Abstract

The subspace-based optimization method (SOM) is an efficient approach to addressing the inverse scattering problem. In this paper, a comparative study, on the basis of numerical experiments, is conducted to evaluate the performances of variants of SOM, so as to find the optimal method for the determination of the ambiguous portion, which has a dominant influence on the computational cost and the reconstruction capability of the algorithm.

© 2010 Optical Society of America

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  1. V. A. Markel, J. A. OSullivan, and J. C. Schotland, “Inverse problem in optical diffusion tomography. IV. Nonlinear inversion formulas,” J. Opt. Soc. Am. A 20, 903–912 (2003).
    [CrossRef]
  2. R. Feced and M. N. Zervas, “Efficient inverse scattering algorithm for the design of grating-assisted codirectional mode couplers,” J. Opt. Soc. Am. A 17, 1573–1582 (2000).
    [CrossRef]
  3. T. S. Ralston, D. L. Marks, P. S. Carney, and S. A. Boppart, “Inverse scattering for optical coherence tomography,” J. Opt. Soc. Am. A 23, 1027–1037 (2006).
    [CrossRef]
  4. P. S. Carney and J. C. Schotland, “Theory of total-internal-reflection tomography,” J. Opt. Soc. Am. A 20, 542–547 (2003).
    [CrossRef]
  5. K. Belkebir, P. C. Chaumet, and A. Sentenac, “Superresolution in total internal reflection tomography,” J. Opt. Soc. Am. A 22, 1889–1897 (2005).
    [CrossRef]
  6. A. Kirsch, An Introduction to the Mathematical Theory of Inverse Problems (Springer, 1996).
    [CrossRef]
  7. R. Aramini, G. Caviglia, A. Massa, and M. Piana, “The linear sampling method and energy conservation,” Inverse Probl. 26, 055004 (2010).
    [CrossRef]
  8. D. Colton, H. Haddar, and M. Piana, “The linear sampling method in inverse electromagnetic scattering theory,” Inverse Probl. 19, S105–S137 (2003).
    [CrossRef]
  9. K. Agarwal, X. Chen, and Y. Zhong, “A multipole-expansion based linear sampling method for solving inverse scattering problems,” Opt. Express 18, 6366–6381 (2010).
    [CrossRef] [PubMed]
  10. M. Donelli, D. Franceschini, A. Massa, M. Pastorino, and A. Zanetti, “Multi-resolution iterative inversion of real inhomogeneous targets,” Inverse Probl. 21, S51–S63 (2005).
    [CrossRef]
  11. E. L. Miller and A. S. Willsky, “A multiscale, statistically based inversion scheme for linearized inverse scattering problems,” IEEE Trans. Geosci. Remote Sens. 34, 346–357 (1996).
    [CrossRef]
  12. O. M. Bucci, L. Crocco, T. Isernia, and V. Pascazio, “An adaptive wavelet-based approach for nondestructive evaluation applications,” in Antennas and Propagation Society International Symposium (IEEE, 2000), Vol. 3, pp. 1756–1759.
  13. G. Leone, R. Persico, and R. Pierri, “Inverse scattering under the distorted Born approximation for cylindrical geometries,” J. Opt. Soc. Am. A 16, 1779–1787 (1999).
    [CrossRef]
  14. R. Persico and F. Soldovieri, “One-dimensional inverse scattering with a Born model in a three-layered medium,” J. Opt. Soc. Am. A 21, 35–45 (2004).
    [CrossRef]
  15. W. C. Chew and Y. M. Wang, “Reconstruction of two-dimensional permittivity distribution using the distorted Born iterative method,” IEEE Trans. Med. Imaging 9, 218–225 (1990).
    [CrossRef] [PubMed]
  16. P. M. van den Berg and R. E. Kleinman, “A contrast source inversion method,” Inverse Probl. 13, 1607–1620 (1997).
    [CrossRef]
  17. P. M. van den Berg, A. L. van Broekhoven, and A. Abubakar, “Extended contrast source inversion,” Inverse Probl. 15, 1325–1344 (1999).
    [CrossRef]
  18. A. Abubakar, P. M. van den Berg, and J. J. Mallorqui, “Imaging of biomedical data using a multiplicative regularized contrast source inversion method,” IEEE Trans. Microwave Theory Tech. 50, 1761–1771 (2002).
    [CrossRef]
  19. A. Abubakar and P. M. van den Berg, “The contrast source inversion method for location and shape reconstructions,” Inverse Probl. 18, 495–510 (2002).
    [CrossRef]
  20. A. Abubakar, T. M. Habashy, P. M. van den Berg, and D. Gisolf, “The diagonalized contrast source approach: an inversion method beyond the Born approximation,” Inverse Probl. 21, 685–702 (2005).
    [CrossRef]
  21. E. Bermani, A. Boni, S. Caorsi, and A. Massa, “An innovative real-time technique for buried object detection,” IEEE Trans. Geosci. Remote Sens. 41, 927–931 (2003).
    [CrossRef]
  22. S. Caorsi, D. Anguita, E. Bermani, A. Boni, M. Donelli, and A. Massa, “A comparative study of NN and SVM-based electromagnetic inverse scattering approaches to on-line detection of buried objects,” Appl. Comput. Electromagn. Soc. J. 18, 1–11 (2003).
  23. E. Bermani, A. Boni, S. Caorsi, M. Donelli, and A. Massa, “A multisource strategy based on a learning-by-examples technique for buried object detection,” PIER 48, 185–200 (2004).
    [CrossRef]
  24. X. Chen, “Application of signal-subspace and optimization methods in reconstructing extended scatterers,” J. Opt. Soc. Am. A 26, 1022–1026 (2009).
    [CrossRef]
  25. X. Chen, “Subspace-based optimization method for solving inverse scattering problems,” IEEE Trans. Geosci. Remote Sens. 48, 42–49 (2010).
    [CrossRef]
  26. L. Pan, K. Agarwal, Y. Zhong, S. P. Yeo, and X. Chen, “Subspace-based optimization method for reconstructing extended scatterers: Transverse electric case,” J. Opt. Soc. Am. A 26, 1932–1937 (2009).
    [CrossRef]
  27. X. Chen and Y. Zhong, “Influence of multiple scattering on the resolution in inverse scattering,” J. Opt. Soc. Am. A 27, 245–250 (2010).
    [CrossRef]
  28. X. Chen, “Subspace-based optimization method in electric impedance tomography,” J. Electromagn. Waves Appl. 23, 1397–1406 (2009).
    [CrossRef]
  29. L. Pan, X. Chen, and S. P. Yeo, “Nondestructive evaluation of nanoscale structures: inverse scattering approach,” Appl. Phys. A (to be published).
  30. K. Agarwal, L. Pan, and X. Chen, “Subspace-based optimization method for reconstruction of two-dimensional complex anisotropic dielectric objects,” IEEE Trans. Microwave Theory Tech. 58, 1065–1074 (2010).
    [CrossRef]
  31. J. Nocedal and S. Wright, Numerical Optimization, 2nd ed. (Springer, 2006).
  32. Y. Zhong and X. Chen, “MUSIC imaging and electromagnetic inverse scattering of multiply scattering small anisotropic spheres,” IEEE Trans. Antennas Propag. 55, 3542–3549 (2007).
    [CrossRef]
  33. R. Pierri and A. Tamburrino, “On the local minima problem in conductivity imaging via a quadratic approach,” Inverse Probl. 13, 1547–1568 (1997).
    [CrossRef]
  34. O. M. Bucci and G. Franceschetti, “On the degrees of freedom of scattered fields,” IEEE Trans. Antennas Propag. 37, 918–926 (1989).
    [CrossRef]
  35. O. M. Bucci, L. Crocco, and T. Isernia, “Improving the reconstruction capabilities in inverse scattering problems by exploitation of close-proximity setups,” J. Opt. Soc. Am. A 16, 1788–1798 (1999).
    [CrossRef]
  36. X. Chen, “MUSIC imaging applied to total internal reflection tomography,” J. Opt. Soc. Am. A 25, 357–364 (2008).
    [CrossRef]

2010 (5)

R. Aramini, G. Caviglia, A. Massa, and M. Piana, “The linear sampling method and energy conservation,” Inverse Probl. 26, 055004 (2010).
[CrossRef]

K. Agarwal, X. Chen, and Y. Zhong, “A multipole-expansion based linear sampling method for solving inverse scattering problems,” Opt. Express 18, 6366–6381 (2010).
[CrossRef] [PubMed]

X. Chen, “Subspace-based optimization method for solving inverse scattering problems,” IEEE Trans. Geosci. Remote Sens. 48, 42–49 (2010).
[CrossRef]

X. Chen and Y. Zhong, “Influence of multiple scattering on the resolution in inverse scattering,” J. Opt. Soc. Am. A 27, 245–250 (2010).
[CrossRef]

K. Agarwal, L. Pan, and X. Chen, “Subspace-based optimization method for reconstruction of two-dimensional complex anisotropic dielectric objects,” IEEE Trans. Microwave Theory Tech. 58, 1065–1074 (2010).
[CrossRef]

2009 (3)

2008 (1)

2007 (1)

Y. Zhong and X. Chen, “MUSIC imaging and electromagnetic inverse scattering of multiply scattering small anisotropic spheres,” IEEE Trans. Antennas Propag. 55, 3542–3549 (2007).
[CrossRef]

2006 (2)

2005 (3)

K. Belkebir, P. C. Chaumet, and A. Sentenac, “Superresolution in total internal reflection tomography,” J. Opt. Soc. Am. A 22, 1889–1897 (2005).
[CrossRef]

M. Donelli, D. Franceschini, A. Massa, M. Pastorino, and A. Zanetti, “Multi-resolution iterative inversion of real inhomogeneous targets,” Inverse Probl. 21, S51–S63 (2005).
[CrossRef]

A. Abubakar, T. M. Habashy, P. M. van den Berg, and D. Gisolf, “The diagonalized contrast source approach: an inversion method beyond the Born approximation,” Inverse Probl. 21, 685–702 (2005).
[CrossRef]

2004 (2)

E. Bermani, A. Boni, S. Caorsi, M. Donelli, and A. Massa, “A multisource strategy based on a learning-by-examples technique for buried object detection,” PIER 48, 185–200 (2004).
[CrossRef]

R. Persico and F. Soldovieri, “One-dimensional inverse scattering with a Born model in a three-layered medium,” J. Opt. Soc. Am. A 21, 35–45 (2004).
[CrossRef]

2003 (5)

D. Colton, H. Haddar, and M. Piana, “The linear sampling method in inverse electromagnetic scattering theory,” Inverse Probl. 19, S105–S137 (2003).
[CrossRef]

P. S. Carney and J. C. Schotland, “Theory of total-internal-reflection tomography,” J. Opt. Soc. Am. A 20, 542–547 (2003).
[CrossRef]

V. A. Markel, J. A. OSullivan, and J. C. Schotland, “Inverse problem in optical diffusion tomography. IV. Nonlinear inversion formulas,” J. Opt. Soc. Am. A 20, 903–912 (2003).
[CrossRef]

E. Bermani, A. Boni, S. Caorsi, and A. Massa, “An innovative real-time technique for buried object detection,” IEEE Trans. Geosci. Remote Sens. 41, 927–931 (2003).
[CrossRef]

S. Caorsi, D. Anguita, E. Bermani, A. Boni, M. Donelli, and A. Massa, “A comparative study of NN and SVM-based electromagnetic inverse scattering approaches to on-line detection of buried objects,” Appl. Comput. Electromagn. Soc. J. 18, 1–11 (2003).

2002 (2)

A. Abubakar, P. M. van den Berg, and J. J. Mallorqui, “Imaging of biomedical data using a multiplicative regularized contrast source inversion method,” IEEE Trans. Microwave Theory Tech. 50, 1761–1771 (2002).
[CrossRef]

A. Abubakar and P. M. van den Berg, “The contrast source inversion method for location and shape reconstructions,” Inverse Probl. 18, 495–510 (2002).
[CrossRef]

2000 (2)

R. Feced and M. N. Zervas, “Efficient inverse scattering algorithm for the design of grating-assisted codirectional mode couplers,” J. Opt. Soc. Am. A 17, 1573–1582 (2000).
[CrossRef]

O. M. Bucci, L. Crocco, T. Isernia, and V. Pascazio, “An adaptive wavelet-based approach for nondestructive evaluation applications,” in Antennas and Propagation Society International Symposium (IEEE, 2000), Vol. 3, pp. 1756–1759.

1999 (3)

1997 (2)

R. Pierri and A. Tamburrino, “On the local minima problem in conductivity imaging via a quadratic approach,” Inverse Probl. 13, 1547–1568 (1997).
[CrossRef]

P. M. van den Berg and R. E. Kleinman, “A contrast source inversion method,” Inverse Probl. 13, 1607–1620 (1997).
[CrossRef]

1996 (2)

E. L. Miller and A. S. Willsky, “A multiscale, statistically based inversion scheme for linearized inverse scattering problems,” IEEE Trans. Geosci. Remote Sens. 34, 346–357 (1996).
[CrossRef]

A. Kirsch, An Introduction to the Mathematical Theory of Inverse Problems (Springer, 1996).
[CrossRef]

1990 (1)

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

1989 (1)

O. M. Bucci and G. Franceschetti, “On the degrees of freedom of scattered fields,” IEEE Trans. Antennas Propag. 37, 918–926 (1989).
[CrossRef]

Abubakar, A.

A. Abubakar, T. M. Habashy, P. M. van den Berg, and D. Gisolf, “The diagonalized contrast source approach: an inversion method beyond the Born approximation,” Inverse Probl. 21, 685–702 (2005).
[CrossRef]

A. Abubakar and P. M. van den Berg, “The contrast source inversion method for location and shape reconstructions,” Inverse Probl. 18, 495–510 (2002).
[CrossRef]

A. Abubakar, P. M. van den Berg, and J. J. Mallorqui, “Imaging of biomedical data using a multiplicative regularized contrast source inversion method,” IEEE Trans. Microwave Theory Tech. 50, 1761–1771 (2002).
[CrossRef]

P. M. van den Berg, A. L. van Broekhoven, and A. Abubakar, “Extended contrast source inversion,” Inverse Probl. 15, 1325–1344 (1999).
[CrossRef]

Agarwal, K.

Anguita, D.

S. Caorsi, D. Anguita, E. Bermani, A. Boni, M. Donelli, and A. Massa, “A comparative study of NN and SVM-based electromagnetic inverse scattering approaches to on-line detection of buried objects,” Appl. Comput. Electromagn. Soc. J. 18, 1–11 (2003).

Aramini, R.

R. Aramini, G. Caviglia, A. Massa, and M. Piana, “The linear sampling method and energy conservation,” Inverse Probl. 26, 055004 (2010).
[CrossRef]

Belkebir, K.

Bermani, E.

E. Bermani, A. Boni, S. Caorsi, M. Donelli, and A. Massa, “A multisource strategy based on a learning-by-examples technique for buried object detection,” PIER 48, 185–200 (2004).
[CrossRef]

S. Caorsi, D. Anguita, E. Bermani, A. Boni, M. Donelli, and A. Massa, “A comparative study of NN and SVM-based electromagnetic inverse scattering approaches to on-line detection of buried objects,” Appl. Comput. Electromagn. Soc. J. 18, 1–11 (2003).

E. Bermani, A. Boni, S. Caorsi, and A. Massa, “An innovative real-time technique for buried object detection,” IEEE Trans. Geosci. Remote Sens. 41, 927–931 (2003).
[CrossRef]

Boni, A.

E. Bermani, A. Boni, S. Caorsi, M. Donelli, and A. Massa, “A multisource strategy based on a learning-by-examples technique for buried object detection,” PIER 48, 185–200 (2004).
[CrossRef]

E. Bermani, A. Boni, S. Caorsi, and A. Massa, “An innovative real-time technique for buried object detection,” IEEE Trans. Geosci. Remote Sens. 41, 927–931 (2003).
[CrossRef]

S. Caorsi, D. Anguita, E. Bermani, A. Boni, M. Donelli, and A. Massa, “A comparative study of NN and SVM-based electromagnetic inverse scattering approaches to on-line detection of buried objects,” Appl. Comput. Electromagn. Soc. J. 18, 1–11 (2003).

Boppart, S. A.

Bucci, O. M.

O. M. Bucci, L. Crocco, T. Isernia, and V. Pascazio, “An adaptive wavelet-based approach for nondestructive evaluation applications,” in Antennas and Propagation Society International Symposium (IEEE, 2000), Vol. 3, pp. 1756–1759.

O. M. Bucci, L. Crocco, and T. Isernia, “Improving the reconstruction capabilities in inverse scattering problems by exploitation of close-proximity setups,” J. Opt. Soc. Am. A 16, 1788–1798 (1999).
[CrossRef]

O. M. Bucci and G. Franceschetti, “On the degrees of freedom of scattered fields,” IEEE Trans. Antennas Propag. 37, 918–926 (1989).
[CrossRef]

Caorsi, S.

E. Bermani, A. Boni, S. Caorsi, M. Donelli, and A. Massa, “A multisource strategy based on a learning-by-examples technique for buried object detection,” PIER 48, 185–200 (2004).
[CrossRef]

S. Caorsi, D. Anguita, E. Bermani, A. Boni, M. Donelli, and A. Massa, “A comparative study of NN and SVM-based electromagnetic inverse scattering approaches to on-line detection of buried objects,” Appl. Comput. Electromagn. Soc. J. 18, 1–11 (2003).

E. Bermani, A. Boni, S. Caorsi, and A. Massa, “An innovative real-time technique for buried object detection,” IEEE Trans. Geosci. Remote Sens. 41, 927–931 (2003).
[CrossRef]

Carney, P. S.

Caviglia, G.

R. Aramini, G. Caviglia, A. Massa, and M. Piana, “The linear sampling method and energy conservation,” Inverse Probl. 26, 055004 (2010).
[CrossRef]

Chaumet, P. C.

Chen, X.

K. Agarwal, X. Chen, and Y. Zhong, “A multipole-expansion based linear sampling method for solving inverse scattering problems,” Opt. Express 18, 6366–6381 (2010).
[CrossRef] [PubMed]

X. Chen, “Subspace-based optimization method for solving inverse scattering problems,” IEEE Trans. Geosci. Remote Sens. 48, 42–49 (2010).
[CrossRef]

X. Chen and Y. Zhong, “Influence of multiple scattering on the resolution in inverse scattering,” J. Opt. Soc. Am. A 27, 245–250 (2010).
[CrossRef]

K. Agarwal, L. Pan, and X. Chen, “Subspace-based optimization method for reconstruction of two-dimensional complex anisotropic dielectric objects,” IEEE Trans. Microwave Theory Tech. 58, 1065–1074 (2010).
[CrossRef]

X. Chen, “Subspace-based optimization method in electric impedance tomography,” J. Electromagn. Waves Appl. 23, 1397–1406 (2009).
[CrossRef]

X. Chen, “Application of signal-subspace and optimization methods in reconstructing extended scatterers,” J. Opt. Soc. Am. A 26, 1022–1026 (2009).
[CrossRef]

L. Pan, K. Agarwal, Y. Zhong, S. P. Yeo, and X. Chen, “Subspace-based optimization method for reconstructing extended scatterers: Transverse electric case,” J. Opt. Soc. Am. A 26, 1932–1937 (2009).
[CrossRef]

X. Chen, “MUSIC imaging applied to total internal reflection tomography,” J. Opt. Soc. Am. A 25, 357–364 (2008).
[CrossRef]

Y. Zhong and X. Chen, “MUSIC imaging and electromagnetic inverse scattering of multiply scattering small anisotropic spheres,” IEEE Trans. Antennas Propag. 55, 3542–3549 (2007).
[CrossRef]

L. Pan, X. Chen, and S. P. Yeo, “Nondestructive evaluation of nanoscale structures: inverse scattering approach,” Appl. Phys. A (to be published).

Chew, W. C.

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

Colton, D.

D. Colton, H. Haddar, and M. Piana, “The linear sampling method in inverse electromagnetic scattering theory,” Inverse Probl. 19, S105–S137 (2003).
[CrossRef]

Crocco, L.

O. M. Bucci, L. Crocco, T. Isernia, and V. Pascazio, “An adaptive wavelet-based approach for nondestructive evaluation applications,” in Antennas and Propagation Society International Symposium (IEEE, 2000), Vol. 3, pp. 1756–1759.

O. M. Bucci, L. Crocco, and T. Isernia, “Improving the reconstruction capabilities in inverse scattering problems by exploitation of close-proximity setups,” J. Opt. Soc. Am. A 16, 1788–1798 (1999).
[CrossRef]

Donelli, M.

M. Donelli, D. Franceschini, A. Massa, M. Pastorino, and A. Zanetti, “Multi-resolution iterative inversion of real inhomogeneous targets,” Inverse Probl. 21, S51–S63 (2005).
[CrossRef]

E. Bermani, A. Boni, S. Caorsi, M. Donelli, and A. Massa, “A multisource strategy based on a learning-by-examples technique for buried object detection,” PIER 48, 185–200 (2004).
[CrossRef]

S. Caorsi, D. Anguita, E. Bermani, A. Boni, M. Donelli, and A. Massa, “A comparative study of NN and SVM-based electromagnetic inverse scattering approaches to on-line detection of buried objects,” Appl. Comput. Electromagn. Soc. J. 18, 1–11 (2003).

Feced, R.

Franceschetti, G.

O. M. Bucci and G. Franceschetti, “On the degrees of freedom of scattered fields,” IEEE Trans. Antennas Propag. 37, 918–926 (1989).
[CrossRef]

Franceschini, D.

M. Donelli, D. Franceschini, A. Massa, M. Pastorino, and A. Zanetti, “Multi-resolution iterative inversion of real inhomogeneous targets,” Inverse Probl. 21, S51–S63 (2005).
[CrossRef]

Gisolf, D.

A. Abubakar, T. M. Habashy, P. M. van den Berg, and D. Gisolf, “The diagonalized contrast source approach: an inversion method beyond the Born approximation,” Inverse Probl. 21, 685–702 (2005).
[CrossRef]

Habashy, T. M.

A. Abubakar, T. M. Habashy, P. M. van den Berg, and D. Gisolf, “The diagonalized contrast source approach: an inversion method beyond the Born approximation,” Inverse Probl. 21, 685–702 (2005).
[CrossRef]

Haddar, H.

D. Colton, H. Haddar, and M. Piana, “The linear sampling method in inverse electromagnetic scattering theory,” Inverse Probl. 19, S105–S137 (2003).
[CrossRef]

Isernia, T.

O. M. Bucci, L. Crocco, T. Isernia, and V. Pascazio, “An adaptive wavelet-based approach for nondestructive evaluation applications,” in Antennas and Propagation Society International Symposium (IEEE, 2000), Vol. 3, pp. 1756–1759.

O. M. Bucci, L. Crocco, and T. Isernia, “Improving the reconstruction capabilities in inverse scattering problems by exploitation of close-proximity setups,” J. Opt. Soc. Am. A 16, 1788–1798 (1999).
[CrossRef]

Kirsch, A.

A. Kirsch, An Introduction to the Mathematical Theory of Inverse Problems (Springer, 1996).
[CrossRef]

Kleinman, R. E.

P. M. van den Berg and R. E. Kleinman, “A contrast source inversion method,” Inverse Probl. 13, 1607–1620 (1997).
[CrossRef]

Leone, G.

Mallorqui, J. J.

A. Abubakar, P. M. van den Berg, and J. J. Mallorqui, “Imaging of biomedical data using a multiplicative regularized contrast source inversion method,” IEEE Trans. Microwave Theory Tech. 50, 1761–1771 (2002).
[CrossRef]

Markel, V. A.

Marks, D. L.

Massa, A.

R. Aramini, G. Caviglia, A. Massa, and M. Piana, “The linear sampling method and energy conservation,” Inverse Probl. 26, 055004 (2010).
[CrossRef]

M. Donelli, D. Franceschini, A. Massa, M. Pastorino, and A. Zanetti, “Multi-resolution iterative inversion of real inhomogeneous targets,” Inverse Probl. 21, S51–S63 (2005).
[CrossRef]

E. Bermani, A. Boni, S. Caorsi, M. Donelli, and A. Massa, “A multisource strategy based on a learning-by-examples technique for buried object detection,” PIER 48, 185–200 (2004).
[CrossRef]

S. Caorsi, D. Anguita, E. Bermani, A. Boni, M. Donelli, and A. Massa, “A comparative study of NN and SVM-based electromagnetic inverse scattering approaches to on-line detection of buried objects,” Appl. Comput. Electromagn. Soc. J. 18, 1–11 (2003).

E. Bermani, A. Boni, S. Caorsi, and A. Massa, “An innovative real-time technique for buried object detection,” IEEE Trans. Geosci. Remote Sens. 41, 927–931 (2003).
[CrossRef]

Miller, E. L.

E. L. Miller and A. S. Willsky, “A multiscale, statistically based inversion scheme for linearized inverse scattering problems,” IEEE Trans. Geosci. Remote Sens. 34, 346–357 (1996).
[CrossRef]

Nocedal, J.

J. Nocedal and S. Wright, Numerical Optimization, 2nd ed. (Springer, 2006).

OSullivan, J. A.

Pan, L.

K. Agarwal, L. Pan, and X. Chen, “Subspace-based optimization method for reconstruction of two-dimensional complex anisotropic dielectric objects,” IEEE Trans. Microwave Theory Tech. 58, 1065–1074 (2010).
[CrossRef]

L. Pan, K. Agarwal, Y. Zhong, S. P. Yeo, and X. Chen, “Subspace-based optimization method for reconstructing extended scatterers: Transverse electric case,” J. Opt. Soc. Am. A 26, 1932–1937 (2009).
[CrossRef]

L. Pan, X. Chen, and S. P. Yeo, “Nondestructive evaluation of nanoscale structures: inverse scattering approach,” Appl. Phys. A (to be published).

Pascazio, V.

O. M. Bucci, L. Crocco, T. Isernia, and V. Pascazio, “An adaptive wavelet-based approach for nondestructive evaluation applications,” in Antennas and Propagation Society International Symposium (IEEE, 2000), Vol. 3, pp. 1756–1759.

Pastorino, M.

M. Donelli, D. Franceschini, A. Massa, M. Pastorino, and A. Zanetti, “Multi-resolution iterative inversion of real inhomogeneous targets,” Inverse Probl. 21, S51–S63 (2005).
[CrossRef]

Persico, R.

Piana, M.

R. Aramini, G. Caviglia, A. Massa, and M. Piana, “The linear sampling method and energy conservation,” Inverse Probl. 26, 055004 (2010).
[CrossRef]

D. Colton, H. Haddar, and M. Piana, “The linear sampling method in inverse electromagnetic scattering theory,” Inverse Probl. 19, S105–S137 (2003).
[CrossRef]

Pierri, R.

G. Leone, R. Persico, and R. Pierri, “Inverse scattering under the distorted Born approximation for cylindrical geometries,” J. Opt. Soc. Am. A 16, 1779–1787 (1999).
[CrossRef]

R. Pierri and A. Tamburrino, “On the local minima problem in conductivity imaging via a quadratic approach,” Inverse Probl. 13, 1547–1568 (1997).
[CrossRef]

Ralston, T. S.

Schotland, J. C.

Sentenac, A.

Soldovieri, F.

Tamburrino, A.

R. Pierri and A. Tamburrino, “On the local minima problem in conductivity imaging via a quadratic approach,” Inverse Probl. 13, 1547–1568 (1997).
[CrossRef]

van Broekhoven, A. L.

P. M. van den Berg, A. L. van Broekhoven, and A. Abubakar, “Extended contrast source inversion,” Inverse Probl. 15, 1325–1344 (1999).
[CrossRef]

van den Berg, P. M.

A. Abubakar, T. M. Habashy, P. M. van den Berg, and D. Gisolf, “The diagonalized contrast source approach: an inversion method beyond the Born approximation,” Inverse Probl. 21, 685–702 (2005).
[CrossRef]

A. Abubakar and P. M. van den Berg, “The contrast source inversion method for location and shape reconstructions,” Inverse Probl. 18, 495–510 (2002).
[CrossRef]

A. Abubakar, P. M. van den Berg, and J. J. Mallorqui, “Imaging of biomedical data using a multiplicative regularized contrast source inversion method,” IEEE Trans. Microwave Theory Tech. 50, 1761–1771 (2002).
[CrossRef]

P. M. van den Berg, A. L. van Broekhoven, and A. Abubakar, “Extended contrast source inversion,” Inverse Probl. 15, 1325–1344 (1999).
[CrossRef]

P. M. van den Berg and R. E. Kleinman, “A contrast source inversion method,” Inverse Probl. 13, 1607–1620 (1997).
[CrossRef]

Wang, Y. M.

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

Willsky, A. S.

E. L. Miller and A. S. Willsky, “A multiscale, statistically based inversion scheme for linearized inverse scattering problems,” IEEE Trans. Geosci. Remote Sens. 34, 346–357 (1996).
[CrossRef]

Wright, S.

J. Nocedal and S. Wright, Numerical Optimization, 2nd ed. (Springer, 2006).

Yeo, S. P.

L. Pan, K. Agarwal, Y. Zhong, S. P. Yeo, and X. Chen, “Subspace-based optimization method for reconstructing extended scatterers: Transverse electric case,” J. Opt. Soc. Am. A 26, 1932–1937 (2009).
[CrossRef]

L. Pan, X. Chen, and S. P. Yeo, “Nondestructive evaluation of nanoscale structures: inverse scattering approach,” Appl. Phys. A (to be published).

Zanetti, A.

M. Donelli, D. Franceschini, A. Massa, M. Pastorino, and A. Zanetti, “Multi-resolution iterative inversion of real inhomogeneous targets,” Inverse Probl. 21, S51–S63 (2005).
[CrossRef]

Zervas, M. N.

Zhong, Y.

Appl. Comput. Electromagn. Soc. J. (1)

S. Caorsi, D. Anguita, E. Bermani, A. Boni, M. Donelli, and A. Massa, “A comparative study of NN and SVM-based electromagnetic inverse scattering approaches to on-line detection of buried objects,” Appl. Comput. Electromagn. Soc. J. 18, 1–11 (2003).

IEEE Trans. Antennas Propag. (2)

Y. Zhong and X. Chen, “MUSIC imaging and electromagnetic inverse scattering of multiply scattering small anisotropic spheres,” IEEE Trans. Antennas Propag. 55, 3542–3549 (2007).
[CrossRef]

O. M. Bucci and G. Franceschetti, “On the degrees of freedom of scattered fields,” IEEE Trans. Antennas Propag. 37, 918–926 (1989).
[CrossRef]

IEEE Trans. Geosci. Remote Sens. (3)

X. Chen, “Subspace-based optimization method for solving inverse scattering problems,” IEEE Trans. Geosci. Remote Sens. 48, 42–49 (2010).
[CrossRef]

E. L. Miller and A. S. Willsky, “A multiscale, statistically based inversion scheme for linearized inverse scattering problems,” IEEE Trans. Geosci. Remote Sens. 34, 346–357 (1996).
[CrossRef]

E. Bermani, A. Boni, S. Caorsi, and A. Massa, “An innovative real-time technique for buried object detection,” IEEE Trans. Geosci. Remote Sens. 41, 927–931 (2003).
[CrossRef]

IEEE Trans. Med. Imaging (1)

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

IEEE Trans. Microwave Theory Tech. (2)

A. Abubakar, P. M. van den Berg, and J. J. Mallorqui, “Imaging of biomedical data using a multiplicative regularized contrast source inversion method,” IEEE Trans. Microwave Theory Tech. 50, 1761–1771 (2002).
[CrossRef]

K. Agarwal, L. Pan, and X. Chen, “Subspace-based optimization method for reconstruction of two-dimensional complex anisotropic dielectric objects,” IEEE Trans. Microwave Theory Tech. 58, 1065–1074 (2010).
[CrossRef]

Inverse Probl. (8)

R. Pierri and A. Tamburrino, “On the local minima problem in conductivity imaging via a quadratic approach,” Inverse Probl. 13, 1547–1568 (1997).
[CrossRef]

A. Abubakar and P. M. van den Berg, “The contrast source inversion method for location and shape reconstructions,” Inverse Probl. 18, 495–510 (2002).
[CrossRef]

A. Abubakar, T. M. Habashy, P. M. van den Berg, and D. Gisolf, “The diagonalized contrast source approach: an inversion method beyond the Born approximation,” Inverse Probl. 21, 685–702 (2005).
[CrossRef]

M. Donelli, D. Franceschini, A. Massa, M. Pastorino, and A. Zanetti, “Multi-resolution iterative inversion of real inhomogeneous targets,” Inverse Probl. 21, S51–S63 (2005).
[CrossRef]

P. M. van den Berg and R. E. Kleinman, “A contrast source inversion method,” Inverse Probl. 13, 1607–1620 (1997).
[CrossRef]

P. M. van den Berg, A. L. van Broekhoven, and A. Abubakar, “Extended contrast source inversion,” Inverse Probl. 15, 1325–1344 (1999).
[CrossRef]

R. Aramini, G. Caviglia, A. Massa, and M. Piana, “The linear sampling method and energy conservation,” Inverse Probl. 26, 055004 (2010).
[CrossRef]

D. Colton, H. Haddar, and M. Piana, “The linear sampling method in inverse electromagnetic scattering theory,” Inverse Probl. 19, S105–S137 (2003).
[CrossRef]

J. Electromagn. Waves Appl. (1)

X. Chen, “Subspace-based optimization method in electric impedance tomography,” J. Electromagn. Waves Appl. 23, 1397–1406 (2009).
[CrossRef]

J. Opt. Soc. Am. A (12)

L. Pan, K. Agarwal, Y. Zhong, S. P. Yeo, and X. Chen, “Subspace-based optimization method for reconstructing extended scatterers: Transverse electric case,” J. Opt. Soc. Am. A 26, 1932–1937 (2009).
[CrossRef]

X. Chen and Y. Zhong, “Influence of multiple scattering on the resolution in inverse scattering,” J. Opt. Soc. Am. A 27, 245–250 (2010).
[CrossRef]

O. M. Bucci, L. Crocco, and T. Isernia, “Improving the reconstruction capabilities in inverse scattering problems by exploitation of close-proximity setups,” J. Opt. Soc. Am. A 16, 1788–1798 (1999).
[CrossRef]

X. Chen, “MUSIC imaging applied to total internal reflection tomography,” J. Opt. Soc. Am. A 25, 357–364 (2008).
[CrossRef]

X. Chen, “Application of signal-subspace and optimization methods in reconstructing extended scatterers,” J. Opt. Soc. Am. A 26, 1022–1026 (2009).
[CrossRef]

V. A. Markel, J. A. OSullivan, and J. C. Schotland, “Inverse problem in optical diffusion tomography. IV. Nonlinear inversion formulas,” J. Opt. Soc. Am. A 20, 903–912 (2003).
[CrossRef]

R. Feced and M. N. Zervas, “Efficient inverse scattering algorithm for the design of grating-assisted codirectional mode couplers,” J. Opt. Soc. Am. A 17, 1573–1582 (2000).
[CrossRef]

T. S. Ralston, D. L. Marks, P. S. Carney, and S. A. Boppart, “Inverse scattering for optical coherence tomography,” J. Opt. Soc. Am. A 23, 1027–1037 (2006).
[CrossRef]

P. S. Carney and J. C. Schotland, “Theory of total-internal-reflection tomography,” J. Opt. Soc. Am. A 20, 542–547 (2003).
[CrossRef]

K. Belkebir, P. C. Chaumet, and A. Sentenac, “Superresolution in total internal reflection tomography,” J. Opt. Soc. Am. A 22, 1889–1897 (2005).
[CrossRef]

G. Leone, R. Persico, and R. Pierri, “Inverse scattering under the distorted Born approximation for cylindrical geometries,” J. Opt. Soc. Am. A 16, 1779–1787 (1999).
[CrossRef]

R. Persico and F. Soldovieri, “One-dimensional inverse scattering with a Born model in a three-layered medium,” J. Opt. Soc. Am. A 21, 35–45 (2004).
[CrossRef]

Opt. Express (1)

PIER (1)

E. Bermani, A. Boni, S. Caorsi, M. Donelli, and A. Massa, “A multisource strategy based on a learning-by-examples technique for buried object detection,” PIER 48, 185–200 (2004).
[CrossRef]

Other (4)

L. Pan, X. Chen, and S. P. Yeo, “Nondestructive evaluation of nanoscale structures: inverse scattering approach,” Appl. Phys. A (to be published).

J. Nocedal and S. Wright, Numerical Optimization, 2nd ed. (Springer, 2006).

O. M. Bucci, L. Crocco, T. Isernia, and V. Pascazio, “An adaptive wavelet-based approach for nondestructive evaluation applications,” in Antennas and Propagation Society International Symposium (IEEE, 2000), Vol. 3, pp. 1756–1759.

A. Kirsch, An Introduction to the Mathematical Theory of Inverse Problems (Springer, 1996).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Pattern of an annulus. (a1), (a2) Exact patterns of the real and imaginary parts of relative permittivity. (b1), (b2) Reconstructed patterns of the real and imaginary parts using the original SOM under 10% Gaussian white noise. (c1), (c2) Reconstructed patterns of the real and imaginary parts using the CSI-like SOM under 10% Gaussian white noise. (d1), (d2) Reconstructed patterns of the real and imaginary parts using the novel variant of SOM under 10% Gaussian white noise.

Fig. 2
Fig. 2

Pattern of a hollow square. (a1), (a2) Exact patterns of the real and imaginary parts of relative permittivity. (b1), (b2) Reconstructed patterns of the real and imaginary parts using the original SOM under 10% Gaussian white noise. (c1), (c2) Reconstructed patterns of the real and imaginary parts using the CSI-like SOM under 10% Gaussian white noise. (d1), (d2) Reconstructed patterns of the real and imaginary parts using the novel variant of SOM under 10% Gaussian white noise.

Fig. 3
Fig. 3

Pattern of an annulus. (a) Exact pattern of relative permittivity. (b) Reconstructed pattern using the original SOM under 31.6% Gaussian white noise. (c) Reconstructed pattern using the CSI-like SOM under 31.6% Gaussian white noise. (d) Reconstructed pattern using the novel variant of SOM under 31.6% Gaussian white noise.

Fig. 4
Fig. 4

Pattern consisting of two overlapping annuli. (a) Exact pattern of relative permittivity. (b) Reconstructed pattern using the original SOM under 31.6% Gaussian white noise. (c) Reconstructed pattern using the CSI-like SOM under 31.6% Gaussian white noise. (d) Reconstructed pattern using the novel variant of SOM under 31.6% Gaussian white noise.

Fig. 5
Fig. 5

Pattern consisting of a circle and an annulus. (a) Exact pattern of relative permittivity. (b) Reconstructed pattern using the original SOM under 31.6% Gaussian white noise. (c) Reconstructed pattern using the CSI-like SOM under 31.6% Gaussian white noise. (d) Reconstructed pattern using the novel variant of SOM under 31.6% Gaussian white noise.

Fig. 6
Fig. 6

Austria pattern. (a) Exact pattern of relative permittivity. (b) Reconstructed pattern using the original SOM under 31.6% Gaussian white noise. (c) Reconstructed pattern using the CSI-like SOM under 31.6% Gaussian white noise. (d) Reconstructed pattern using the novel variant of SOM under 31.6% Gaussian white noise.

Tables (2)

Tables Icon

Table 1 Variables Used in the Formulation of the Forward Scattering Problem

Tables Icon

Table 2 Comparison of the Performance of the Three Variants of SOM in the Numerical Experiments

Equations (4)

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

I ¯ p d = ξ ¯ ¯ ( E ¯ p inc + G ¯ ¯ D I ¯ p d ) ,
E ¯ p scat = G ¯ ¯ S I ¯ p d .
f ( ξ ¯ ¯ ) = p = 1 N t G ¯ ¯ S V ¯ ¯ n α ¯ p n ( ξ ¯ ¯ ) + G ¯ ¯ S I ¯ p s E ¯ p scat 2 E ¯ p scat 2 + A ¯ ¯ ( ξ ¯ ¯ ) α ¯ p n ( ξ ¯ ¯ ) B ¯ p ( ξ ¯ ¯ ) 2 I ¯ p s 2 .
f ( α ¯ 1 n , α ¯ 2 n , , α ¯ N t n , ξ ¯ ¯ ) = p = 1 N t G ¯ ¯ S V ¯ ¯ n α ¯ p n + G ¯ ¯ S I ¯ p s E ¯ p scat 2 E ¯ p scat 2 + A ¯ ¯ ( ξ ¯ ¯ ) α ¯ p n B ¯ p ( ξ ¯ ¯ ) 2 I ¯ ¯ p s 2 ,

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