Abstract

A signal-subspace approach to reconstruct the permittivities of extended scatterers in two-dimensional settings is proposed. A portion of the scatterers’ information is retrieved by the signal-subspace method, and the remaining part is obtained by solving a nonlinear least-squares problem. The method exhibits several strengths, including robustness against noise, fast convergence, less scattering data, high resolution, and the ability to deal with scatterers of special shapes.

© 2009 Optical Society of America

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  1. H. Ammari, E. Iakovleva, D. Lesselier, and G. Perruson, “MUSIC-type electromagnetic imaging of a collection of small three-dimensional bounded inclusions,” SIAM J. Sci. Comput. (USA) 29, 674-709 (2007).
    [CrossRef]
  2. E. Iakovleva, S. Gdoura, D. Lesselier, and G. Perrusson, “Multistatic response matrix of a 3-d inclusion in half space and MUSIC imaging,” IEEE Trans. Antennas Propag. 55, 2598-2609 (2007).
    [CrossRef]
  3. E. A. Marengo, R. D. Hernandez, and H. Lev-Ari, “Intensity-only signal-subspace-based imaging,” J. Opt. Soc. Am. A 24, 3619-3635 (2007).
    [CrossRef]
  4. E. A. Marengo and F. K. Gruber, “Subspace-based localization and inverse scattering of multiply scattering point targets,” EURASIP J. Adv. Signal Process. 2007, 17342 (2007).
    [CrossRef]
  5. X. Chen and Y. Zhong, “A robust noniterative method for obtaining scattering strengths of multiply scattering point targets,” J. Acoust. Soc. Am. 122, 1325-1327 (2007).
    [CrossRef] [PubMed]
  6. 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]
  7. X. Chen, “Signal-subspace method approach to intensity-only electromagnetic inverse scattering problem,” J. Opt. Soc. Am. A 25, 2018-2024 (2008).
    [CrossRef]
  8. K. Agarwal and X. Chen, “Applicability of MUSIC-type imaging in two-dimensional electromagnetic inverse problems,” IEEE Trans. Antennas Propag. 56, 3217-3223 (2008).
    [CrossRef]
  9. E. A. Marengo and F. K. Gruber, “Noniterative analytical formula for inverse scattering of multiply scattering point targets,” J. Acoust. Soc. Am. 120, 3782-3788 (2006).
    [CrossRef]
  10. A. Kirsch, “The MUSIC-algorithm and the factorization method in inverse scattering theory for inhomogeneous media,” Inverse Probl. 18, 1025-1040 (2002).
    [CrossRef]
  11. X. Chen and Y. Zhong, “MUSIC electromagnetic imaging with enhanced resolution for small inclusions,” Inverse Probl. 25, 015008 (2009).
    [CrossRef]
  12. E. A. Marengo, F. K. Gruber, and F. Simonetti, “Time-reversal MUSIC imaging of extended targets,” IEEE Trans. Image Process. 16, 1967-1984 (2007).
    [CrossRef] [PubMed]
  13. S. Hou, K. Solna, and H. Zhao, “A direct imaging algorithm for extended targets,” Inverse Probl. 22, 1151-1178 (2006).
    [CrossRef]
  14. T. M. Habashy, E. Y. Chow, and D. G. Dudley, “Profile inversion using the renormalized source-type integral equation approach,” IEEE Trans. Antennas Propag. 38, 668-681 (1990).
    [CrossRef]
  15. T. M. Habashy, M. L. Oristaglio, and A. T. D. Hoop, “Simultaneous nonlinear reconstruction of two dimensional permittivity and conductivity,” Radio Sci. 29, 1101-1118 (1994).
    [CrossRef]
  16. P. M. van den Berg and R. E. Kleinman, “A contrast source inversion method,” Inverse Probl. 13, 1607-1620 (1997).
    [CrossRef]
  17. 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]
  18. K. Belkebir, P. C. Chaumet, and A. Sentenac, “Superresolution in total internal reflection tomography,” J. Opt. Soc. Am. A 22, 1889-1897 (2005).
    [CrossRef]
  19. A. Lakhtakia, “Strong and weak forms of the method of moments and the coupled dipole method for scattering of time-harmonic electromagnetics fields,” Int. J. Mod. Phys. C 3, 583-603 (1992).
    [CrossRef]
  20. X. Chen and Y. Zhong, “Electromagnetic imaging of multiple-scattering small objects: noniterative analytical approach,” J. Phys.: Conf. Ser. 124, 012016 (2008).
    [CrossRef]
  21. X. Chen, “MUSIC imaging applied to total internal reflection tomography,” J. Opt. Soc. Am. A 25, 357-364 (2008).
    [CrossRef]
  22. D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, 2nd ed. (Springer-Verlag, 1998).
  23. A. Horn and C. R. Johnson, Matrix Analysis (Cambridge U. Press, 1985).
  24. I. Catapano, L. Crocco, and T. Isernia, “On simple methods for shape reconstruction of unknown scatterers,” IEEE Trans. Antennas Propag. 55, 1431-1436 (2007).
    [CrossRef]
  25. D. Colton and R. Kress, “Using fundamental solutions in inverse scattering,” Inverse Probl. 22, R49-R66 (2006).
    [CrossRef]

2009 (1)

X. Chen and Y. Zhong, “MUSIC electromagnetic imaging with enhanced resolution for small inclusions,” Inverse Probl. 25, 015008 (2009).
[CrossRef]

2008 (4)

X. Chen, “Signal-subspace method approach to intensity-only electromagnetic inverse scattering problem,” J. Opt. Soc. Am. A 25, 2018-2024 (2008).
[CrossRef]

K. Agarwal and X. Chen, “Applicability of MUSIC-type imaging in two-dimensional electromagnetic inverse problems,” IEEE Trans. Antennas Propag. 56, 3217-3223 (2008).
[CrossRef]

X. Chen and Y. Zhong, “Electromagnetic imaging of multiple-scattering small objects: noniterative analytical approach,” J. Phys.: Conf. Ser. 124, 012016 (2008).
[CrossRef]

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

2007 (8)

I. Catapano, L. Crocco, and T. Isernia, “On simple methods for shape reconstruction of unknown scatterers,” IEEE Trans. Antennas Propag. 55, 1431-1436 (2007).
[CrossRef]

H. Ammari, E. Iakovleva, D. Lesselier, and G. Perruson, “MUSIC-type electromagnetic imaging of a collection of small three-dimensional bounded inclusions,” SIAM J. Sci. Comput. (USA) 29, 674-709 (2007).
[CrossRef]

E. Iakovleva, S. Gdoura, D. Lesselier, and G. Perrusson, “Multistatic response matrix of a 3-d inclusion in half space and MUSIC imaging,” IEEE Trans. Antennas Propag. 55, 2598-2609 (2007).
[CrossRef]

E. A. Marengo, R. D. Hernandez, and H. Lev-Ari, “Intensity-only signal-subspace-based imaging,” J. Opt. Soc. Am. A 24, 3619-3635 (2007).
[CrossRef]

E. A. Marengo and F. K. Gruber, “Subspace-based localization and inverse scattering of multiply scattering point targets,” EURASIP J. Adv. Signal Process. 2007, 17342 (2007).
[CrossRef]

X. Chen and Y. Zhong, “A robust noniterative method for obtaining scattering strengths of multiply scattering point targets,” J. Acoust. Soc. Am. 122, 1325-1327 (2007).
[CrossRef] [PubMed]

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]

E. A. Marengo, F. K. Gruber, and F. Simonetti, “Time-reversal MUSIC imaging of extended targets,” IEEE Trans. Image Process. 16, 1967-1984 (2007).
[CrossRef] [PubMed]

2006 (3)

S. Hou, K. Solna, and H. Zhao, “A direct imaging algorithm for extended targets,” Inverse Probl. 22, 1151-1178 (2006).
[CrossRef]

E. A. Marengo and F. K. Gruber, “Noniterative analytical formula for inverse scattering of multiply scattering point targets,” J. Acoust. Soc. Am. 120, 3782-3788 (2006).
[CrossRef]

D. Colton and R. Kress, “Using fundamental solutions in inverse scattering,” Inverse Probl. 22, R49-R66 (2006).
[CrossRef]

2005 (2)

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]

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

2002 (1)

A. Kirsch, “The MUSIC-algorithm and the factorization method in inverse scattering theory for inhomogeneous media,” Inverse Probl. 18, 1025-1040 (2002).
[CrossRef]

1997 (1)

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

1994 (1)

T. M. Habashy, M. L. Oristaglio, and A. T. D. Hoop, “Simultaneous nonlinear reconstruction of two dimensional permittivity and conductivity,” Radio Sci. 29, 1101-1118 (1994).
[CrossRef]

1992 (1)

A. Lakhtakia, “Strong and weak forms of the method of moments and the coupled dipole method for scattering of time-harmonic electromagnetics fields,” Int. J. Mod. Phys. C 3, 583-603 (1992).
[CrossRef]

1990 (1)

T. M. Habashy, E. Y. Chow, and D. G. Dudley, “Profile inversion using the renormalized source-type integral equation approach,” IEEE Trans. Antennas Propag. 38, 668-681 (1990).
[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]

Agarwal, K.

K. Agarwal and X. Chen, “Applicability of MUSIC-type imaging in two-dimensional electromagnetic inverse problems,” IEEE Trans. Antennas Propag. 56, 3217-3223 (2008).
[CrossRef]

Ammari, H.

H. Ammari, E. Iakovleva, D. Lesselier, and G. Perruson, “MUSIC-type electromagnetic imaging of a collection of small three-dimensional bounded inclusions,” SIAM J. Sci. Comput. (USA) 29, 674-709 (2007).
[CrossRef]

Belkebir, K.

Catapano, I.

I. Catapano, L. Crocco, and T. Isernia, “On simple methods for shape reconstruction of unknown scatterers,” IEEE Trans. Antennas Propag. 55, 1431-1436 (2007).
[CrossRef]

Chaumet, P. C.

Chen, X.

X. Chen and Y. Zhong, “MUSIC electromagnetic imaging with enhanced resolution for small inclusions,” Inverse Probl. 25, 015008 (2009).
[CrossRef]

X. Chen, “Signal-subspace method approach to intensity-only electromagnetic inverse scattering problem,” J. Opt. Soc. Am. A 25, 2018-2024 (2008).
[CrossRef]

K. Agarwal and X. Chen, “Applicability of MUSIC-type imaging in two-dimensional electromagnetic inverse problems,” IEEE Trans. Antennas Propag. 56, 3217-3223 (2008).
[CrossRef]

X. Chen and Y. Zhong, “Electromagnetic imaging of multiple-scattering small objects: noniterative analytical approach,” J. Phys.: Conf. Ser. 124, 012016 (2008).
[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]

X. Chen and Y. Zhong, “A robust noniterative method for obtaining scattering strengths of multiply scattering point targets,” J. Acoust. Soc. Am. 122, 1325-1327 (2007).
[CrossRef] [PubMed]

Chow, E. Y.

T. M. Habashy, E. Y. Chow, and D. G. Dudley, “Profile inversion using the renormalized source-type integral equation approach,” IEEE Trans. Antennas Propag. 38, 668-681 (1990).
[CrossRef]

Colton, D.

D. Colton and R. Kress, “Using fundamental solutions in inverse scattering,” Inverse Probl. 22, R49-R66 (2006).
[CrossRef]

D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, 2nd ed. (Springer-Verlag, 1998).

Crocco, L.

I. Catapano, L. Crocco, and T. Isernia, “On simple methods for shape reconstruction of unknown scatterers,” IEEE Trans. Antennas Propag. 55, 1431-1436 (2007).
[CrossRef]

Dudley, D. G.

T. M. Habashy, E. Y. Chow, and D. G. Dudley, “Profile inversion using the renormalized source-type integral equation approach,” IEEE Trans. Antennas Propag. 38, 668-681 (1990).
[CrossRef]

Gdoura, S.

E. Iakovleva, S. Gdoura, D. Lesselier, and G. Perrusson, “Multistatic response matrix of a 3-d inclusion in half space and MUSIC imaging,” IEEE Trans. Antennas Propag. 55, 2598-2609 (2007).
[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]

Gruber, F. K.

E. A. Marengo and F. K. Gruber, “Subspace-based localization and inverse scattering of multiply scattering point targets,” EURASIP J. Adv. Signal Process. 2007, 17342 (2007).
[CrossRef]

E. A. Marengo, F. K. Gruber, and F. Simonetti, “Time-reversal MUSIC imaging of extended targets,” IEEE Trans. Image Process. 16, 1967-1984 (2007).
[CrossRef] [PubMed]

E. A. Marengo and F. K. Gruber, “Noniterative analytical formula for inverse scattering of multiply scattering point targets,” J. Acoust. Soc. Am. 120, 3782-3788 (2006).
[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]

T. M. Habashy, M. L. Oristaglio, and A. T. D. Hoop, “Simultaneous nonlinear reconstruction of two dimensional permittivity and conductivity,” Radio Sci. 29, 1101-1118 (1994).
[CrossRef]

T. M. Habashy, E. Y. Chow, and D. G. Dudley, “Profile inversion using the renormalized source-type integral equation approach,” IEEE Trans. Antennas Propag. 38, 668-681 (1990).
[CrossRef]

Hernandez, R. D.

Hoop, A. T. D.

T. M. Habashy, M. L. Oristaglio, and A. T. D. Hoop, “Simultaneous nonlinear reconstruction of two dimensional permittivity and conductivity,” Radio Sci. 29, 1101-1118 (1994).
[CrossRef]

Horn, A.

A. Horn and C. R. Johnson, Matrix Analysis (Cambridge U. Press, 1985).

Hou, S.

S. Hou, K. Solna, and H. Zhao, “A direct imaging algorithm for extended targets,” Inverse Probl. 22, 1151-1178 (2006).
[CrossRef]

Iakovleva, E.

E. Iakovleva, S. Gdoura, D. Lesselier, and G. Perrusson, “Multistatic response matrix of a 3-d inclusion in half space and MUSIC imaging,” IEEE Trans. Antennas Propag. 55, 2598-2609 (2007).
[CrossRef]

H. Ammari, E. Iakovleva, D. Lesselier, and G. Perruson, “MUSIC-type electromagnetic imaging of a collection of small three-dimensional bounded inclusions,” SIAM J. Sci. Comput. (USA) 29, 674-709 (2007).
[CrossRef]

Isernia, T.

I. Catapano, L. Crocco, and T. Isernia, “On simple methods for shape reconstruction of unknown scatterers,” IEEE Trans. Antennas Propag. 55, 1431-1436 (2007).
[CrossRef]

Johnson, C. R.

A. Horn and C. R. Johnson, Matrix Analysis (Cambridge U. Press, 1985).

Kirsch, A.

A. Kirsch, “The MUSIC-algorithm and the factorization method in inverse scattering theory for inhomogeneous media,” Inverse Probl. 18, 1025-1040 (2002).
[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]

Kress, R.

D. Colton and R. Kress, “Using fundamental solutions in inverse scattering,” Inverse Probl. 22, R49-R66 (2006).
[CrossRef]

D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, 2nd ed. (Springer-Verlag, 1998).

Lakhtakia, A.

A. Lakhtakia, “Strong and weak forms of the method of moments and the coupled dipole method for scattering of time-harmonic electromagnetics fields,” Int. J. Mod. Phys. C 3, 583-603 (1992).
[CrossRef]

Lesselier, D.

H. Ammari, E. Iakovleva, D. Lesselier, and G. Perruson, “MUSIC-type electromagnetic imaging of a collection of small three-dimensional bounded inclusions,” SIAM J. Sci. Comput. (USA) 29, 674-709 (2007).
[CrossRef]

E. Iakovleva, S. Gdoura, D. Lesselier, and G. Perrusson, “Multistatic response matrix of a 3-d inclusion in half space and MUSIC imaging,” IEEE Trans. Antennas Propag. 55, 2598-2609 (2007).
[CrossRef]

Lev-Ari, H.

Marengo, E. A.

E. A. Marengo and F. K. Gruber, “Subspace-based localization and inverse scattering of multiply scattering point targets,” EURASIP J. Adv. Signal Process. 2007, 17342 (2007).
[CrossRef]

E. A. Marengo, R. D. Hernandez, and H. Lev-Ari, “Intensity-only signal-subspace-based imaging,” J. Opt. Soc. Am. A 24, 3619-3635 (2007).
[CrossRef]

E. A. Marengo, F. K. Gruber, and F. Simonetti, “Time-reversal MUSIC imaging of extended targets,” IEEE Trans. Image Process. 16, 1967-1984 (2007).
[CrossRef] [PubMed]

E. A. Marengo and F. K. Gruber, “Noniterative analytical formula for inverse scattering of multiply scattering point targets,” J. Acoust. Soc. Am. 120, 3782-3788 (2006).
[CrossRef]

Oristaglio, M. L.

T. M. Habashy, M. L. Oristaglio, and A. T. D. Hoop, “Simultaneous nonlinear reconstruction of two dimensional permittivity and conductivity,” Radio Sci. 29, 1101-1118 (1994).
[CrossRef]

Perruson, G.

H. Ammari, E. Iakovleva, D. Lesselier, and G. Perruson, “MUSIC-type electromagnetic imaging of a collection of small three-dimensional bounded inclusions,” SIAM J. Sci. Comput. (USA) 29, 674-709 (2007).
[CrossRef]

Perrusson, G.

E. Iakovleva, S. Gdoura, D. Lesselier, and G. Perrusson, “Multistatic response matrix of a 3-d inclusion in half space and MUSIC imaging,” IEEE Trans. Antennas Propag. 55, 2598-2609 (2007).
[CrossRef]

Sentenac, A.

Simonetti, F.

E. A. Marengo, F. K. Gruber, and F. Simonetti, “Time-reversal MUSIC imaging of extended targets,” IEEE Trans. Image Process. 16, 1967-1984 (2007).
[CrossRef] [PubMed]

Solna, K.

S. Hou, K. Solna, and H. Zhao, “A direct imaging algorithm for extended targets,” Inverse Probl. 22, 1151-1178 (2006).
[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]

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

Zhao, H.

S. Hou, K. Solna, and H. Zhao, “A direct imaging algorithm for extended targets,” Inverse Probl. 22, 1151-1178 (2006).
[CrossRef]

Zhong, Y.

X. Chen and Y. Zhong, “MUSIC electromagnetic imaging with enhanced resolution for small inclusions,” Inverse Probl. 25, 015008 (2009).
[CrossRef]

X. Chen and Y. Zhong, “Electromagnetic imaging of multiple-scattering small objects: noniterative analytical approach,” J. Phys.: Conf. Ser. 124, 012016 (2008).
[CrossRef]

X. Chen and Y. Zhong, “A robust noniterative method for obtaining scattering strengths of multiply scattering point targets,” J. Acoust. Soc. Am. 122, 1325-1327 (2007).
[CrossRef] [PubMed]

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]

EURASIP J. Adv. Signal Process. (1)

E. A. Marengo and F. K. Gruber, “Subspace-based localization and inverse scattering of multiply scattering point targets,” EURASIP J. Adv. Signal Process. 2007, 17342 (2007).
[CrossRef]

IEEE Trans. Antennas Propag. (5)

E. Iakovleva, S. Gdoura, D. Lesselier, and G. Perrusson, “Multistatic response matrix of a 3-d inclusion in half space and MUSIC imaging,” IEEE Trans. Antennas Propag. 55, 2598-2609 (2007).
[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]

K. Agarwal and X. Chen, “Applicability of MUSIC-type imaging in two-dimensional electromagnetic inverse problems,” IEEE Trans. Antennas Propag. 56, 3217-3223 (2008).
[CrossRef]

T. M. Habashy, E. Y. Chow, and D. G. Dudley, “Profile inversion using the renormalized source-type integral equation approach,” IEEE Trans. Antennas Propag. 38, 668-681 (1990).
[CrossRef]

I. Catapano, L. Crocco, and T. Isernia, “On simple methods for shape reconstruction of unknown scatterers,” IEEE Trans. Antennas Propag. 55, 1431-1436 (2007).
[CrossRef]

IEEE Trans. Image Process. (1)

E. A. Marengo, F. K. Gruber, and F. Simonetti, “Time-reversal MUSIC imaging of extended targets,” IEEE Trans. Image Process. 16, 1967-1984 (2007).
[CrossRef] [PubMed]

Int. J. Mod. Phys. C (1)

A. Lakhtakia, “Strong and weak forms of the method of moments and the coupled dipole method for scattering of time-harmonic electromagnetics fields,” Int. J. Mod. Phys. C 3, 583-603 (1992).
[CrossRef]

Inverse Probl. (6)

D. Colton and R. Kress, “Using fundamental solutions in inverse scattering,” Inverse Probl. 22, R49-R66 (2006).
[CrossRef]

S. Hou, K. Solna, and H. Zhao, “A direct imaging algorithm for extended targets,” Inverse Probl. 22, 1151-1178 (2006).
[CrossRef]

A. Kirsch, “The MUSIC-algorithm and the factorization method in inverse scattering theory for inhomogeneous media,” Inverse Probl. 18, 1025-1040 (2002).
[CrossRef]

X. Chen and Y. Zhong, “MUSIC electromagnetic imaging with enhanced resolution for small inclusions,” Inverse Probl. 25, 015008 (2009).
[CrossRef]

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

J. Acoust. Soc. Am. (2)

E. A. Marengo and F. K. Gruber, “Noniterative analytical formula for inverse scattering of multiply scattering point targets,” J. Acoust. Soc. Am. 120, 3782-3788 (2006).
[CrossRef]

X. Chen and Y. Zhong, “A robust noniterative method for obtaining scattering strengths of multiply scattering point targets,” J. Acoust. Soc. Am. 122, 1325-1327 (2007).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (4)

J. Phys.: Conf. Ser. (1)

X. Chen and Y. Zhong, “Electromagnetic imaging of multiple-scattering small objects: noniterative analytical approach,” J. Phys.: Conf. Ser. 124, 012016 (2008).
[CrossRef]

Radio Sci. (1)

T. M. Habashy, M. L. Oristaglio, and A. T. D. Hoop, “Simultaneous nonlinear reconstruction of two dimensional permittivity and conductivity,” Radio Sci. 29, 1101-1118 (1994).
[CrossRef]

SIAM J. Sci. Comput. (USA) (1)

H. Ammari, E. Iakovleva, D. Lesselier, and G. Perruson, “MUSIC-type electromagnetic imaging of a collection of small three-dimensional bounded inclusions,” SIAM J. Sci. Comput. (USA) 29, 674-709 (2007).
[CrossRef]

Other (2)

D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, 2nd ed. (Springer-Verlag, 1998).

A. Horn and C. R. Johnson, Matrix Analysis (Cambridge U. Press, 1985).

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Figures (4)

Fig. 1
Fig. 1

Two squares separated by 0.2 λ . (a) Exact permittivity. (b) Reconstructed permittivity under 20 dB white Gaussian noise.

Fig. 2
Fig. 2

Singular values of the matrix G ̿ s .

Fig. 3
Fig. 3

Annulus with inner radius 0.15 λ and outer radius 0.3 λ . (a) Exact permittivity. (b) Reconstructed permittivity under 20 dB white Gaussian noise.

Fig. 4
Fig. 4

Same as in Fig. 3 except that 10 dB white Gaussian noise is added.

Equations (15)

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

E tot ( r m ) = E inc ( r m ) + n m i k η 0 g ( r m , r n ) ξ n E tot ( r n ) ,
m = 1 , 2 , , M ,
I d ( r n ) = ξ n E tot ( r n ) , n = 1 , 2 , , M .
E p sca ( r q ) = m = 1 M i k η 0 g ( r q , r m ) ξ m E tot ( r m ) , p = 1 , 2 , , N i ,
q = 1 , 2 , , N s .
I ¯ d = ξ ̿ ( E ¯ inc + G ̿ D I ¯ d ) ,
E ¯ sca = G ̿ s I ¯ d ,
α j s = u ¯ j * E ¯ sca σ j , j = 1 , 2 , , L .
Δ fie = G ̿ s V ̿ n α ¯ n + G ̿ s I ¯ s E ¯ sca 2 ,
[ V ̿ n ξ ̿ ( G ̿ D V ̿ n ) ] α ¯ n = ξ ̿ ( E ¯ inc + G ̿ D I ¯ s ) I ¯ s ,
A ̿ α ¯ n = B ¯ .
α ¯ opt n = ( A ̿ * A ̿ ) 1 ( A ̿ * B ¯ ) .
Δ sta = A ̿ α ¯ opt n B ¯ 2 .
Δ tot = Δ fie E ¯ sca 2 + Δ sta I ¯ s 2 .
f ( ξ ̿ ) = ( 1 2 ) p = 1 N i ( Δ p tot ) 2 .

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