Abstract

Linear sampling method (LSM) is a qualitative method used to reconstruct the support of scatterers. This paper presents a modification of the LSM approach. The proposed method analyses the multipole expansion of the scattered field. Only monopole and dipole terms are used for the reconstruction of the scatterer support and all other higher order multipoles are truncated. It is shown that such modification performs better than the mathematical regularization typically used in LSM. The justification for truncation of higher order multipoles is presented. Various examples are presented to demonstrate the performance of the proposed method for dielectric as well as perfectly conducting scatterers in presence of significant amount of additive Gaussian noise.

© 2010 Optical Society of America

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  1. K. Agarwal and X. Chen, “Application of differential evolution in 2-dimensional electromagnetic inverse problems,” in IEEE Congress on Evolutionary Computation, (2007), 4305–4312.
    [Crossref]
  2. K. Agarwal and X. Chen, “Applicability of MUSIC-Type Imaging in Two-Dimensional Electromagnetic Inverse Problems,” IEEE Trans. Antenn. Propag. 56(10), 3217–3223 (2008).
    [Crossref]
  3. Y. Zhong and X. Chen, “MUSIC imaging and electromagnetic inverse scattering of multiple-scattering small anisotropic spheres,” IEEE Trans. Antenn. Propag. 55(12), 3542–3549 (2007).
    [Crossref]
  4. M. Brignone, G. Bozza, A. Randazzo, M. Piana, and M. Pastorino, “A Hybrid Approach to 3D Microwave Imaging by Using Linear Sampling and ACO,” IEEE Trans. Antenn. Propag. 56(10), 3224–3232 (2008).
    [Crossref]
  5. I. Catapano, L. Crocco, M. D’Urso, and T. Isernia, “On the effect of support estimation and of a new model in 2D inverse scattering problems,” IEEE Trans. Antenn. Propag. 55(6), 1895–1899 (2007).
    [Crossref]
  6. X. Chen and Y. Zhong, “A robust noniterative method for obtaining scattering strengths of multiply scattering point targets,” J. Acoust. Soc. Am. 122(3), 1325–1327 (2007).
    [Crossref] [PubMed]
  7. H. Ammari, E. Iakovleva, D. Lesselier, and G. Perrusson, “Music-type electromagnetic imaging of a collection of small three-dimensional inclusions,” SIAM J. Sci. Comput. 29(2), 674–709 (2007).
    [Crossref]
  8. X. Chen and Y. Zhong, “MUSIC electromagnetic imaging with enhanced resolution for small inclusions,” Inverse Probl. 25(1), 015008 (2009).
    [Crossref]
  9. M. Fink and C. Prada, “Acoustic time-reversal mirrors,” Inverse Probl. 17(1), 201 (2001).
    [Crossref]
  10. A. J. Devaney, “Time reversal imaging of obscured targets from multistatic data,” IEEE Trans. Antenn. Propag. 53(5), 1600–1610 (2005).
    [Crossref]
  11. T. Rao and X. Chen, “Analysis of the time-reversal operator for a single cylinder under two-dimensional settings,” J. Electromagn. Waves Appl. 20(15), 2153–2165 (2006).
    [Crossref]
  12. K. Mayer, R. Marklein, K. J. Langenberg, and T. Kreutter, “Three-dimensional imaging system based on Fourier transform synthetic aperture focusing technique,” Ultrasonics 28(4), 241–255 (1990).
    [Crossref]
  13. C. K. Liao, M. L. Li, and P. C. Li, “Optoacoustic imaging with synthetic aperture focusing and coherence weighting,” Opt. Lett. 29(21), 2506–2508 (2004).
    [Crossref] [PubMed]
  14. T. Arens and A. Kirsch, “The factorization method in inverse scattering from periodic structures,” Inverse Probl. 19(5), 1195–1211 (2003).
    [Crossref]
  15. A. Kirsch, “The factorization method for Maxwell’s equations,” Inverse Probl. 20(6), S117–S134 (2004).
    [Crossref]
  16. A. Kirsch, “Characterization of the shape of a scattering obstacle using the spectral data of the far field operator,” Inverse Probl. 14(6), 1489–1512 (1998).
    [Crossref]
  17. A. Kirsch and S. Ritter, “A linear sampling method for inverse scattering from an open arc,” Inverse Probl. 16(1), 89–105 (2000).
    [Crossref]
  18. D. Colton, J. Coyle, and P. Monk, “Recent developments in inverse acoustic scattering theory,” SIAM Rev. 42(3), 369–414 (2000).
    [Crossref]
  19. F. Cakoni, D. Colton, and H. Haddar, “The linear sampling method for anisotropic media,” J. Comput. Appl. Math. 146(2), 285–299 (2002).
    [Crossref]
  20. D. Colton, H. Haddar, and M. Piana, “The linear sampling method in inverse electromagnetic scattering theory,” Inverse Probl. 19(6), S105–S137 (2003).
    [Crossref]
  21. D. Colton and R. Kress, “Using fundamental solutions in inverse scattering,” Inverse Probl. 22(3), R49–R66 (2006).
    [Crossref]
  22. F. Cakoni and D. Colton, Qualitative methods in inverse scattering theory: An introduction (Springer, Berlin, 2006).
  23. A. Kirsch and N. Grinberg, The factorization method for inverse problems (Lecture series in mathematics and its applications, Oxford University Press, 2008).
  24. I. Catapano, L. Crocco, and T. Isernia, “On simple methods for shape reconstruction of unknown scatterers,” IEEE Trans. Antenn. Propag. 55(5), 1431–1436 (2007).
    [Crossref]
  25. N. Shelton and K. F. Warnick, “Behavior of the regularized sampling inverse scattering method at internal resonance frequencies,” J. Electromagn. Waves Appl. 17(3), 487–488 (2003).
    [Crossref]
  26. I. Catapano, L. Crocco, and T. Isernia, “Improved Sampling Methods for Shape Reconstruction of 3-D Buried Targets,” IEEE Trans. Geosci. Rem. Sens. 46(10), 3265–3273 (2008).
    [Crossref]
  27. D. L. Colton and R. Kress, Inverse acoustic and electromagnetic scattering theory, 2nd ed. (Springer, New York, 1998).
  28. M. Abramowitz and I. A. Stegun, Handbook of mathematical functions: with formulas, graphs, and mathematical tables, 7th ed. (Dover Publications, New York, 1972).
  29. R. A. Horn and C. R. Johnson, Matrix analysis (Cambridge University Press, Cambridge; New York, 1985).

2009 (1)

X. Chen and Y. Zhong, “MUSIC electromagnetic imaging with enhanced resolution for small inclusions,” Inverse Probl. 25(1), 015008 (2009).
[Crossref]

2008 (3)

K. Agarwal and X. Chen, “Applicability of MUSIC-Type Imaging in Two-Dimensional Electromagnetic Inverse Problems,” IEEE Trans. Antenn. Propag. 56(10), 3217–3223 (2008).
[Crossref]

M. Brignone, G. Bozza, A. Randazzo, M. Piana, and M. Pastorino, “A Hybrid Approach to 3D Microwave Imaging by Using Linear Sampling and ACO,” IEEE Trans. Antenn. Propag. 56(10), 3224–3232 (2008).
[Crossref]

I. Catapano, L. Crocco, and T. Isernia, “Improved Sampling Methods for Shape Reconstruction of 3-D Buried Targets,” IEEE Trans. Geosci. Rem. Sens. 46(10), 3265–3273 (2008).
[Crossref]

2007 (6)

I. Catapano, L. Crocco, and T. Isernia, “On simple methods for shape reconstruction of unknown scatterers,” IEEE Trans. Antenn. Propag. 55(5), 1431–1436 (2007).
[Crossref]

I. Catapano, L. Crocco, M. D’Urso, and T. Isernia, “On the effect of support estimation and of a new model in 2D inverse scattering problems,” IEEE Trans. Antenn. Propag. 55(6), 1895–1899 (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(3), 1325–1327 (2007).
[Crossref] [PubMed]

H. Ammari, E. Iakovleva, D. Lesselier, and G. Perrusson, “Music-type electromagnetic imaging of a collection of small three-dimensional inclusions,” SIAM J. Sci. Comput. 29(2), 674–709 (2007).
[Crossref]

Y. Zhong and X. Chen, “MUSIC imaging and electromagnetic inverse scattering of multiple-scattering small anisotropic spheres,” IEEE Trans. Antenn. Propag. 55(12), 3542–3549 (2007).
[Crossref]

K. Agarwal and X. Chen, “Application of differential evolution in 2-dimensional electromagnetic inverse problems,” in IEEE Congress on Evolutionary Computation, (2007), 4305–4312.
[Crossref]

2006 (2)

T. Rao and X. Chen, “Analysis of the time-reversal operator for a single cylinder under two-dimensional settings,” J. Electromagn. Waves Appl. 20(15), 2153–2165 (2006).
[Crossref]

D. Colton and R. Kress, “Using fundamental solutions in inverse scattering,” Inverse Probl. 22(3), R49–R66 (2006).
[Crossref]

2005 (1)

A. J. Devaney, “Time reversal imaging of obscured targets from multistatic data,” IEEE Trans. Antenn. Propag. 53(5), 1600–1610 (2005).
[Crossref]

2004 (2)

2003 (3)

T. Arens and A. Kirsch, “The factorization method in inverse scattering from periodic structures,” Inverse Probl. 19(5), 1195–1211 (2003).
[Crossref]

N. Shelton and K. F. Warnick, “Behavior of the regularized sampling inverse scattering method at internal resonance frequencies,” J. Electromagn. Waves Appl. 17(3), 487–488 (2003).
[Crossref]

D. Colton, H. Haddar, and M. Piana, “The linear sampling method in inverse electromagnetic scattering theory,” Inverse Probl. 19(6), S105–S137 (2003).
[Crossref]

2002 (1)

F. Cakoni, D. Colton, and H. Haddar, “The linear sampling method for anisotropic media,” J. Comput. Appl. Math. 146(2), 285–299 (2002).
[Crossref]

2001 (1)

M. Fink and C. Prada, “Acoustic time-reversal mirrors,” Inverse Probl. 17(1), 201 (2001).
[Crossref]

2000 (2)

A. Kirsch and S. Ritter, “A linear sampling method for inverse scattering from an open arc,” Inverse Probl. 16(1), 89–105 (2000).
[Crossref]

D. Colton, J. Coyle, and P. Monk, “Recent developments in inverse acoustic scattering theory,” SIAM Rev. 42(3), 369–414 (2000).
[Crossref]

1998 (1)

A. Kirsch, “Characterization of the shape of a scattering obstacle using the spectral data of the far field operator,” Inverse Probl. 14(6), 1489–1512 (1998).
[Crossref]

1990 (1)

K. Mayer, R. Marklein, K. J. Langenberg, and T. Kreutter, “Three-dimensional imaging system based on Fourier transform synthetic aperture focusing technique,” Ultrasonics 28(4), 241–255 (1990).
[Crossref]

Abramowitz, M.

M. Abramowitz and I. A. Stegun, Handbook of mathematical functions: with formulas, graphs, and mathematical tables, 7th ed. (Dover Publications, New York, 1972).

Agarwal, K.

K. Agarwal and X. Chen, “Applicability of MUSIC-Type Imaging in Two-Dimensional Electromagnetic Inverse Problems,” IEEE Trans. Antenn. Propag. 56(10), 3217–3223 (2008).
[Crossref]

K. Agarwal and X. Chen, “Application of differential evolution in 2-dimensional electromagnetic inverse problems,” in IEEE Congress on Evolutionary Computation, (2007), 4305–4312.
[Crossref]

Ammari, H.

H. Ammari, E. Iakovleva, D. Lesselier, and G. Perrusson, “Music-type electromagnetic imaging of a collection of small three-dimensional inclusions,” SIAM J. Sci. Comput. 29(2), 674–709 (2007).
[Crossref]

Arens, T.

T. Arens and A. Kirsch, “The factorization method in inverse scattering from periodic structures,” Inverse Probl. 19(5), 1195–1211 (2003).
[Crossref]

Bozza, G.

M. Brignone, G. Bozza, A. Randazzo, M. Piana, and M. Pastorino, “A Hybrid Approach to 3D Microwave Imaging by Using Linear Sampling and ACO,” IEEE Trans. Antenn. Propag. 56(10), 3224–3232 (2008).
[Crossref]

Brignone, M.

M. Brignone, G. Bozza, A. Randazzo, M. Piana, and M. Pastorino, “A Hybrid Approach to 3D Microwave Imaging by Using Linear Sampling and ACO,” IEEE Trans. Antenn. Propag. 56(10), 3224–3232 (2008).
[Crossref]

Cakoni, F.

F. Cakoni, D. Colton, and H. Haddar, “The linear sampling method for anisotropic media,” J. Comput. Appl. Math. 146(2), 285–299 (2002).
[Crossref]

F. Cakoni and D. Colton, Qualitative methods in inverse scattering theory: An introduction (Springer, Berlin, 2006).

Catapano, I.

I. Catapano, L. Crocco, and T. Isernia, “Improved Sampling Methods for Shape Reconstruction of 3-D Buried Targets,” IEEE Trans. Geosci. Rem. Sens. 46(10), 3265–3273 (2008).
[Crossref]

I. Catapano, L. Crocco, and T. Isernia, “On simple methods for shape reconstruction of unknown scatterers,” IEEE Trans. Antenn. Propag. 55(5), 1431–1436 (2007).
[Crossref]

I. Catapano, L. Crocco, M. D’Urso, and T. Isernia, “On the effect of support estimation and of a new model in 2D inverse scattering problems,” IEEE Trans. Antenn. Propag. 55(6), 1895–1899 (2007).
[Crossref]

Chen, X.

X. Chen and Y. Zhong, “MUSIC electromagnetic imaging with enhanced resolution for small inclusions,” Inverse Probl. 25(1), 015008 (2009).
[Crossref]

K. Agarwal and X. Chen, “Applicability of MUSIC-Type Imaging in Two-Dimensional Electromagnetic Inverse Problems,” IEEE Trans. Antenn. Propag. 56(10), 3217–3223 (2008).
[Crossref]

K. Agarwal and X. Chen, “Application of differential evolution in 2-dimensional electromagnetic inverse problems,” in IEEE Congress on Evolutionary Computation, (2007), 4305–4312.
[Crossref]

Y. Zhong and X. Chen, “MUSIC imaging and electromagnetic inverse scattering of multiple-scattering small anisotropic spheres,” IEEE Trans. Antenn. Propag. 55(12), 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(3), 1325–1327 (2007).
[Crossref] [PubMed]

T. Rao and X. Chen, “Analysis of the time-reversal operator for a single cylinder under two-dimensional settings,” J. Electromagn. Waves Appl. 20(15), 2153–2165 (2006).
[Crossref]

Colton, D.

D. Colton and R. Kress, “Using fundamental solutions in inverse scattering,” Inverse Probl. 22(3), R49–R66 (2006).
[Crossref]

D. Colton, H. Haddar, and M. Piana, “The linear sampling method in inverse electromagnetic scattering theory,” Inverse Probl. 19(6), S105–S137 (2003).
[Crossref]

F. Cakoni, D. Colton, and H. Haddar, “The linear sampling method for anisotropic media,” J. Comput. Appl. Math. 146(2), 285–299 (2002).
[Crossref]

D. Colton, J. Coyle, and P. Monk, “Recent developments in inverse acoustic scattering theory,” SIAM Rev. 42(3), 369–414 (2000).
[Crossref]

F. Cakoni and D. Colton, Qualitative methods in inverse scattering theory: An introduction (Springer, Berlin, 2006).

Colton, D. L.

D. L. Colton and R. Kress, Inverse acoustic and electromagnetic scattering theory, 2nd ed. (Springer, New York, 1998).

Coyle, J.

D. Colton, J. Coyle, and P. Monk, “Recent developments in inverse acoustic scattering theory,” SIAM Rev. 42(3), 369–414 (2000).
[Crossref]

Crocco, L.

I. Catapano, L. Crocco, and T. Isernia, “Improved Sampling Methods for Shape Reconstruction of 3-D Buried Targets,” IEEE Trans. Geosci. Rem. Sens. 46(10), 3265–3273 (2008).
[Crossref]

I. Catapano, L. Crocco, and T. Isernia, “On simple methods for shape reconstruction of unknown scatterers,” IEEE Trans. Antenn. Propag. 55(5), 1431–1436 (2007).
[Crossref]

I. Catapano, L. Crocco, M. D’Urso, and T. Isernia, “On the effect of support estimation and of a new model in 2D inverse scattering problems,” IEEE Trans. Antenn. Propag. 55(6), 1895–1899 (2007).
[Crossref]

D’Urso, M.

I. Catapano, L. Crocco, M. D’Urso, and T. Isernia, “On the effect of support estimation and of a new model in 2D inverse scattering problems,” IEEE Trans. Antenn. Propag. 55(6), 1895–1899 (2007).
[Crossref]

Devaney, A. J.

A. J. Devaney, “Time reversal imaging of obscured targets from multistatic data,” IEEE Trans. Antenn. Propag. 53(5), 1600–1610 (2005).
[Crossref]

Fink, M.

M. Fink and C. Prada, “Acoustic time-reversal mirrors,” Inverse Probl. 17(1), 201 (2001).
[Crossref]

Grinberg, N.

A. Kirsch and N. Grinberg, The factorization method for inverse problems (Lecture series in mathematics and its applications, Oxford University Press, 2008).

Haddar, H.

D. Colton, H. Haddar, and M. Piana, “The linear sampling method in inverse electromagnetic scattering theory,” Inverse Probl. 19(6), S105–S137 (2003).
[Crossref]

F. Cakoni, D. Colton, and H. Haddar, “The linear sampling method for anisotropic media,” J. Comput. Appl. Math. 146(2), 285–299 (2002).
[Crossref]

Horn, R. A.

R. A. Horn and C. R. Johnson, Matrix analysis (Cambridge University Press, Cambridge; New York, 1985).

Iakovleva, E.

H. Ammari, E. Iakovleva, D. Lesselier, and G. Perrusson, “Music-type electromagnetic imaging of a collection of small three-dimensional inclusions,” SIAM J. Sci. Comput. 29(2), 674–709 (2007).
[Crossref]

Isernia, T.

I. Catapano, L. Crocco, and T. Isernia, “Improved Sampling Methods for Shape Reconstruction of 3-D Buried Targets,” IEEE Trans. Geosci. Rem. Sens. 46(10), 3265–3273 (2008).
[Crossref]

I. Catapano, L. Crocco, and T. Isernia, “On simple methods for shape reconstruction of unknown scatterers,” IEEE Trans. Antenn. Propag. 55(5), 1431–1436 (2007).
[Crossref]

I. Catapano, L. Crocco, M. D’Urso, and T. Isernia, “On the effect of support estimation and of a new model in 2D inverse scattering problems,” IEEE Trans. Antenn. Propag. 55(6), 1895–1899 (2007).
[Crossref]

Johnson, C. R.

R. A. Horn and C. R. Johnson, Matrix analysis (Cambridge University Press, Cambridge; New York, 1985).

Kirsch, A.

A. Kirsch, “The factorization method for Maxwell’s equations,” Inverse Probl. 20(6), S117–S134 (2004).
[Crossref]

T. Arens and A. Kirsch, “The factorization method in inverse scattering from periodic structures,” Inverse Probl. 19(5), 1195–1211 (2003).
[Crossref]

A. Kirsch and S. Ritter, “A linear sampling method for inverse scattering from an open arc,” Inverse Probl. 16(1), 89–105 (2000).
[Crossref]

A. Kirsch, “Characterization of the shape of a scattering obstacle using the spectral data of the far field operator,” Inverse Probl. 14(6), 1489–1512 (1998).
[Crossref]

A. Kirsch and N. Grinberg, The factorization method for inverse problems (Lecture series in mathematics and its applications, Oxford University Press, 2008).

Kress, R.

D. Colton and R. Kress, “Using fundamental solutions in inverse scattering,” Inverse Probl. 22(3), R49–R66 (2006).
[Crossref]

D. L. Colton and R. Kress, Inverse acoustic and electromagnetic scattering theory, 2nd ed. (Springer, New York, 1998).

Kreutter, T.

K. Mayer, R. Marklein, K. J. Langenberg, and T. Kreutter, “Three-dimensional imaging system based on Fourier transform synthetic aperture focusing technique,” Ultrasonics 28(4), 241–255 (1990).
[Crossref]

Langenberg, K. J.

K. Mayer, R. Marklein, K. J. Langenberg, and T. Kreutter, “Three-dimensional imaging system based on Fourier transform synthetic aperture focusing technique,” Ultrasonics 28(4), 241–255 (1990).
[Crossref]

Lesselier, D.

H. Ammari, E. Iakovleva, D. Lesselier, and G. Perrusson, “Music-type electromagnetic imaging of a collection of small three-dimensional inclusions,” SIAM J. Sci. Comput. 29(2), 674–709 (2007).
[Crossref]

Li, M. L.

Li, P. C.

Liao, C. K.

Marklein, R.

K. Mayer, R. Marklein, K. J. Langenberg, and T. Kreutter, “Three-dimensional imaging system based on Fourier transform synthetic aperture focusing technique,” Ultrasonics 28(4), 241–255 (1990).
[Crossref]

Mayer, K.

K. Mayer, R. Marklein, K. J. Langenberg, and T. Kreutter, “Three-dimensional imaging system based on Fourier transform synthetic aperture focusing technique,” Ultrasonics 28(4), 241–255 (1990).
[Crossref]

Monk, P.

D. Colton, J. Coyle, and P. Monk, “Recent developments in inverse acoustic scattering theory,” SIAM Rev. 42(3), 369–414 (2000).
[Crossref]

Pastorino, M.

M. Brignone, G. Bozza, A. Randazzo, M. Piana, and M. Pastorino, “A Hybrid Approach to 3D Microwave Imaging by Using Linear Sampling and ACO,” IEEE Trans. Antenn. Propag. 56(10), 3224–3232 (2008).
[Crossref]

Perrusson, G.

H. Ammari, E. Iakovleva, D. Lesselier, and G. Perrusson, “Music-type electromagnetic imaging of a collection of small three-dimensional inclusions,” SIAM J. Sci. Comput. 29(2), 674–709 (2007).
[Crossref]

Piana, M.

M. Brignone, G. Bozza, A. Randazzo, M. Piana, and M. Pastorino, “A Hybrid Approach to 3D Microwave Imaging by Using Linear Sampling and ACO,” IEEE Trans. Antenn. Propag. 56(10), 3224–3232 (2008).
[Crossref]

D. Colton, H. Haddar, and M. Piana, “The linear sampling method in inverse electromagnetic scattering theory,” Inverse Probl. 19(6), S105–S137 (2003).
[Crossref]

Prada, C.

M. Fink and C. Prada, “Acoustic time-reversal mirrors,” Inverse Probl. 17(1), 201 (2001).
[Crossref]

Randazzo, A.

M. Brignone, G. Bozza, A. Randazzo, M. Piana, and M. Pastorino, “A Hybrid Approach to 3D Microwave Imaging by Using Linear Sampling and ACO,” IEEE Trans. Antenn. Propag. 56(10), 3224–3232 (2008).
[Crossref]

Rao, T.

T. Rao and X. Chen, “Analysis of the time-reversal operator for a single cylinder under two-dimensional settings,” J. Electromagn. Waves Appl. 20(15), 2153–2165 (2006).
[Crossref]

Ritter, S.

A. Kirsch and S. Ritter, “A linear sampling method for inverse scattering from an open arc,” Inverse Probl. 16(1), 89–105 (2000).
[Crossref]

Shelton, N.

N. Shelton and K. F. Warnick, “Behavior of the regularized sampling inverse scattering method at internal resonance frequencies,” J. Electromagn. Waves Appl. 17(3), 487–488 (2003).
[Crossref]

Stegun, I. A.

M. Abramowitz and I. A. Stegun, Handbook of mathematical functions: with formulas, graphs, and mathematical tables, 7th ed. (Dover Publications, New York, 1972).

Warnick, K. F.

N. Shelton and K. F. Warnick, “Behavior of the regularized sampling inverse scattering method at internal resonance frequencies,” J. Electromagn. Waves Appl. 17(3), 487–488 (2003).
[Crossref]

Zhong, Y.

X. Chen and Y. Zhong, “MUSIC electromagnetic imaging with enhanced resolution for small inclusions,” Inverse Probl. 25(1), 015008 (2009).
[Crossref]

Y. Zhong and X. Chen, “MUSIC imaging and electromagnetic inverse scattering of multiple-scattering small anisotropic spheres,” IEEE Trans. Antenn. Propag. 55(12), 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(3), 1325–1327 (2007).
[Crossref] [PubMed]

IEEE Trans. Antenn. Propag. (6)

K. Agarwal and X. Chen, “Applicability of MUSIC-Type Imaging in Two-Dimensional Electromagnetic Inverse Problems,” IEEE Trans. Antenn. Propag. 56(10), 3217–3223 (2008).
[Crossref]

Y. Zhong and X. Chen, “MUSIC imaging and electromagnetic inverse scattering of multiple-scattering small anisotropic spheres,” IEEE Trans. Antenn. Propag. 55(12), 3542–3549 (2007).
[Crossref]

M. Brignone, G. Bozza, A. Randazzo, M. Piana, and M. Pastorino, “A Hybrid Approach to 3D Microwave Imaging by Using Linear Sampling and ACO,” IEEE Trans. Antenn. Propag. 56(10), 3224–3232 (2008).
[Crossref]

I. Catapano, L. Crocco, M. D’Urso, and T. Isernia, “On the effect of support estimation and of a new model in 2D inverse scattering problems,” IEEE Trans. Antenn. Propag. 55(6), 1895–1899 (2007).
[Crossref]

A. J. Devaney, “Time reversal imaging of obscured targets from multistatic data,” IEEE Trans. Antenn. Propag. 53(5), 1600–1610 (2005).
[Crossref]

I. Catapano, L. Crocco, and T. Isernia, “On simple methods for shape reconstruction of unknown scatterers,” IEEE Trans. Antenn. Propag. 55(5), 1431–1436 (2007).
[Crossref]

IEEE Trans. Geosci. Rem. Sens. (1)

I. Catapano, L. Crocco, and T. Isernia, “Improved Sampling Methods for Shape Reconstruction of 3-D Buried Targets,” IEEE Trans. Geosci. Rem. Sens. 46(10), 3265–3273 (2008).
[Crossref]

in IEEE Congress on Evolutionary Computation, (1)

K. Agarwal and X. Chen, “Application of differential evolution in 2-dimensional electromagnetic inverse problems,” in IEEE Congress on Evolutionary Computation, (2007), 4305–4312.
[Crossref]

Inverse Probl. (8)

X. Chen and Y. Zhong, “MUSIC electromagnetic imaging with enhanced resolution for small inclusions,” Inverse Probl. 25(1), 015008 (2009).
[Crossref]

M. Fink and C. Prada, “Acoustic time-reversal mirrors,” Inverse Probl. 17(1), 201 (2001).
[Crossref]

T. Arens and A. Kirsch, “The factorization method in inverse scattering from periodic structures,” Inverse Probl. 19(5), 1195–1211 (2003).
[Crossref]

A. Kirsch, “The factorization method for Maxwell’s equations,” Inverse Probl. 20(6), S117–S134 (2004).
[Crossref]

A. Kirsch, “Characterization of the shape of a scattering obstacle using the spectral data of the far field operator,” Inverse Probl. 14(6), 1489–1512 (1998).
[Crossref]

A. Kirsch and S. Ritter, “A linear sampling method for inverse scattering from an open arc,” Inverse Probl. 16(1), 89–105 (2000).
[Crossref]

D. Colton, H. Haddar, and M. Piana, “The linear sampling method in inverse electromagnetic scattering theory,” Inverse Probl. 19(6), S105–S137 (2003).
[Crossref]

D. Colton and R. Kress, “Using fundamental solutions in inverse scattering,” Inverse Probl. 22(3), R49–R66 (2006).
[Crossref]

J. Acoust. Soc. Am. (1)

X. Chen and Y. Zhong, “A robust noniterative method for obtaining scattering strengths of multiply scattering point targets,” J. Acoust. Soc. Am. 122(3), 1325–1327 (2007).
[Crossref] [PubMed]

J. Comput. Appl. Math. (1)

F. Cakoni, D. Colton, and H. Haddar, “The linear sampling method for anisotropic media,” J. Comput. Appl. Math. 146(2), 285–299 (2002).
[Crossref]

J. Electromagn. Waves Appl. (2)

N. Shelton and K. F. Warnick, “Behavior of the regularized sampling inverse scattering method at internal resonance frequencies,” J. Electromagn. Waves Appl. 17(3), 487–488 (2003).
[Crossref]

T. Rao and X. Chen, “Analysis of the time-reversal operator for a single cylinder under two-dimensional settings,” J. Electromagn. Waves Appl. 20(15), 2153–2165 (2006).
[Crossref]

Opt. Lett. (1)

SIAM J. Sci. Comput. (1)

H. Ammari, E. Iakovleva, D. Lesselier, and G. Perrusson, “Music-type electromagnetic imaging of a collection of small three-dimensional inclusions,” SIAM J. Sci. Comput. 29(2), 674–709 (2007).
[Crossref]

SIAM Rev. (1)

D. Colton, J. Coyle, and P. Monk, “Recent developments in inverse acoustic scattering theory,” SIAM Rev. 42(3), 369–414 (2000).
[Crossref]

Ultrasonics (1)

K. Mayer, R. Marklein, K. J. Langenberg, and T. Kreutter, “Three-dimensional imaging system based on Fourier transform synthetic aperture focusing technique,” Ultrasonics 28(4), 241–255 (1990).
[Crossref]

Other (5)

F. Cakoni and D. Colton, Qualitative methods in inverse scattering theory: An introduction (Springer, Berlin, 2006).

A. Kirsch and N. Grinberg, The factorization method for inverse problems (Lecture series in mathematics and its applications, Oxford University Press, 2008).

D. L. Colton and R. Kress, Inverse acoustic and electromagnetic scattering theory, 2nd ed. (Springer, New York, 1998).

M. Abramowitz and I. A. Stegun, Handbook of mathematical functions: with formulas, graphs, and mathematical tables, 7th ed. (Dover Publications, New York, 1972).

R. A. Horn and C. R. Johnson, Matrix analysis (Cambridge University Press, Cambridge; New York, 1985).

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Figures (8)

Fig. 1.
Fig. 1.

Illustration of the current distribution for the sampling point r⃗p = (0,0) and the proposed multipole-based interpretation.

Fig. 2.
Fig. 2.

Comparison of MLSM (N = 20) and MLSM (N = 1) for noise-free and noisy (10% additive Gaussian noise) scenarios.

Fig. 3.
Fig. 3.

Effect of reduction of multipoles. After obtaining the values of υn by substituting the source distribution computed using conventional LSM and the matrix A̿ computed using Eq. (14) for N = 20 and N = 1 respectively, the absolute value of difference in υn corresponding to these cases for n = − 1 to 1 is computed. First, second, and third columns show this absolute value of difference for n equals to −1, 0, and 1 respectively.

Fig. 4.
Fig. 4.

Effect of noise on the multipoles. First column shows the values of υn obtained by the proposed method in the noise-free scenario. Second column is similar to the first column with the only difference being the noisy scenario (10% additive Gaussian noise). Third column displays the absolute value of the difference between the data plotted in first and second columns. Fourth column shows the difference relative to the magnitude of υn averaged over the noisy and noise-free cases.

Fig. 5.
Fig. 5.

Comparison of LSM and MLSM. In (b), ‘Error’ refers to the error measure defined in (21).The above results are in the presence of 10% noise.

Fig. 6.
Fig. 6.

Plot of error measure defined in (21) for the examples of dielectric scatterers presented in Fig. 7. The presented results are in the presence of 10% noise.

Fig. 7.
Fig. 7.

Examples of reconstruction of dielectric cylinders. The first column shows the scatterer profile (relative permittivity), the second column shows the reconstruction using conventional LSM and the third column shows the reconstruction using the proposed method. The presented results are in the presence of 10% noise.

Fig. 8.
Fig. 8.

Examples of reconstruction of perfectly conducting cylinders. The first column shows the scatterer profile (contours of cylinders), the second column shows the reconstruction using conventional LSM and the third column shows the reconstruction using the proposed method. The presented results are in the presence of 10% noise.

Equations (22)

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Γ E φ θ g θ r p = Φ φ r p .
u ( r ) = Φ r r p u ( r ) n = Φ r r p n } for r Ω ,
u ( r ) = Ω [ Φ r r u n ( r ) u ( r ) Φ r r n ( r ) ] ds ( r ) Ω [ 2 u ( r ) + k 2 u ( r ) ] Φ r r d r ,
u ( r ) = Ω [ Φ r r Φ r r p n ( r ) Φ r r p Φ r r n ( r ) ] ds ( r ) + Ω J ( r ) Φ r r d r .
Ω + Γ [ Φ r r Φ r r p n ( r ) Φ r r p Φ r r n ( r ) ] ds ( r ) ,
= 2 \ Ω - ( Φ r r 2 Φ r r p Φ r r p 2 Φ r r ) d r = 0
u ( r ) = Ω J ( r ) Φ r r d r , r Ω .
E r φ θ = J r θ Φ r φ r d r ,
E r φ θ = n = α ( n ) r p θ Φ ( n ) r φ r p ,
α ( n ) r p θ = J r θ J n ( k r p r ) e in arg ( r r p ) d r ,
Φ ( n ) r φ r p = i 4 H n ( 1 ) ( k r φ r p ) e in arg ( r φ r p ) .
Γ α ( n ) r p θ g θ r p = { 1 n = 0 0 otherwise .
υ n = Γ α ( n ) r p θ g θ r p d θ .
E φ θ n = N N α ( n ) r p θ Φ ( n ) φ r p .
E ¯ = Φ ̿ A ¯ ,
A ̿ g ¯ = D ¯ ,
g ¯ LSM = E ̿ + Φ ¯ ,
g ¯ LSM = s σ s σ s 2 + α 2 v ¯ s u ¯ s * Φ ¯ ,
A ¯ = Φ ̿ + E ¯ .
g ¯ MLSM = ( Φ ̿ + E ̿ ) + D ¯ .
= { r p : log 10 g θ r p > Min + β ( Max Min ) }
Error ( β ) = M err ( β ) M ,

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