Abstract

This paper investigates an approach to inverse scattering problems based on the integration of the subspace-based optimization method (SOM) within a multifocusing scheme in the framework of the contrast source formulation. The scattering equations are solved by a nested three-step procedure composed of (a) an outer multiresolution loop dealing with the identification of the regions of interest within the investigation domain through an iterative information-acquisition process, (b) a spectrum analysis step devoted to the reconstruction of the deterministic components of the contrast sources, and (c) an inner optimization loop aimed at retrieving the ambiguous components of the contrast sources through a conjugate gradient minimization of a suitable objective function. A set of representative reconstruction results is discussed to provide numerical evidence of the effectiveness of the proposed algorithmic approach as well as to assess the features and potentialities of the multifocusing integration in comparison with the state-of-the-art SOM implementation.

© 2011 Optical Society of America

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  6. I. T. Rekanos, S. M. Panas, and T. D. Tsiboukis, “Microwave imaging using the finite-element method and a sensitivity analysis approach,” IEEE Trans. Med. Imaging 18, 1108–1114 (1999).
    [CrossRef]
  7. P. M. Meaney, M. W. Fanning, D. Li, S. P. Poplack, and K. D. Paulsen, “A clinical prototype for active microwave imaging of the breast,” IEEE Trans. Microwave Theory Tech. 48, 1841–1853 (2000).
    [CrossRef]
  8. C. Yu, M. Yuan, J. Stang, E. Bresslour, R. T. George, G. A. Ybarra, W. T. Joines, and Q. Liu, “Active microwave imaging II: 3-D system prototype and image reconstruction from experimental data,” IEEE Trans. Microwave Theory Tech. 56, 991–1000(2008).
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  9. D. Lesselier and T. Habashy, “Foreword,” Inverse Probl. 16(5) (2000).
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  11. M. Benedetti, M. Donelli, G. Franceschini, A. Massa, and M. Pastorino, “Evaluation study of the effectiveness of the integrated genetic-algorithm-based strategy for the tomographic subsurface detection of defects,” J. Opt. Soc. Am. A 23, 1311–1325 (2006).
    [CrossRef]
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  13. P. Lobel, L. Blanc-Feraud, C. Pichot, and M. Barlaud, “A new regularization scheme for inverse scattering,” Inverse Probl. 13, 403–410 (1997).
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  14. A. Massa and S. Caorsi, eds.,Special issue on “Microwave Imaging and Inverse Scattering Techniques ,” J. Electromagn. Waves Appl. 17, 151–386 (2003).
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  16. M. Benedetti, D. Lesselier, M. Lambert, and A. Massa, “Multiple shapes reconstruction by means of multi-region level sets,” IEEE Trans. Geosci. Remote Sens. 48, 2330–2342 (2010).
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  21. T. M. Habashy and A. Abubakar, “A general framework for constraint minimization for the inversion of electromagnetic measurements,” PIER 46, 265–312 (2004).
    [CrossRef]
  22. G. Bozza and M. Pastorino, “An inexact Newton-based approach to microwave imaging within the contrast source formulation,” IEEE Trans. Antennas Propag. Mag. 57, 1122–1132 (2009).
    [CrossRef]
  23. T. Takenaka, H. Zhou, and T. Tanaka, “Inverse scattering for a three-dimensional object in the time domain,” J. Opt. Soc. Am. A 20, 1867–1874 (2003).
    [CrossRef]
  24. N. Bleistein and J. K. Cohen, “Nonuniqueness of the inverse source problem in acoustic and electromagnetics,” J. Math. Phys. 18, 194–201 (1977).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  27. P. Rocca, M. Donelli, G. L. Gragnani, and A. Massa, “Iterative multi-resolution retrieval of non-measurable equivalent currents for the imaging of dielectric objects,” Inverse Probl. 25(2009).
    [CrossRef]
  28. X. Chen, “Subspace-based optimization method for solving inverse-scattering problems,” IEEE Trans. Geosci. Remote Sens. 48, 42–49 (2010).
    [CrossRef]
  29. L. Pan, X. Chen, Y. Zhong, and S. Yeo, “Comparison among the variants of subspace-based optimization method for addressing inverse scattering problems: transverse electric case,” J. Opt. Soc. Am. A 27, 2208–2215 (2010).
    [CrossRef]
  30. K. Agarwal, L. Pan, and X. Chen, “Subspace-based optimization method for reconstruction of 2-D complex anisotropic dielectric objects,” IEEE Trans. Microwave Theory Tech. 58, 1065–1074(2010).
    [CrossRef]
  31. Y. Zhong, X. Chen, and K. Agarwal, “An improved subspace-based optimization method and its implementation in solving three-dimensional inverse problems,” IEEE Trans. Geosci. Remote Sens. 48, 3763–3768 (2010).
    [CrossRef]
  32. X. Chen, “Application of signal-subspace and optimization methods in reconstructing extended scatterers,” J. Opt. Soc. Am. A 26, 1022–1026 (2009).
    [CrossRef]
  33. L. Pan, K. Agarwal, Y. Zhong, S. 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]
  34. X. Chen, “Signal-subspace method approach to the intensity-only electromagnetic inverse scattering problem,” J. Opt. Soc. Am. A 25, 2018–2024 (2008).
    [CrossRef]
  35. T. Isernia, V. Pascazio, and R. Pierri, “On the local minima in a tomographic imaging technique,” IEEE Trans. Geosci. Remote Sens. 39, 1596–1607 (2001).
    [CrossRef]
  36. S. Caorsi, M. Donelli, D. Franceschini, and A. Massa, “A new methodology based on an iterative multiscaling for microwave imaging,” IEEE Trans. Microwave Theory Tech. 51, 1162–1173(2003).
    [CrossRef]
  37. S. Caorsi, M. Donelli, and A. Massa, “Detection, location, and imaging of multiple scatterers by means of the iterative multiscaling method,” IEEE Trans. Microwave Theory Tech. 52, 1217–1228 (2004).
    [CrossRef]
  38. M. Donelli, G. Franceschini, A. Martini, and A. Massa, “An integrated multiscaling strategy based on a particle swarm algorithm for inverse scattering problems,” IEEE Trans. Geosci. Remote Sens. 44, 298–312 (2006).
    [CrossRef]
  39. M. Donelli, D. Franceschini, P. Rocca, and A. Massa, “Three-dimensional microwave imaging problems solved through an efficient multi-scaling particle swarm optimization,” IEEE Trans. Geosci. Remote Sens. 47, 1467–1481 (2009).
    [CrossRef]
  40. O. M. Bucci and T. Isernia, “Electromagnetic inverse scattering: retrievable information and measurement strategies,” Radio Sci. 32, 2123–2137 (1997).
    [CrossRef]
  41. 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]
  42. J. H. Richmond, “Scattering by a dielectric cylinder of arbitrary cross shape,” IEEE Trans. Antennas Propag. Mag. 13, 334–341(1965).
    [CrossRef]

2010 (5)

M. Benedetti, D. Lesselier, M. Lambert, and A. Massa, “Multiple shapes reconstruction by means of multi-region level sets,” IEEE Trans. Geosci. Remote Sens. 48, 2330–2342 (2010).
[CrossRef]

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

K. Agarwal, L. Pan, and X. Chen, “Subspace-based optimization method for reconstruction of 2-D complex anisotropic dielectric objects,” IEEE Trans. Microwave Theory Tech. 58, 1065–1074(2010).
[CrossRef]

Y. Zhong, X. Chen, and K. Agarwal, “An improved subspace-based optimization method and its implementation in solving three-dimensional inverse problems,” IEEE Trans. Geosci. Remote Sens. 48, 3763–3768 (2010).
[CrossRef]

L. Pan, X. Chen, Y. Zhong, and S. Yeo, “Comparison among the variants of subspace-based optimization method for addressing inverse scattering problems: transverse electric case,” J. Opt. Soc. Am. A 27, 2208–2215 (2010).
[CrossRef]

2009 (6)

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. 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]

G. Bozza and M. Pastorino, “An inexact Newton-based approach to microwave imaging within the contrast source formulation,” IEEE Trans. Antennas Propag. Mag. 57, 1122–1132 (2009).
[CrossRef]

P. Rocca, M. Donelli, G. L. Gragnani, and A. Massa, “Iterative multi-resolution retrieval of non-measurable equivalent currents for the imaging of dielectric objects,” Inverse Probl. 25(2009).
[CrossRef]

M. Donelli, D. Franceschini, P. Rocca, and A. Massa, “Three-dimensional microwave imaging problems solved through an efficient multi-scaling particle swarm optimization,” IEEE Trans. Geosci. Remote Sens. 47, 1467–1481 (2009).
[CrossRef]

P. Rocca, M. Benedetti, M. Donelli, D. Franceschini, and A. Massa, “Evolutionary optimization as applied to inverse scattering problems,” Inverse Probl. 25, 123003 (2009).
[CrossRef]

2008 (2)

C. Yu, M. Yuan, J. Stang, E. Bresslour, R. T. George, G. A. Ybarra, W. T. Joines, and Q. Liu, “Active microwave imaging II: 3-D system prototype and image reconstruction from experimental data,” IEEE Trans. Microwave Theory Tech. 56, 991–1000(2008).
[CrossRef]

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

2007 (3)

C.-C. Chen, J. T. Johnson, M. Sato, and A. G. Yarovoy, “Foreword to the special issue on Subsurface Sensing Using Ground-Penetrating Radar (GPR),” IEEE Trans. Geosci. Remote Sens. 45, 2419–2421 (2007).
[CrossRef]

S. Kharkovsky and R. Zoughi, “Microwave and millimeter wave nondestructive testing and evaluation—Overview and recent advances,” IEEE Instrum. Meas. Mag. 10, 26–38 (2007).
[CrossRef]

M. Pastorino, “Stochastic optimization methods applied to microwave imaging: a review,” IEEE Trans. Antennas Propag. Mag 55, 538–548 (2007).
[CrossRef]

2006 (2)

M. Donelli, G. Franceschini, A. Martini, and A. Massa, “An integrated multiscaling strategy based on a particle swarm algorithm for inverse scattering problems,” IEEE Trans. Geosci. Remote Sens. 44, 298–312 (2006).
[CrossRef]

M. Benedetti, M. Donelli, G. Franceschini, A. Massa, and M. Pastorino, “Evaluation study of the effectiveness of the integrated genetic-algorithm-based strategy for the tomographic subsurface detection of defects,” J. Opt. Soc. Am. A 23, 1311–1325 (2006).
[CrossRef]

2004 (3)

S. Caorsi, M. Donelli, and A. Massa, “Detection, location, and imaging of multiple scatterers by means of the iterative multiscaling method,” IEEE Trans. Microwave Theory Tech. 52, 1217–1228 (2004).
[CrossRef]

T. M. Habashy and A. Abubakar, “A general framework for constraint minimization for the inversion of electromagnetic measurements,” PIER 46, 265–312 (2004).
[CrossRef]

D. Lesselier and W. C. Chew, “Special section on Electromagnetic Characterization of Buried Obstacles,” Inverse Probl. 20(6) (2004).
[CrossRef]

2003 (3)

A. Massa and S. Caorsi, eds.,Special issue on “Microwave Imaging and Inverse Scattering Techniques ,” J. Electromagn. Waves Appl. 17, 151–386 (2003).

S. Caorsi, M. Donelli, D. Franceschini, and A. Massa, “A new methodology based on an iterative multiscaling for microwave imaging,” IEEE Trans. Microwave Theory Tech. 51, 1162–1173(2003).
[CrossRef]

T. Takenaka, H. Zhou, and T. Tanaka, “Inverse scattering for a three-dimensional object in the time domain,” J. Opt. Soc. Am. A 20, 1867–1874 (2003).
[CrossRef]

2002 (1)

D. Lesselier and J. Bowler, “Foreword to the special section on Electromagnetic and Ultrasonic Nondestructive Evaluation,” Inverse Probl. 18(6) (2002).
[CrossRef]

2001 (3)

T. Lasri and R. Zoughi, “"Editorial" from the issue on Advances and Applications in Microwave and Millimeter Wave Nondestructive Evaluation, Subsurf. Sens. Technol. Appl. 2, 343–345(2001).
[CrossRef]

P. M. van den Berg and A. Abubakar, “Contrast source inversion method: sate of the art,” PIER 34, 189–218 (2001).
[CrossRef]

T. Isernia, V. Pascazio, and R. Pierri, “On the local minima in a tomographic imaging technique,” IEEE Trans. Geosci. Remote Sens. 39, 1596–1607 (2001).
[CrossRef]

2000 (2)

P. M. Meaney, M. W. Fanning, D. Li, S. P. Poplack, and K. D. Paulsen, “A clinical prototype for active microwave imaging of the breast,” IEEE Trans. Microwave Theory Tech. 48, 1841–1853 (2000).
[CrossRef]

D. Lesselier and T. Habashy, “Foreword,” Inverse Probl. 16(5) (2000).
[CrossRef]

1999 (3)

I. T. Rekanos, S. M. Panas, and T. D. Tsiboukis, “Microwave imaging using the finite-element method and a sensitivity analysis approach,” IEEE Trans. Med. Imaging 18, 1108–1114 (1999).
[CrossRef]

G. C. Giakos, M. Pastorino, F. Russo, S. Chowdhury, N. Shah, and W. Davros, “Noninvasive imaging for the new century,” IEEE Instrum. Meas. Mag. 2(2), 32–35 (1999).
[CrossRef]

S. Caorsi and G. L. Gragnani, “Inverse-scattering method for dielectric objects based on the reconstruction of the nonmeasurable equivalent current density,” Radio Sci. 34, 1–8 (1999).
[CrossRef]

1997 (2)

O. M. Bucci and T. Isernia, “Electromagnetic inverse scattering: retrievable information and measurement strategies,” Radio Sci. 32, 2123–2137 (1997).
[CrossRef]

P. Lobel, L. Blanc-Feraud, C. Pichot, and M. Barlaud, “A new regularization scheme for inverse scattering,” Inverse Probl. 13, 403–410 (1997).
[CrossRef]

1996 (1)

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]

1995 (1)

H. Harada, D. J. N. Wall, T. Takenaka, and T. Tanaka, “Conjugate gradient method applied to inverse scattering problems,” IEEE Trans. Antennas Propag. Mag. 43, 784–792 (1995).
[CrossRef]

1994 (1)

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

1977 (1)

N. Bleistein and J. K. Cohen, “Nonuniqueness of the inverse source problem in acoustic and electromagnetics,” J. Math. Phys. 18, 194–201 (1977).
[CrossRef]

1965 (1)

J. H. Richmond, “Scattering by a dielectric cylinder of arbitrary cross shape,” IEEE Trans. Antennas Propag. Mag. 13, 334–341(1965).
[CrossRef]

Abubakar, A.

T. M. Habashy and A. Abubakar, “A general framework for constraint minimization for the inversion of electromagnetic measurements,” PIER 46, 265–312 (2004).
[CrossRef]

P. M. van den Berg and A. Abubakar, “Contrast source inversion method: sate of the art,” PIER 34, 189–218 (2001).
[CrossRef]

Agarwal, K.

K. Agarwal, L. Pan, and X. Chen, “Subspace-based optimization method for reconstruction of 2-D complex anisotropic dielectric objects,” IEEE Trans. Microwave Theory Tech. 58, 1065–1074(2010).
[CrossRef]

Y. Zhong, X. Chen, and K. Agarwal, “An improved subspace-based optimization method and its implementation in solving three-dimensional inverse problems,” IEEE Trans. Geosci. Remote Sens. 48, 3763–3768 (2010).
[CrossRef]

L. Pan, K. Agarwal, Y. Zhong, S. 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]

Barlaud, M.

P. Lobel, L. Blanc-Feraud, C. Pichot, and M. Barlaud, “A new regularization scheme for inverse scattering,” Inverse Probl. 13, 403–410 (1997).
[CrossRef]

Benedetti, M.

M. Benedetti, D. Lesselier, M. Lambert, and A. Massa, “Multiple shapes reconstruction by means of multi-region level sets,” IEEE Trans. Geosci. Remote Sens. 48, 2330–2342 (2010).
[CrossRef]

P. Rocca, M. Benedetti, M. Donelli, D. Franceschini, and A. Massa, “Evolutionary optimization as applied to inverse scattering problems,” Inverse Probl. 25, 123003 (2009).
[CrossRef]

M. Benedetti, M. Donelli, G. Franceschini, A. Massa, and M. Pastorino, “Evaluation study of the effectiveness of the integrated genetic-algorithm-based strategy for the tomographic subsurface detection of defects,” J. Opt. Soc. Am. A 23, 1311–1325 (2006).
[CrossRef]

Blanc-Feraud, L.

P. Lobel, L. Blanc-Feraud, C. Pichot, and M. Barlaud, “A new regularization scheme for inverse scattering,” Inverse Probl. 13, 403–410 (1997).
[CrossRef]

Bleistein, N.

N. Bleistein and J. K. Cohen, “Nonuniqueness of the inverse source problem in acoustic and electromagnetics,” J. Math. Phys. 18, 194–201 (1977).
[CrossRef]

Bowler, J.

D. Lesselier and J. Bowler, “Foreword to the special section on Electromagnetic and Ultrasonic Nondestructive Evaluation,” Inverse Probl. 18(6) (2002).
[CrossRef]

Bozza, G.

G. Bozza and M. Pastorino, “An inexact Newton-based approach to microwave imaging within the contrast source formulation,” IEEE Trans. Antennas Propag. Mag. 57, 1122–1132 (2009).
[CrossRef]

Bresslour, E.

C. Yu, M. Yuan, J. Stang, E. Bresslour, R. T. George, G. A. Ybarra, W. T. Joines, and Q. Liu, “Active microwave imaging II: 3-D system prototype and image reconstruction from experimental data,” IEEE Trans. Microwave Theory Tech. 56, 991–1000(2008).
[CrossRef]

Bucci, O. M.

O. M. Bucci and T. Isernia, “Electromagnetic inverse scattering: retrievable information and measurement strategies,” Radio Sci. 32, 2123–2137 (1997).
[CrossRef]

Caorsi, S.

S. Caorsi, M. Donelli, and A. Massa, “Detection, location, and imaging of multiple scatterers by means of the iterative multiscaling method,” IEEE Trans. Microwave Theory Tech. 52, 1217–1228 (2004).
[CrossRef]

A. Massa and S. Caorsi, eds.,Special issue on “Microwave Imaging and Inverse Scattering Techniques ,” J. Electromagn. Waves Appl. 17, 151–386 (2003).

S. Caorsi, M. Donelli, D. Franceschini, and A. Massa, “A new methodology based on an iterative multiscaling for microwave imaging,” IEEE Trans. Microwave Theory Tech. 51, 1162–1173(2003).
[CrossRef]

S. Caorsi and G. L. Gragnani, “Inverse-scattering method for dielectric objects based on the reconstruction of the nonmeasurable equivalent current density,” Radio Sci. 34, 1–8 (1999).
[CrossRef]

Chen, C.-C.

C.-C. Chen, J. T. Johnson, M. Sato, and A. G. Yarovoy, “Foreword to the special issue on Subsurface Sensing Using Ground-Penetrating Radar (GPR),” IEEE Trans. Geosci. Remote Sens. 45, 2419–2421 (2007).
[CrossRef]

Chen, X.

K. Agarwal, L. Pan, and X. Chen, “Subspace-based optimization method for reconstruction of 2-D complex anisotropic dielectric objects,” IEEE Trans. Microwave Theory Tech. 58, 1065–1074(2010).
[CrossRef]

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

L. Pan, X. Chen, Y. Zhong, and S. Yeo, “Comparison among the variants of subspace-based optimization method for addressing inverse scattering problems: transverse electric case,” J. Opt. Soc. Am. A 27, 2208–2215 (2010).
[CrossRef]

Y. Zhong, X. Chen, and K. Agarwal, “An improved subspace-based optimization method and its implementation in solving three-dimensional inverse problems,” IEEE Trans. Geosci. Remote Sens. 48, 3763–3768 (2010).
[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. 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, “Signal-subspace method approach to the intensity-only electromagnetic inverse scattering problem,” J. Opt. Soc. Am. A 25, 2018–2024 (2008).
[CrossRef]

Chew, W. C.

D. Lesselier and W. C. Chew, “Special section on Electromagnetic Characterization of Buried Obstacles,” Inverse Probl. 20(6) (2004).
[CrossRef]

Chowdhury, S.

G. C. Giakos, M. Pastorino, F. Russo, S. Chowdhury, N. Shah, and W. Davros, “Noninvasive imaging for the new century,” IEEE Instrum. Meas. Mag. 2(2), 32–35 (1999).
[CrossRef]

Cohen, J. K.

N. Bleistein and J. K. Cohen, “Nonuniqueness of the inverse source problem in acoustic and electromagnetics,” J. Math. Phys. 18, 194–201 (1977).
[CrossRef]

Davros, W.

G. C. Giakos, M. Pastorino, F. Russo, S. Chowdhury, N. Shah, and W. Davros, “Noninvasive imaging for the new century,” IEEE Instrum. Meas. Mag. 2(2), 32–35 (1999).
[CrossRef]

de Hoop, A. T.

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

Donelli, M.

P. Rocca, M. Donelli, G. L. Gragnani, and A. Massa, “Iterative multi-resolution retrieval of non-measurable equivalent currents for the imaging of dielectric objects,” Inverse Probl. 25(2009).
[CrossRef]

M. Donelli, D. Franceschini, P. Rocca, and A. Massa, “Three-dimensional microwave imaging problems solved through an efficient multi-scaling particle swarm optimization,” IEEE Trans. Geosci. Remote Sens. 47, 1467–1481 (2009).
[CrossRef]

P. Rocca, M. Benedetti, M. Donelli, D. Franceschini, and A. Massa, “Evolutionary optimization as applied to inverse scattering problems,” Inverse Probl. 25, 123003 (2009).
[CrossRef]

M. Benedetti, M. Donelli, G. Franceschini, A. Massa, and M. Pastorino, “Evaluation study of the effectiveness of the integrated genetic-algorithm-based strategy for the tomographic subsurface detection of defects,” J. Opt. Soc. Am. A 23, 1311–1325 (2006).
[CrossRef]

M. Donelli, G. Franceschini, A. Martini, and A. Massa, “An integrated multiscaling strategy based on a particle swarm algorithm for inverse scattering problems,” IEEE Trans. Geosci. Remote Sens. 44, 298–312 (2006).
[CrossRef]

S. Caorsi, M. Donelli, and A. Massa, “Detection, location, and imaging of multiple scatterers by means of the iterative multiscaling method,” IEEE Trans. Microwave Theory Tech. 52, 1217–1228 (2004).
[CrossRef]

S. Caorsi, M. Donelli, D. Franceschini, and A. Massa, “A new methodology based on an iterative multiscaling for microwave imaging,” IEEE Trans. Microwave Theory Tech. 51, 1162–1173(2003).
[CrossRef]

Fanning, M. W.

P. M. Meaney, M. W. Fanning, D. Li, S. P. Poplack, and K. D. Paulsen, “A clinical prototype for active microwave imaging of the breast,” IEEE Trans. Microwave Theory Tech. 48, 1841–1853 (2000).
[CrossRef]

Franceschini, D.

M. Donelli, D. Franceschini, P. Rocca, and A. Massa, “Three-dimensional microwave imaging problems solved through an efficient multi-scaling particle swarm optimization,” IEEE Trans. Geosci. Remote Sens. 47, 1467–1481 (2009).
[CrossRef]

P. Rocca, M. Benedetti, M. Donelli, D. Franceschini, and A. Massa, “Evolutionary optimization as applied to inverse scattering problems,” Inverse Probl. 25, 123003 (2009).
[CrossRef]

S. Caorsi, M. Donelli, D. Franceschini, and A. Massa, “A new methodology based on an iterative multiscaling for microwave imaging,” IEEE Trans. Microwave Theory Tech. 51, 1162–1173(2003).
[CrossRef]

Franceschini, G.

M. Donelli, G. Franceschini, A. Martini, and A. Massa, “An integrated multiscaling strategy based on a particle swarm algorithm for inverse scattering problems,” IEEE Trans. Geosci. Remote Sens. 44, 298–312 (2006).
[CrossRef]

M. Benedetti, M. Donelli, G. Franceschini, A. Massa, and M. Pastorino, “Evaluation study of the effectiveness of the integrated genetic-algorithm-based strategy for the tomographic subsurface detection of defects,” J. Opt. Soc. Am. A 23, 1311–1325 (2006).
[CrossRef]

George, R. T.

C. Yu, M. Yuan, J. Stang, E. Bresslour, R. T. George, G. A. Ybarra, W. T. Joines, and Q. Liu, “Active microwave imaging II: 3-D system prototype and image reconstruction from experimental data,” IEEE Trans. Microwave Theory Tech. 56, 991–1000(2008).
[CrossRef]

Giakos, G. C.

G. C. Giakos, M. Pastorino, F. Russo, S. Chowdhury, N. Shah, and W. Davros, “Noninvasive imaging for the new century,” IEEE Instrum. Meas. Mag. 2(2), 32–35 (1999).
[CrossRef]

Gragnani, G. L.

P. Rocca, M. Donelli, G. L. Gragnani, and A. Massa, “Iterative multi-resolution retrieval of non-measurable equivalent currents for the imaging of dielectric objects,” Inverse Probl. 25(2009).
[CrossRef]

S. Caorsi and G. L. Gragnani, “Inverse-scattering method for dielectric objects based on the reconstruction of the nonmeasurable equivalent current density,” Radio Sci. 34, 1–8 (1999).
[CrossRef]

Habashy, T.

D. Lesselier and T. Habashy, “Foreword,” Inverse Probl. 16(5) (2000).
[CrossRef]

Habashy, T. M.

T. M. Habashy and A. Abubakar, “A general framework for constraint minimization for the inversion of electromagnetic measurements,” PIER 46, 265–312 (2004).
[CrossRef]

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

Harada, H.

H. Harada, D. J. N. Wall, T. Takenaka, and T. Tanaka, “Conjugate gradient method applied to inverse scattering problems,” IEEE Trans. Antennas Propag. Mag. 43, 784–792 (1995).
[CrossRef]

Isernia, T.

T. Isernia, V. Pascazio, and R. Pierri, “On the local minima in a tomographic imaging technique,” IEEE Trans. Geosci. Remote Sens. 39, 1596–1607 (2001).
[CrossRef]

O. M. Bucci and T. Isernia, “Electromagnetic inverse scattering: retrievable information and measurement strategies,” Radio Sci. 32, 2123–2137 (1997).
[CrossRef]

Johnson, J. T.

C.-C. Chen, J. T. Johnson, M. Sato, and A. G. Yarovoy, “Foreword to the special issue on Subsurface Sensing Using Ground-Penetrating Radar (GPR),” IEEE Trans. Geosci. Remote Sens. 45, 2419–2421 (2007).
[CrossRef]

Joines, W. T.

C. Yu, M. Yuan, J. Stang, E. Bresslour, R. T. George, G. A. Ybarra, W. T. Joines, and Q. Liu, “Active microwave imaging II: 3-D system prototype and image reconstruction from experimental data,” IEEE Trans. Microwave Theory Tech. 56, 991–1000(2008).
[CrossRef]

Kharkovsky, S.

S. Kharkovsky and R. Zoughi, “Microwave and millimeter wave nondestructive testing and evaluation—Overview and recent advances,” IEEE Instrum. Meas. Mag. 10, 26–38 (2007).
[CrossRef]

Lambert, M.

M. Benedetti, D. Lesselier, M. Lambert, and A. Massa, “Multiple shapes reconstruction by means of multi-region level sets,” IEEE Trans. Geosci. Remote Sens. 48, 2330–2342 (2010).
[CrossRef]

Lasri, T.

T. Lasri and R. Zoughi, “"Editorial" from the issue on Advances and Applications in Microwave and Millimeter Wave Nondestructive Evaluation, Subsurf. Sens. Technol. Appl. 2, 343–345(2001).
[CrossRef]

Lesselier, D.

M. Benedetti, D. Lesselier, M. Lambert, and A. Massa, “Multiple shapes reconstruction by means of multi-region level sets,” IEEE Trans. Geosci. Remote Sens. 48, 2330–2342 (2010).
[CrossRef]

D. Lesselier and W. C. Chew, “Special section on Electromagnetic Characterization of Buried Obstacles,” Inverse Probl. 20(6) (2004).
[CrossRef]

D. Lesselier and J. Bowler, “Foreword to the special section on Electromagnetic and Ultrasonic Nondestructive Evaluation,” Inverse Probl. 18(6) (2002).
[CrossRef]

D. Lesselier and T. Habashy, “Foreword,” Inverse Probl. 16(5) (2000).
[CrossRef]

Li, D.

P. M. Meaney, M. W. Fanning, D. Li, S. P. Poplack, and K. D. Paulsen, “A clinical prototype for active microwave imaging of the breast,” IEEE Trans. Microwave Theory Tech. 48, 1841–1853 (2000).
[CrossRef]

Liu, Q.

C. Yu, M. Yuan, J. Stang, E. Bresslour, R. T. George, G. A. Ybarra, W. T. Joines, and Q. Liu, “Active microwave imaging II: 3-D system prototype and image reconstruction from experimental data,” IEEE Trans. Microwave Theory Tech. 56, 991–1000(2008).
[CrossRef]

Lobel, P.

P. Lobel, L. Blanc-Feraud, C. Pichot, and M. Barlaud, “A new regularization scheme for inverse scattering,” Inverse Probl. 13, 403–410 (1997).
[CrossRef]

Martini, A.

M. Donelli, G. Franceschini, A. Martini, and A. Massa, “An integrated multiscaling strategy based on a particle swarm algorithm for inverse scattering problems,” IEEE Trans. Geosci. Remote Sens. 44, 298–312 (2006).
[CrossRef]

Massa, A.

M. Benedetti, D. Lesselier, M. Lambert, and A. Massa, “Multiple shapes reconstruction by means of multi-region level sets,” IEEE Trans. Geosci. Remote Sens. 48, 2330–2342 (2010).
[CrossRef]

P. Rocca, M. Benedetti, M. Donelli, D. Franceschini, and A. Massa, “Evolutionary optimization as applied to inverse scattering problems,” Inverse Probl. 25, 123003 (2009).
[CrossRef]

P. Rocca, M. Donelli, G. L. Gragnani, and A. Massa, “Iterative multi-resolution retrieval of non-measurable equivalent currents for the imaging of dielectric objects,” Inverse Probl. 25(2009).
[CrossRef]

M. Donelli, D. Franceschini, P. Rocca, and A. Massa, “Three-dimensional microwave imaging problems solved through an efficient multi-scaling particle swarm optimization,” IEEE Trans. Geosci. Remote Sens. 47, 1467–1481 (2009).
[CrossRef]

M. Donelli, G. Franceschini, A. Martini, and A. Massa, “An integrated multiscaling strategy based on a particle swarm algorithm for inverse scattering problems,” IEEE Trans. Geosci. Remote Sens. 44, 298–312 (2006).
[CrossRef]

M. Benedetti, M. Donelli, G. Franceschini, A. Massa, and M. Pastorino, “Evaluation study of the effectiveness of the integrated genetic-algorithm-based strategy for the tomographic subsurface detection of defects,” J. Opt. Soc. Am. A 23, 1311–1325 (2006).
[CrossRef]

S. Caorsi, M. Donelli, and A. Massa, “Detection, location, and imaging of multiple scatterers by means of the iterative multiscaling method,” IEEE Trans. Microwave Theory Tech. 52, 1217–1228 (2004).
[CrossRef]

Massa, A.

A. Massa and S. Caorsi, eds.,Special issue on “Microwave Imaging and Inverse Scattering Techniques ,” J. Electromagn. Waves Appl. 17, 151–386 (2003).

Massa, A.

S. Caorsi, M. Donelli, D. Franceschini, and A. Massa, “A new methodology based on an iterative multiscaling for microwave imaging,” IEEE Trans. Microwave Theory Tech. 51, 1162–1173(2003).
[CrossRef]

Meaney, P. M.

P. M. Meaney, M. W. Fanning, D. Li, S. P. Poplack, and K. D. Paulsen, “A clinical prototype for active microwave imaging of the breast,” IEEE Trans. Microwave Theory Tech. 48, 1841–1853 (2000).
[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]

Oristaglio, M. L.

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

Pan, L.

Panas, S. M.

I. T. Rekanos, S. M. Panas, and T. D. Tsiboukis, “Microwave imaging using the finite-element method and a sensitivity analysis approach,” IEEE Trans. Med. Imaging 18, 1108–1114 (1999).
[CrossRef]

Pascazio, V.

T. Isernia, V. Pascazio, and R. Pierri, “On the local minima in a tomographic imaging technique,” IEEE Trans. Geosci. Remote Sens. 39, 1596–1607 (2001).
[CrossRef]

Pastorino, M.

G. Bozza and M. Pastorino, “An inexact Newton-based approach to microwave imaging within the contrast source formulation,” IEEE Trans. Antennas Propag. Mag. 57, 1122–1132 (2009).
[CrossRef]

M. Pastorino, “Stochastic optimization methods applied to microwave imaging: a review,” IEEE Trans. Antennas Propag. Mag 55, 538–548 (2007).
[CrossRef]

M. Benedetti, M. Donelli, G. Franceschini, A. Massa, and M. Pastorino, “Evaluation study of the effectiveness of the integrated genetic-algorithm-based strategy for the tomographic subsurface detection of defects,” J. Opt. Soc. Am. A 23, 1311–1325 (2006).
[CrossRef]

G. C. Giakos, M. Pastorino, F. Russo, S. Chowdhury, N. Shah, and W. Davros, “Noninvasive imaging for the new century,” IEEE Instrum. Meas. Mag. 2(2), 32–35 (1999).
[CrossRef]

M. Pastorino, Microwave Imaging (Wiley, 2010).
[CrossRef]

Paulsen, K. D.

P. M. Meaney, M. W. Fanning, D. Li, S. P. Poplack, and K. D. Paulsen, “A clinical prototype for active microwave imaging of the breast,” IEEE Trans. Microwave Theory Tech. 48, 1841–1853 (2000).
[CrossRef]

Pichot, C.

P. Lobel, L. Blanc-Feraud, C. Pichot, and M. Barlaud, “A new regularization scheme for inverse scattering,” Inverse Probl. 13, 403–410 (1997).
[CrossRef]

Pierri, R.

T. Isernia, V. Pascazio, and R. Pierri, “On the local minima in a tomographic imaging technique,” IEEE Trans. Geosci. Remote Sens. 39, 1596–1607 (2001).
[CrossRef]

Poplack, S. P.

P. M. Meaney, M. W. Fanning, D. Li, S. P. Poplack, and K. D. Paulsen, “A clinical prototype for active microwave imaging of the breast,” IEEE Trans. Microwave Theory Tech. 48, 1841–1853 (2000).
[CrossRef]

Rekanos, I. T.

I. T. Rekanos, S. M. Panas, and T. D. Tsiboukis, “Microwave imaging using the finite-element method and a sensitivity analysis approach,” IEEE Trans. Med. Imaging 18, 1108–1114 (1999).
[CrossRef]

Richmond, J. H.

J. H. Richmond, “Scattering by a dielectric cylinder of arbitrary cross shape,” IEEE Trans. Antennas Propag. Mag. 13, 334–341(1965).
[CrossRef]

Rocca, P.

P. Rocca, M. Donelli, G. L. Gragnani, and A. Massa, “Iterative multi-resolution retrieval of non-measurable equivalent currents for the imaging of dielectric objects,” Inverse Probl. 25(2009).
[CrossRef]

M. Donelli, D. Franceschini, P. Rocca, and A. Massa, “Three-dimensional microwave imaging problems solved through an efficient multi-scaling particle swarm optimization,” IEEE Trans. Geosci. Remote Sens. 47, 1467–1481 (2009).
[CrossRef]

P. Rocca, M. Benedetti, M. Donelli, D. Franceschini, and A. Massa, “Evolutionary optimization as applied to inverse scattering problems,” Inverse Probl. 25, 123003 (2009).
[CrossRef]

Russo, F.

G. C. Giakos, M. Pastorino, F. Russo, S. Chowdhury, N. Shah, and W. Davros, “Noninvasive imaging for the new century,” IEEE Instrum. Meas. Mag. 2(2), 32–35 (1999).
[CrossRef]

Sato, M.

C.-C. Chen, J. T. Johnson, M. Sato, and A. G. Yarovoy, “Foreword to the special issue on Subsurface Sensing Using Ground-Penetrating Radar (GPR),” IEEE Trans. Geosci. Remote Sens. 45, 2419–2421 (2007).
[CrossRef]

Shah, N.

G. C. Giakos, M. Pastorino, F. Russo, S. Chowdhury, N. Shah, and W. Davros, “Noninvasive imaging for the new century,” IEEE Instrum. Meas. Mag. 2(2), 32–35 (1999).
[CrossRef]

Stang, J.

C. Yu, M. Yuan, J. Stang, E. Bresslour, R. T. George, G. A. Ybarra, W. T. Joines, and Q. Liu, “Active microwave imaging II: 3-D system prototype and image reconstruction from experimental data,” IEEE Trans. Microwave Theory Tech. 56, 991–1000(2008).
[CrossRef]

Takenaka, T.

T. Takenaka, H. Zhou, and T. Tanaka, “Inverse scattering for a three-dimensional object in the time domain,” J. Opt. Soc. Am. A 20, 1867–1874 (2003).
[CrossRef]

H. Harada, D. J. N. Wall, T. Takenaka, and T. Tanaka, “Conjugate gradient method applied to inverse scattering problems,” IEEE Trans. Antennas Propag. Mag. 43, 784–792 (1995).
[CrossRef]

Tanaka, T.

T. Takenaka, H. Zhou, and T. Tanaka, “Inverse scattering for a three-dimensional object in the time domain,” J. Opt. Soc. Am. A 20, 1867–1874 (2003).
[CrossRef]

H. Harada, D. J. N. Wall, T. Takenaka, and T. Tanaka, “Conjugate gradient method applied to inverse scattering problems,” IEEE Trans. Antennas Propag. Mag. 43, 784–792 (1995).
[CrossRef]

Tsiboukis, T. D.

I. T. Rekanos, S. M. Panas, and T. D. Tsiboukis, “Microwave imaging using the finite-element method and a sensitivity analysis approach,” IEEE Trans. Med. Imaging 18, 1108–1114 (1999).
[CrossRef]

van den Berg, P. M.

P. M. van den Berg and A. Abubakar, “Contrast source inversion method: sate of the art,” PIER 34, 189–218 (2001).
[CrossRef]

Wall, D. J. N.

H. Harada, D. J. N. Wall, T. Takenaka, and T. Tanaka, “Conjugate gradient method applied to inverse scattering problems,” IEEE Trans. Antennas Propag. Mag. 43, 784–792 (1995).
[CrossRef]

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]

Yarovoy, A. G.

C.-C. Chen, J. T. Johnson, M. Sato, and A. G. Yarovoy, “Foreword to the special issue on Subsurface Sensing Using Ground-Penetrating Radar (GPR),” IEEE Trans. Geosci. Remote Sens. 45, 2419–2421 (2007).
[CrossRef]

Ybarra, G. A.

C. Yu, M. Yuan, J. Stang, E. Bresslour, R. T. George, G. A. Ybarra, W. T. Joines, and Q. Liu, “Active microwave imaging II: 3-D system prototype and image reconstruction from experimental data,” IEEE Trans. Microwave Theory Tech. 56, 991–1000(2008).
[CrossRef]

Yeo, S.

Yu, C.

C. Yu, M. Yuan, J. Stang, E. Bresslour, R. T. George, G. A. Ybarra, W. T. Joines, and Q. Liu, “Active microwave imaging II: 3-D system prototype and image reconstruction from experimental data,” IEEE Trans. Microwave Theory Tech. 56, 991–1000(2008).
[CrossRef]

Yuan, M.

C. Yu, M. Yuan, J. Stang, E. Bresslour, R. T. George, G. A. Ybarra, W. T. Joines, and Q. Liu, “Active microwave imaging II: 3-D system prototype and image reconstruction from experimental data,” IEEE Trans. Microwave Theory Tech. 56, 991–1000(2008).
[CrossRef]

Zhong, Y.

Zhou, H.

Zoughi, R.

S. Kharkovsky and R. Zoughi, “Microwave and millimeter wave nondestructive testing and evaluation—Overview and recent advances,” IEEE Instrum. Meas. Mag. 10, 26–38 (2007).
[CrossRef]

T. Lasri and R. Zoughi, “"Editorial" from the issue on Advances and Applications in Microwave and Millimeter Wave Nondestructive Evaluation, Subsurf. Sens. Technol. Appl. 2, 343–345(2001).
[CrossRef]

R. Zoughi, Microwave Nondestructive Testing and Evaluation (Kluwer, 2000).

IEEE Instrum. Meas. Mag. (2)

G. C. Giakos, M. Pastorino, F. Russo, S. Chowdhury, N. Shah, and W. Davros, “Noninvasive imaging for the new century,” IEEE Instrum. Meas. Mag. 2(2), 32–35 (1999).
[CrossRef]

S. Kharkovsky and R. Zoughi, “Microwave and millimeter wave nondestructive testing and evaluation—Overview and recent advances,” IEEE Instrum. Meas. Mag. 10, 26–38 (2007).
[CrossRef]

IEEE Trans. Antennas Propag. Mag (1)

M. Pastorino, “Stochastic optimization methods applied to microwave imaging: a review,” IEEE Trans. Antennas Propag. Mag 55, 538–548 (2007).
[CrossRef]

IEEE Trans. Antennas Propag. Mag. (3)

H. Harada, D. J. N. Wall, T. Takenaka, and T. Tanaka, “Conjugate gradient method applied to inverse scattering problems,” IEEE Trans. Antennas Propag. Mag. 43, 784–792 (1995).
[CrossRef]

G. Bozza and M. Pastorino, “An inexact Newton-based approach to microwave imaging within the contrast source formulation,” IEEE Trans. Antennas Propag. Mag. 57, 1122–1132 (2009).
[CrossRef]

J. H. Richmond, “Scattering by a dielectric cylinder of arbitrary cross shape,” IEEE Trans. Antennas Propag. Mag. 13, 334–341(1965).
[CrossRef]

IEEE Trans. Geosci. Remote Sens. (8)

Y. Zhong, X. Chen, and K. Agarwal, “An improved subspace-based optimization method and its implementation in solving three-dimensional inverse problems,” IEEE Trans. Geosci. Remote Sens. 48, 3763–3768 (2010).
[CrossRef]

T. Isernia, V. Pascazio, and R. Pierri, “On the local minima in a tomographic imaging technique,” IEEE Trans. Geosci. Remote Sens. 39, 1596–1607 (2001).
[CrossRef]

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

M. Benedetti, D. Lesselier, M. Lambert, and A. Massa, “Multiple shapes reconstruction by means of multi-region level sets,” IEEE Trans. Geosci. Remote Sens. 48, 2330–2342 (2010).
[CrossRef]

C.-C. Chen, J. T. Johnson, M. Sato, and A. G. Yarovoy, “Foreword to the special issue on Subsurface Sensing Using Ground-Penetrating Radar (GPR),” IEEE Trans. Geosci. Remote Sens. 45, 2419–2421 (2007).
[CrossRef]

M. Donelli, G. Franceschini, A. Martini, and A. Massa, “An integrated multiscaling strategy based on a particle swarm algorithm for inverse scattering problems,” IEEE Trans. Geosci. Remote Sens. 44, 298–312 (2006).
[CrossRef]

M. Donelli, D. Franceschini, P. Rocca, and A. Massa, “Three-dimensional microwave imaging problems solved through an efficient multi-scaling particle swarm optimization,” IEEE Trans. Geosci. Remote Sens. 47, 1467–1481 (2009).
[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]

IEEE Trans. Med. Imaging (1)

I. T. Rekanos, S. M. Panas, and T. D. Tsiboukis, “Microwave imaging using the finite-element method and a sensitivity analysis approach,” IEEE Trans. Med. Imaging 18, 1108–1114 (1999).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (5)

P. M. Meaney, M. W. Fanning, D. Li, S. P. Poplack, and K. D. Paulsen, “A clinical prototype for active microwave imaging of the breast,” IEEE Trans. Microwave Theory Tech. 48, 1841–1853 (2000).
[CrossRef]

C. Yu, M. Yuan, J. Stang, E. Bresslour, R. T. George, G. A. Ybarra, W. T. Joines, and Q. Liu, “Active microwave imaging II: 3-D system prototype and image reconstruction from experimental data,” IEEE Trans. Microwave Theory Tech. 56, 991–1000(2008).
[CrossRef]

K. Agarwal, L. Pan, and X. Chen, “Subspace-based optimization method for reconstruction of 2-D complex anisotropic dielectric objects,” IEEE Trans. Microwave Theory Tech. 58, 1065–1074(2010).
[CrossRef]

S. Caorsi, M. Donelli, D. Franceschini, and A. Massa, “A new methodology based on an iterative multiscaling for microwave imaging,” IEEE Trans. Microwave Theory Tech. 51, 1162–1173(2003).
[CrossRef]

S. Caorsi, M. Donelli, and A. Massa, “Detection, location, and imaging of multiple scatterers by means of the iterative multiscaling method,” IEEE Trans. Microwave Theory Tech. 52, 1217–1228 (2004).
[CrossRef]

Inverse Probl. (6)

P. Rocca, M. Benedetti, M. Donelli, D. Franceschini, and A. Massa, “Evolutionary optimization as applied to inverse scattering problems,” Inverse Probl. 25, 123003 (2009).
[CrossRef]

P. Rocca, M. Donelli, G. L. Gragnani, and A. Massa, “Iterative multi-resolution retrieval of non-measurable equivalent currents for the imaging of dielectric objects,” Inverse Probl. 25(2009).
[CrossRef]

D. Lesselier and T. Habashy, “Foreword,” Inverse Probl. 16(5) (2000).
[CrossRef]

D. Lesselier and W. C. Chew, “Special section on Electromagnetic Characterization of Buried Obstacles,” Inverse Probl. 20(6) (2004).
[CrossRef]

D. Lesselier and J. Bowler, “Foreword to the special section on Electromagnetic and Ultrasonic Nondestructive Evaluation,” Inverse Probl. 18(6) (2002).
[CrossRef]

P. Lobel, L. Blanc-Feraud, C. Pichot, and M. Barlaud, “A new regularization scheme for inverse scattering,” Inverse Probl. 13, 403–410 (1997).
[CrossRef]

J. Math. Phys. (1)

N. Bleistein and J. K. Cohen, “Nonuniqueness of the inverse source problem in acoustic and electromagnetics,” J. Math. Phys. 18, 194–201 (1977).
[CrossRef]

J. Opt. Soc. Am. A (6)

PIER (2)

P. M. van den Berg and A. Abubakar, “Contrast source inversion method: sate of the art,” PIER 34, 189–218 (2001).
[CrossRef]

T. M. Habashy and A. Abubakar, “A general framework for constraint minimization for the inversion of electromagnetic measurements,” PIER 46, 265–312 (2004).
[CrossRef]

Radio Sci. (3)

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

S. Caorsi and G. L. Gragnani, “Inverse-scattering method for dielectric objects based on the reconstruction of the nonmeasurable equivalent current density,” Radio Sci. 34, 1–8 (1999).
[CrossRef]

O. M. Bucci and T. Isernia, “Electromagnetic inverse scattering: retrievable information and measurement strategies,” Radio Sci. 32, 2123–2137 (1997).
[CrossRef]

Special issue on “Microwave Imaging and Inverse Scattering Techniques (1)

A. Massa and S. Caorsi, eds.,Special issue on “Microwave Imaging and Inverse Scattering Techniques ,” J. Electromagn. Waves Appl. 17, 151–386 (2003).

Subsurf. Sens. Technol. Appl. (1)

T. Lasri and R. Zoughi, “"Editorial" from the issue on Advances and Applications in Microwave and Millimeter Wave Nondestructive Evaluation, Subsurf. Sens. Technol. Appl. 2, 343–345(2001).
[CrossRef]

Other (2)

R. Zoughi, Microwave Nondestructive Testing and Evaluation (Kluwer, 2000).

M. Pastorino, Microwave Imaging (Wiley, 2010).
[CrossRef]

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Figures (15)

Fig. 1
Fig. 1

Flowchart of the proposed IMSA-SOM procedure.

Fig. 2
Fig. 2

Sensitivity analysis (square cylinder: l = 2.4 λ , V = 24 , M = 24 , τ = 1.0 ). Behavior of the objective function versus k: (a)  SNR = 20 dB and (b)  α = 0.7 (adaptive IMSA-SOM).

Fig. 3
Fig. 3

Sensitivity analysis (square cylinder: l = 2.4 λ , V = 24 , M = 24 , τ = 1.0 ). Behavior of Ψ tot versus SNR when applying the adaptive IMSA-SOM with different α values.

Fig. 4
Fig. 4

Sensitivity analysis (square cylinder: l = 2.4 λ , V = 24 , M = 24 , τ = 1.0 , α = 0.7 ). Reconstruction of the dielectric profile (a) when applying the adaptive IMSA-SOM to process (b) noiseless and noisy data with a (c)  SNR = 30 dB and a (d)  SNR = 10 dB .

Fig. 5
Fig. 5

Sensitivity analysis (square cylinder: l = 2.4 λ , V = 24 , M = 24 , τ = 1.0 , α = 0.7 ). Behavior of Ψ tot versus T 0 when applying the adaptive IMSA-SOM and for different SNRs. (a) Retrieved dielectric profiles when (b) and (d) ( T 0 = 25 ) and (c) and (e) ( T 0 = 25 ) by processing (b) and (c) noiseless ( SNR = ) and (d) and (e) noisy data ( SNR = 10 dB ).

Fig. 6
Fig. 6

Sensitivity analysis (square cylinder: l = 2.4 λ , V = 24 , M = 24 , α = 0.7 , T 0 = 50 ). Behavior of Ψ tot versus τ for different SNRs.

Fig. 7
Fig. 7

Numerical assessment (inhomogeneous cylinder: l = 2.4 λ , V = 24 , M = 24 , τ out = 0.6 , τ in = 1.2 , SNR = 30 dB ). (a) Actual distribution and dielectric profiles retrieved with the IMSA-SOM at (b)  s = 1 , (c)  s = 2 , and (d)  s = S = 3 .

Fig. 8
Fig. 8

Numerical assessment (inhomogeneous cylinder: l = 2.4 λ , V = 24 , M = 24 , τ out = 0.6 , τ in = 1.2 , SNR = 30 dB ). Behavior of (a) the objective function versus k and (b) the singular values of the mapping operator G ( s ) .

Fig. 9
Fig. 9

Numerical assessment (inhomogeneous cylinder: l = 2.4 λ , V = 24 , M = 24 , τ out = 0.6 , τ in = 1.2 ). Dielectric profiles reconstructed by means of (a), (c), and (e) as the standard SOM and (b), (d), and (f) as the adaptive IMSA-SOM processing. (a) and (b) are noiseless data and noisy samples with (c) and (d) having a SNR = 20 dB and (e) and (f) having a SNR = 10 dB .

Fig. 10
Fig. 10

Numerical assessment (inhomogeneous cylinder: l = 2.4 λ , V = 24 , M = 24 , τ out = 0.6 ). Plots of (a)  Ψ tot , (b)  Ψ int , and (c)  Ψ ext versus τ in for different SNR values.

Fig. 11
Fig. 11

Numerical assessment (inhomogeneous cylinder: l = 2.4 λ , V = 24 , M = 24 , τ out = 0.6 , SNR = 20 dB ). Actual distribution [(a), (d), and (g)] and dielectric profiles retrieved with [(b), (e), and (h)] the SOM and [(c), (f), and (i)] the adaptive IMSA-SOM when [(a), (b), and (c)] τ in = 0.0 , [(d), (e), and (f)] τ in = 0.6 , and [g), (h), and (i)] τ in = 1.0 .

Fig. 12
Fig. 12

Numerical assessment (inhomogeneous cylinder: l = 6 λ , V = 60 , M = 60 , τ out = 0.6 , τ in = 1.2 , SNR = 10 dB ). Dielectric profiles retrieved with [(a) and (c)] the SOM and [(b) and (d)] the adaptive IMSA-SOM. Reconstructions (a) and (b) are within the investigation domain ( 6 λ × 6 λ ), and (c) and (d) are on a smaller region around the scatterer ( 2.4 λ × 2.4 λ ).

Fig. 13
Fig. 13

Numerical assessment (irregular cylinder: l = 6 λ , V = 60 , M = 60 , τ = 1.0 , SNR = 10 dB ). (a) Actual profile and reconstructions with the (b) SOM and (c) the adaptive IMSA-SOM.

Fig. 14
Fig. 14

Numerical assessment (irregular cylinder: l = 2.4 λ , V = 24 , M = 24 , τ = 1.0 ). (a) Actual distribution and dielectric profiles reconstructed with [(b) and (d)] the SOM and [(c) and (e)] the adaptive IMSA-SOM when (b) and (c) have a SNR = 30 dB and (d) and (e) have a SNR = 10 dB .

Fig. 15
Fig. 15

Numerical assessment (separate cylinders: l = 6 λ , V = 60 , M = 60 , τ square = 1.2 , τ L = 0.6 , SNR = 10 dB ). (a) Actual distribution and dielectric profiles reconstructed with (b) the SOM and (c) the adaptive IMSA-SOM.

Tables (2)

Tables Icon

Table 1 Numerical Assessment ( V = 24 , M = 24 , α = 0.7 , T 0 = 50 ): Reconstruction Errors and Computational Indices

Tables Icon

Table 2 Performance Assessment ( l = 6 λ , V = 60 , M = 60 , α = 0.7 , T 0 = 50 , SNR = 10 dB ): Reconstruction Errors and Computational Indices

Equations (22)

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E v scatt ( r m ) = k 0 2 Ω J v ( r ) G ( r m / r ) d r , v = 1 , V ; m = 1 , , M ,
τ ( r ) E v inc ( r ) = J v ( r ) k 0 2 τ ( r ) Ω J v ( r ) G ( r / r ) d r , v = 1 , V ; r D .
E v scatt ( r m v ) = p = 1 N I v ( r p ( s ) ) g ( r m v , r p ( s ) ) d r , v = 1 , V ; m = 1 , , M ,
ξ n ( s ) E v inc ( r n ( s ) ) = I v ( r n ( s ) ) ξ n ( s ) p = 1 N I v ( r p ( s ) ) g ( r n ( s ) , r p ( s ) ) , v = 1 , V ; n = 1 , , N ( s ) ,
ξ n ( s ) = j k 0 η 0 A n ( s ) τ ( r n ( s ) ) ,
I v ( s ) = Ξ ( s ) ( { E v inc } ( s ) + H ( s ) I v ( s ) ) , v = 1 , , V ,
E v scatt = G ( s ) I v ( s ) , v = 1 , , V ,
G ( s ) = U ( s ) X ( s ) ( V ( s ) ) H ,
I v ( s ) = { I v det } ( s ) + { I v amb } ( s ) , v = 1 , , V ,
{ I v det } ( s ) = V det ( s ) ( X det ( s ) ) 1 ( U det ( s ) ) H E v scatt ,
{ I v amb } ( s ) = V amb ( s ) a v ( s ) .
Δ data ( s ) ( a v ( s ) , Ξ ( s ) ) = v = 1 V ( G ( s ) V amb ( s ) a v ( s ) + G ( s ) { I v det } ( s ) E v scatt 2 E v scatt 2 ) ,
Δ state ( s ) ( a v ( s ) , Ξ ( s ) ) = v = 1 V ( ( V amb ( s ) Ξ ( s ) H ( s ) V amb ( s ) ) a v ( s ) Ξ ( s ) ( { E v inc } ( s ) + H ( s ) { I v det } ( s ) ) + { I v det } ( s ) 2 { I v det } ( s ) 2 ) .
F ( s ) ( a v ( s ) , Ξ ( s ) ) Δ data ( s ) ( a v ( s ) , Ξ ( s ) ) + Δ state ( s ) ( a v ( s ) , Ξ ( s ) ) .
a v ( s ) | t + 1 = a v ( s ) | t + δ v ( s ) | t h v ( s ) | t .
h v ( s ) | t = F ( s ) ( a v ( s ) | t , Ξ ( s ) | t ) + h v ( s ) | t 1 Re [ ( F ( s ) ( a v ( s ) | t , Ξ ( s ) | t ) F ( s ) ( a v ( s ) | t 1 , Ξ ( s ) | t 1 ) ) * ] F ( s ) ( a v ( s ) | t , Ξ ( s ) | t ) 2
ξ n ( s ) | t + 1 = { v = 1 V [ E v tot ( r n ( s ) ) | t + 1 ] * [ I v ( r n ( s ) ) | t + 1 ] { I v det } ( s ) 2 } / { v = 1 V E v tot ( r n ( s ) ) | t + 1 2 { I v det } ( s ) 2 } ,
τ ˜ ( r n ( s ) ) = j η 0 k 0 ξ n ( s ) | t = T ( s ) A ( D n ( s ) ) , n = 1 , , N ( s ) ,
{ I ˜ v amb } ( s ) = V amb ( s ) a v ( s ) | t = T ( s ) , v = 1 , , V .
L NA ( s ) = L 0 s = 1 , , S .
L A ( s ) = arg { min L ( s ) [ m = 1 L ( s ) ( χ m ( s ) ) m = 1 M ( χ m ( s ) ) α ] } , subject to     m = 1 L ( s ) ( χ m ( s ) ) m = 1 M ( χ m ( s ) ) α > 0 , s = 1 , , S ,
Ψ R = 1 A ( D R ) D R | τ ˜ ( r ) τ ( r ) | | τ ( r ) + 1 | d r , R = tot , ext , int,

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