. C. Chew, "Study of some practical issues in inversion with the Born iterative method using time-domain data," IEEE Trans. Antennas Propag. 41, 177-184 (1993).
[CrossRef]

Norton, S.

S. Norton and J. Bowler, "Theory of eddy current inversion," J. Appl. Phys. 73, 501-512 (1993).
[CrossRef]

Nyfors, E.

E. Nyfors, "Industrial microwave sensors—a review," Subsurf. Sens. Technol. Appl. 1, 23-43 (2000).
[CrossRef]

Pascazio, V.

T. Isernia, V. Pascazio, and R. Pierri, "A nonlinear estimation method in tomographic imaging," IEEE Trans. Geosci. Remote Sens. 35, 910-923 (1997).
[CrossRef]

Pastorino, M.

S. Caorsi, A. Massa, M. Pastorino, and M. Donelli, "Improved microwave imaging procedure for non-destructive evaluations of two-dimensional structures," IEEE Trans. Antennas Propag. 52, 1386-1396 (2004).
[CrossRef]

S. Caorsi, A. Massa, and M. Pastorino, "A crack identification microwave procedure based on a genetic algorithm for non-destructive testing," IEEE Trans. Antennas Propag. 49, 1812-1820 (2001).
[CrossRef]

S. Caorsi, A. Massa, and M. Pastorino, "A computational technique based on a real-coded genetic algorithm for microwave imaging purposes," IEEE Trans. Geosci. Remote Sens. 38, 1679-1708 (2000).
[CrossRef]

S. Caorsi, G. L. Gragnani, M. Pastorino, and M. Rebagliati, "A model-driven approach to microwave diagnostics in biomedical applications," IEEE Trans. Microwave Theory Tech. 44, 1910-1920 (1996).
[CrossRef]

Pichot, Ch.

A. Franchois and Ch. Pichot, "Microwave imaging - Complex permittivity reconstruction with a Levenberg-Marquardt method," IEEE Trans. Antennas Propag. 45, 203-215 (1997).
[CrossRef]

Pierri, R.

T. Isernia, V. Pascazio, and R. Pierri, "A nonlinear estimation method in tomographic imaging," IEEE Trans. Geosci. Remote Sens. 35, 910-923 (1997).
[CrossRef]

Pons, F.

R. Zorgati, B. Duchene, D. Lesselier, and F. Pons, "Eddy current testing of anomalies in conductive materials, Part II: Quantitative imaging via generalized inverse techniques," IEEE Trans. Magn. 28, 1850-1862 (1992).
[CrossRef]

R. Zorgati, B. Duchene, D. Lesselier, and F. Pons, "Eddy current testing of anomalies in conductive materials, Part I: Qualitative imaging via diffraction tomography technique," IEEE Trans. Magn. 27, 4416-4437 (1991).
[CrossRef]

Ra, J. W.

J. W. Ra, H. K. Choi, and J. S. Kim, "Two-and-half dimensional reconstruction of buried tunnel and pipes from cross-borehole and reflection measurements by using a genetic and Levenburg-Marquardt hybrid algorithm," Inverse Probl. 17, 233-252 (2003).

Rebagliati, M.

S. Caorsi, G. L. Gragnani, M. Pastorino, and M. Rebagliati, "A model-driven approach to microwave diagnostics in biomedical applications," IEEE Trans. Microwave Theory Tech. 44, 1910-1920 (1996).
[CrossRef]

Richmond, J. H.

J. H. Richmond, "Scattering by a dielectric cylinder of arbitrary cross section shape," IEEE Trans. Antennas Propag. 13, 334-341 (1965).
[CrossRef]

Subramaniam, S.

A. A. Arkadan, Y. Chen, S. Subramaniam, and S. R. H. Hoole, "NDT identification of a crack using ANNs with stochastic gradient descent," IEEE Trans. Magn. 31, 1984-1987 (1995).
[CrossRef]

Takenaka, T.

Z. Q. Meng, T. Takenaka, and T. Tanaka, "Image reconstruction of two-dimensional impenetrable objects using genetic algorithms," J. Electromagn. Waves Appl. 13, 95-118 (1999).
[CrossRef]

H. Harada, D. J. N. Wall, T. Takenaka, and M. Tanaka, "Conjugate gradient method applied to inverse scattering problem," IEEE Trans. Antennas Propag. 43, 784-792 (1995).
[CrossRef]

Tanaka, M.

H. Harada, D. J. N. Wall, T. Takenaka, and M. Tanaka, "Conjugate gradient method applied to inverse scattering problem," IEEE Trans. Antennas Propag. 43, 784-792 (1995).
[CrossRef]

Tanaka, T.

Z. Q. Meng, T. Takenaka, and T. Tanaka, "Image reconstruction of two-dimensional impenetrable objects using genetic algorithms," J. Electromagn. Waves Appl. 13, 95-118 (1999).
[CrossRef]

van den Berg, P. M.

P. M. van den Berg and A. Abubakar, "Contrast source inversion: state of art," Prog. Electromagn. Res. 34, 189-218 (2001).
[CrossRef]

R. E. Kleinman and P. M. van den Berg, "A modified gradient method for two-dimensional problems in tomography," J. Comput. Appl. Math. 42, 17-35 (1992).
[CrossRef]

Wall, D. J. N.

H. Harada, D. J. N. Wall, T. Takenaka, and M. Tanaka, "Conjugate gradient method applied to inverse scattering problem," IEEE Trans. Antennas Propag. 43, 784-792 (1995).
[CrossRef]

Wang, Y. M.

W. C. Chew and Y. M. Wang, "Reconstruction of two-dimensional permittivity using the distorted Born iterative method," IEEE Trans. Med. Imaging 9, 218-225 (1990).
[CrossRef] [PubMed]

Zorgati, R.

R. Zorgati, B. Duchene, D. Lesselier, and F. Pons, "Eddy current testing of anomalies in conductive materials, Part II: Quantitative imaging via generalized inverse techniques," IEEE Trans. Magn. 28, 1850-1862 (1992).
[CrossRef]

R. Zorgati, B. Duchene, D. Lesselier, and F. Pons, "Eddy current testing of anomalies in conductive materials, Part I: Qualitative imaging via diffraction tomography technique," IEEE Trans. Magn. 27, 4416-4437 (1991).
[CrossRef]

Complex Syst. (1)

D. E. Goldberg, "Real-coded genetic algorithms, virtual alphabets, and blocking," Complex Syst. 5, 139-167 (1991).

IEEE Trans. Antennas Propag. (6)

S. Caorsi, A. Massa, and M. Pastorino, "A crack identification microwave procedure based on a genetic algorithm for non-destructive testing," IEEE Trans. Antennas Propag. 49, 1812-1820 (2001).
[CrossRef]

S. Caorsi, A. Massa, M. Pastorino, and M. Donelli, "Improved microwave imaging procedure for non-destructive evaluations of two-dimensional structures," IEEE Trans. Antennas Propag. 52, 1386-1396 (2004).
[CrossRef]

J. H. Richmond, "Scattering by a dielectric cylinder of arbitrary cross section shape," IEEE Trans. Antennas Propag. 13, 334-341 (1965).
[CrossRef]

M. Moghaddam and W. C. Chew, "Study of some practical issues in inversion with the Born iterative method using time-domain data," IEEE Trans. Antennas Propag. 41, 177-184 (1993).
[CrossRef]

A. Franchois and Ch. Pichot, "Microwave imaging - Complex permittivity reconstruction with a Levenberg-Marquardt method," IEEE Trans. Antennas Propag. 45, 203-215 (1997).
[CrossRef]

H. Harada, D. J. N. Wall, T. Takenaka, and M. Tanaka, "Conjugate gradient method applied to inverse scattering problem," IEEE Trans. Antennas Propag. 43, 784-792 (1995).
[CrossRef]

IEEE Trans. Geosci. Remote Sens. (2)

T. Isernia, V. Pascazio, and R. Pierri, "A nonlinear estimation method in tomographic imaging," IEEE Trans. Geosci. Remote Sens. 35, 910-923 (1997).
[CrossRef]

S. Caorsi, A. Massa, and M. Pastorino, "A computational technique based on a real-coded genetic algorithm for microwave imaging purposes," IEEE Trans. Geosci. Remote Sens. 38, 1679-1708 (2000).
[CrossRef]

IEEE Trans. Magn. (3)

A. A. Arkadan, Y. Chen, S. Subramaniam, and S. R. H. Hoole, "NDT identification of a crack using ANNs with stochastic gradient descent," IEEE Trans. Magn. 31, 1984-1987 (1995).
[CrossRef]

R. Zorgati, B. Duchene, D. Lesselier, and F. Pons, "Eddy current testing of anomalies in conductive materials, Part I: Qualitative imaging via diffraction tomography technique," IEEE Trans. Magn. 27, 4416-4437 (1991).
[CrossRef]

R. Zorgati, B. Duchene, D. Lesselier, and F. Pons, "Eddy current testing of anomalies in conductive materials, Part II: Quantitative imaging via generalized inverse techniques," IEEE Trans. Magn. 28, 1850-1862 (1992).
[CrossRef]

IEEE Trans. Med. Imaging (2)

N. Joachimowicz, J. J. Mallorqui, J.-C. Bolomey, and A. Broquetas, "Convergence and stability assessment of Newton-Kantorovich reconstruction algorithms for microwave tomography," IEEE Trans. Med. Imaging 17, 562-570 (1998).
[CrossRef] [PubMed]

W. C. Chew and Y. M. Wang, "Reconstruction of two-dimensional permittivity using the distorted Born iterative method," IEEE Trans. Med. Imaging 9, 218-225 (1990).
[CrossRef] [PubMed]

IEEE Trans. Microwave Theory Tech. (1)

S. Caorsi, G. L. Gragnani, M. Pastorino, and M. Rebagliati, "A model-driven approach to microwave diagnostics in biomedical applications," IEEE Trans. Microwave Theory Tech. 44, 1910-1920 (1996).
[CrossRef]

Inverse Probl. (1)

J. W. Ra, H. K. Choi, and J. S. Kim, "Two-and-half dimensional reconstruction of buried tunnel and pipes from cross-borehole and reflection measurements by using a genetic and Levenburg-Marquardt hybrid algorithm," Inverse Probl. 17, 233-252 (2003).

J. Appl. Phys. (1)

S. Norton and J. Bowler, "Theory of eddy current inversion," J. Appl. Phys. 73, 501-512 (1993).
[CrossRef]

J. Comput. Appl. Math. (1)

R. E. Kleinman and P. M. van den Berg, "A modified gradient method for two-dimensional problems in tomography," J. Comput. Appl. Math. 42, 17-35 (1992).
[CrossRef]

J. Electromagn. Waves Appl. (2)

Z. Q. Meng, T. Takenaka, and T. Tanaka, "Image reconstruction of two-dimensional impenetrable objects using genetic algorithms," J. Electromagn. Waves Appl. 13, 95-118 (1999).
[CrossRef]

R. de Oliveira, D. Lesselier, and B. Duchene, "Mapping defects in a conductive half-space by simulated annealing with connectivity and size as constraints," J. Electromagn. Waves Appl. 10, 983-1004 (1996).

Prog. Electromagn. Res. (1)

P. M. van den Berg and A. Abubakar, "Contrast source inversion: state of art," Prog. Electromagn. Res. 34, 189-218 (2001).
[CrossRef]

Subsurf. Sens. Technol. Appl. (1)

E. Nyfors, "Industrial microwave sensors—a review," Subsurf. Sens. Technol. Appl. 1, 23-43 (2000).
[CrossRef]

Other (5)

A. Massa, "Genetic algorithm (GA) based techniques for 2D microwave inverse scattering," in Recent Research Developments in Microwave Theory and Techniques (Special issue on Microwave Non-Destructive Evaluation and Imaging), S. G. Pandalai, ed. (Transworld Research Network Press, Trivandrum, India, 2002), pp. 193-218.

D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning (Addison-Wesley, 1989).

J. H. Holland, Adaption in Natural and Artificial Systems (U. Michigan Press, 1975).

A. Ishimaru, Electromagnetic Wave, Propagation, Radiation and Scattering (Prentice Hall, 1991).

Z. Michalewicz, Genetic Algorithms + Data Structures = Evolution Programs (Springer-Verlag, 1996).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (14)

Fig. 1
Fig. 1

Geometry of the problem.

Fig. 2
Fig. 2

Hybrid-coded, variable-length chromosome for the IGA.

Fig. 3
Fig. 3

Numerically computed inhomogeneous Green’s function for a source located at x = y = 0.025 λ 0 . The host medium is characterized by ( a ) σ D = 0.0 , ε D = 1.0 (free-space Green’s function); ( b ) σ D = 0.0 , ε D = 2.0 ; ( c ) σ D = 0.0 , ε D = 5.0 ; ( d ) σ D = 0.1 , ε D = 2.0 ; ( e ) σ D = 0.5 , ε D = 2.0 ; ( f ) σ D = 1.0 , ε D = 2.0 .

Fig. 4
Fig. 4

Example of the behavior of the cost function in the plane ( x C λ 0 , y C λ 0 ) of the solution space.

Fig. 5
Fig. 5

Reconstruction accuracy versus the area of the host medium for different values of SNR. ( a ) , ( b ) Localization error δ C ; ( c ) , ( d ) error in the crack area estimate δ A . ( a ) , ( c ) FGA; ( b ) , ( d ) IGA; ( e ) Δ δ C ; ( f ) Δ δ A .

Fig. 6
Fig. 6

Reconstruction accuracy versus the area of the host medium for different values of SNR. Behaviors of ( a ) δ C , ( b ) δ A versus A D for SNR = 13.75 dB . Behaviors of ( c ) δ C , ( d ) δ A versus SNR when A D λ 0 2 = 1.25 .

Fig. 7
Fig. 7

Effects of the dielectric permittivity on the reconstruction accuracy ( SNR = 15 dB ) . ( a ) , ( b ) Localization error δ C ; ( c ) , ( d ) error in the crack area estimate δ A . ( a ) , ( c ) FGA; ( b ) , ( d ) IGA; ( e ) Δ δ C ; ( f ) Δ δ A .

Fig. 8
Fig. 8

Reconstruction accuracy versus the values of the dielectric of the host medium for different SNR values. Effects of the dielectric permittivity of the host medium ε D : ( a ) , ( b ) localization error δ C ; ( c ) , ( d ) error in the crack area estimate δ A . ( a ) , ( c ) FGA; ( b ) , ( d ) IGA; ( e ) Δ δ C ; ( f ) Δ δ A .

Fig. 9
Fig. 9

Dependence of the reconstruction accuracy on crack dielectric characteristics ( SNR = 15 dB ) . Effects of the dielectric permittivity ε C and conductivity σ C : ( a ) , ( b ) localization error δ C ; ( c ) , ( d ) error in the crack area estimate δ A . ( a ) , ( c ) FGA; ( b ) , ( d ) IGA; ( e ) Δ δ C ; ( f ) Δ δ A .

Fig. 10
Fig. 10

Dependence of the reconstruction accuracy on crack and host medium dielectric characteristics ( SNR = 15 dB ) . Effects of the dielectric permittivity ε C and conductivity σ D : ( a ) , ( b ) localization error δ C ; ( c ) , ( d ) error in the crack area estimate δ A . ( a ) , ( c ) FGA; ( b ) , ( d ) IGA; ( e ) Δ δ C ; ( f ) Δ δ A .

Fig. 11
Fig. 11

Dependence of the reconstruction accuracy on crack and host medium dielectric characteristics ( SNR = 15 dB ) . Effects of the dielectric permittivity ε D and conductivity σ C : ( a ) , ( b ) localization error δ C ; ( c ) , ( d ) error in the crack area estimate δ A . ( a ) , ( c ) FGA; ( b ) , ( d ) IGA; ( e ) Δ δ C ; ( f ) Δ δ A .

Fig. 12
Fig. 12

Dependence of the reconstruction accuracy on host medium dielectric characteristics ( SNR = 15 dB ) . Effects of the dielectric permittivity ε D and conductivity σ D : ( a ) , ( b ) localization error δ C ; ( c ) , ( d ) error in the crack area estimate δ A . ( a ) , ( c ) FGA; ( b ) , ( d ) IGA; ( e ) Δ δ C ; ( f ) Δ δ A .

Fig. 13
Fig. 13

Dependence of the reconstruction accuracy on dielectric characteristics ratio ( SNR = 15 dB ) . Effects of the ratio σ C σ D : ( a ) , ( b ) localization error δ C ; ( c ) , ( d ) error in the crack area estimate δ A . ( a ) , ( c ) FGA; ( b ) , ( d ) IGA; ( e ) Δ δ C ; ( f ) Δ δ A .

Fig. 14
Fig. 14

Evolution of the crack detection and reconstruction ( SNR = 15 dB ) during the iteration process (k. iteration number). ( a ) ( b ) k = 1 , ( c ) ( d ) k = 50 , ( e ) ( f ) k = 100 , ( g ) ( h ) k = k * . ( i ) Actual configuration. ( a ) ( c ) ( e ) ( g ) FGA, ( b ) ( d ) ( f ) ( h ) IGA.

Tables (1)

Tables Icon

Table 1 Summary of the Parameters Employed in the Test Cases a

Equations (17)

Equations on this page are rendered with MathJax. Learn more.

E v t o t ( r ) = E v i n c ( r ) + D D γ ( r ) E v t o t ( r ) G 0 ( r r ) d r ,
γ C ( r ) = 1 j 2 π f ε 0 { [ σ C ( r ) σ B ] + j 2 π f ε 0 [ ε C ( r ) ε B ( r ) ] }
γ D ( r ) = 1 j 2 π f ε 0 { [ σ D ( r ) σ B ] + j 2 π f ε 0 [ ε D ( r ) ε B ( r ) ] }
γ D ˜ ( x , y ) = { γ C , X [ l 2 , l 2 ] and Y [ w 2 , w 2 ] γ D , otherwise ,
χ = { x C , y C , w , , θ , γ C , [ ξ n v , n = 1 , , N t ; v = 1 , , V ] } ,
Ψ ( χ ) = α M V v = 1 V m = 1 M { E v s c a t t ( r m ) n = 1 N t γ D ˜ ( r n ) ξ n v A n G m n 0 2 E v s c a t t ( r m ) } + β N t V v = 1 V n = 1 N t { ξ n C v E v i n c ( r n ) p = 1 N t γ D ˜ ( r p ) ξ p v A n G n p 0 2 E v i n c ( r n ) 2 } ,
G n p 0 = D n G 0 ( k ρ p ) d r , n , p = 1 , , N t ,
E v t o t ( r ) = E v i n c ( r ) + D D γ D ( r ) E v t o t ( c f ) ( r ) G 0 ( r r ) d r + D C γ ̃ C ( r ) E v t o t ( r ) G I ( r r ) d r ,
G I ( r r ) = G 0 ( r r ) + D D γ D ( r ) G I ( r r ) G 0 ( r r ) d r .
G h h I = G n h 0 + m = 1 ( m k ) N t γ m D G m h I A m G 0 ( r r ) d r ,
[ G n ] g n = g 0 n , n = 1 , , N t ,
{ [ F ] } m k = { 0 if m k and k j 1 if m = k and k j { [ G ] } m k { [ G ] } k k if m k and k = j 1 { [ G ] } k k if m = k and k = j , m , k , j = 1 , , N t .
δ C = ( x C x ̂ C ) 2 + ( y C y ̂ C ) 2 d m a x × 100
δ A = A C A ̂ C A C × 100 .
Δ δ C = δ C I G A δ C F G A ,
Δ δ A = δ A I G A δ A F G A ,
SNR = 10 log 10 v = 1 V m = 1 M E v s c a t t ( x m , y m ) 2 2 M V σ 2 ,

Metrics