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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    [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 2-D 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]
  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).
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    [CrossRef]
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    [CrossRef]
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    [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]
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    [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]
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    [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]
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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 (5)

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 2-D 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]

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]

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)

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]

T. Arens, and A. Kirsch, "The factorization method in inverse scattering from periodic structures," Inverse Probl. 19(5), 1195-1211 (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]

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]

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]

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 2-D 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]

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]

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]

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 2-D 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]

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 2-D inverse scattering problems," IEEE Trans. Antenn. Propag. 55(6), 1895-1899 (2007).
[CrossRef]

Fink, M.

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

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]

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 2-D inverse scattering problems," IEEE Trans. Antenn. Propag. 55(6), 1895-1899 (2007).
[CrossRef]

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]

Kress, R.

D. Colton, and R. Kress, "Using fundamental solutions in inverse scattering," Inverse Probl. 22(3), R49-R66 (2006).
[CrossRef]

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]

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]

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]

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]

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 2-D inverse scattering problems," IEEE Trans. Antenn. Propag. 55(6), 1895-1899 (2007).
[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]

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

Inverse Probl. (8)

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]

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]

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]

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)

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]

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]

Opt. Lett. (1)

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