Abstract

We introduce a new imaging technique that integrates the inexact Newton method into a multifocusing scheme within the contrast-source formulation of the inverse scattering problem. Representative results from an extensive validation concerned with both synthetic and experimental scattering data are reported to assess, also through comparisons, advantages and limitations of the proposed approach in terms of accuracy, robustness, and computational efficiency.

© 2012 Optical Society of America

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  1. D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory (Springer-Verlag, 1998).
  2. G. C. Giakos, M. Pastorino, F. Russo, S. Chiwdhury, N. Shah, and W. Davros, “Noninvasive imaging for the new century,” IEEE Instrum. Meas. Mag. 2 (2), 32–35 (1999).
    [CrossRef]
  3. R. Zoughi, Microwave Nondestructive Testing and Evaluation (Kluwer Academic, 2000).
  4. D. Lesselier and J. Bowler, “Foreword to the special section on electromagnetic and ultrasonic nondestructive evaluation,” Inverse Probl. 18 (2002).
    [CrossRef]
  5. S. Kharkovsky and R. Zoughi, “Microwave and millimeter wave nondestructive testing and evaluation—overview and recent advances,” IEEE Instrum. Meas. Mag. 10(2), 26–38 (2007).
    [CrossRef]
  6. O. Dorn and D. Lesselier, “Introduction to the special issue on electromagnetic inverse problems: emerging methods and novel applications,” Inverse Probl. 26, 070201 (2010).
    [CrossRef]
  7. C.-C. Chen, J. T. Johnson, M. Sato, and A. G. Yarovoy, “Foreword to the special issue on subsurface sensing using ground-penetrating radar,” IEEE Trans. Geosci. Remote Sens. 45, 2419–2421 (2007).
    [CrossRef]
  8. E. Bermani, A. Boni, S. Caorsi, and A. Massa, “An innovative real-time technique for buried object detection,” IEEE Trans. Geosci. Remote Sens. 41, 927–931 (2003).
    [CrossRef]
  9. A. Baussard, E. L. Miller, and D. Lesselier, “Adaptive multiscale reconstruction of buried objects,” Inverse Probl. 20, S1–S15 (2004).
    [CrossRef]
  10. A. Massa, M. Pastorino, and A. Randazzo, “Reconstruction of two-dimensional buried objects by a hybrid differential evolution method,” Inverse Probl. 20, S135–S150 (2004).
    [CrossRef]
  11. C.-H. Kuo and M. Moghaddam, “Electromagnetic scattering from a buried cylinder in layered media with rough interfaces,” IEEE Trans. Antennas Propag. 54, 2392–2401 (2006).
    [CrossRef]
  12. A. Bréard, G. Perrusson, and D. Lesselier, “Hybrid differential evolution and retrieval of buried spheres in subsoil,” IEEE Geosci. Remote Sens. Lett. 5, 788–792 (2008).
    [CrossRef]
  13. M. El-Shenawee, O. Dorn, and M. Moscoso, “An adjoint-field technique for shape reconstruction of 3-D penetrable object immersed in lossy medium,” IEEE Trans. Antennas Propag. 57, 520–534 (2009).
    [CrossRef]
  14. A. Tabatabaeenejad and M. Moghaddam, “Inversion of subsurface properties of layered dielectric structures with random slightly rough interfaces using the method of simulated annealing,” IEEE Trans. Geosci. Remote Sens. 47, 2035–2046 (2009).
    [CrossRef]
  15. 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. Microw. Theory Technol. 48, 1841–1853 (2000).
    [CrossRef]
  16. S. Caorsi, A. Massa, and M. Pastorino, “Numerical assessment concerning a focused microwave diagnostic method for medical applications,” IEEE Trans. Microw. Theory Technol. 48, 1815–1830 (2000).
    [CrossRef]
  17. Z. Q. Zhang and Q. H. Liu, “Three-dimensional nonlinear image reconstruction for microwave biomedical imaging,” IEEE Trans. Biomed. Eng. 51, 544–548 (2004).
    [CrossRef]
  18. M. El-Shenawee and E. Miller, “Spherical harmonics microwave algorithm for shape and location reconstruction of breast cancer tumors,” IEEE Trans. Med. Imag. 25, 1258–1271(2006).
    [CrossRef]
  19. T. Rubk, P. M. Meaney, P. Meincke, and K. D. Paulsen, “Nonlinear microwave imaging for breast-cancer screening using Gauss–Newton’s method and the CGLS inversion algorithm,” IEEE Trans. Antennas Propag. 55, 2320–2331 (2007).
    [CrossRef]
  20. H. Zhou, T. Takenaka, J. Johnson, and T. Tanaka, “Breast imaging model using microwaves and a time domain three dimensional reconstruction method,” Progr. Electromagn. Res. 93, 57–70 (2009).
    [CrossRef]
  21. J. E. Johnson, T. Takenaka, K. Ping, S. Honda, and T. Tanaka, “Advances in the 3-D forward-backward time-stepping (FBTS) inverse scattering technique for breast cancer detection,” IEEE Trans. Biomed. Eng. 56, 2232–2243 (2009).
    [CrossRef]
  22. G. Bozza and M. Brignone, “Application of the no-sampling linear sampling method to breast cancer detection,” IEEE Trans. Biomed. Eng. 57, 2525–2534 (2010).
    [CrossRef]
  23. M. A. Ali and M. Moghaddam, “3D nonlinear super-resolution microwave inversion technique using time-domain data,” IEEE Trans. Antennas Propag. 58, 2327–2336 (2010).
    [CrossRef]
  24. J. D. Shea, P. Kosmas, B. D. Van Veen, and S. C. Hagness, “Contrast-enhanced microwave imaging of breast tumors: a computational study using 3D realistic numerical phantoms,” Inverse Probl. 26, 074009 (2010).
    [CrossRef]
  25. G. Bellizzi, O. Bucci, and I. Catapano, “Microwave cancer imaging exploiting magnetic nanoparticles as contrast agent,” IEEE Trans. Biomed. Eng. 58, 2528–2536 (2011).
    [CrossRef]
  26. H. Harada, D. J. N. Wall, T. Takenaka, and T. Tanaka, “Conjugate gradient method applied to inverse scattering problems,” IEEE Trans. Antennas Propag. 43, 784–792 (1995).
    [CrossRef]
  27. P. M. van Den Berg and A. Abubakar, “Contrast source inversion method: state of the art,” Progr. Electromagn. Res. 34, 189–218 (2001).
    [CrossRef]
  28. 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]
  29. T. M. Habashy and A. Abubakar, “A general framework for constraint minimization for the inversion of electromagnetic measurements,” Progr. Electromagn. Res. 46, 265–312 (2004).
    [CrossRef]
  30. M. Pastorino, “Stochastic optimization methods applied to microwave imaging: a review,” IEEE Trans. Antennas Propag. 55, 538–548 (2007).
    [CrossRef]
  31. I. T. Rekanos, “Shape reconstruction of a perfectly conducting scatterer using differential evolution and particle swarm optimization,” IEEE Trans. Geosci. Remote Sens. 46, 1967–1974 (2008).
    [CrossRef]
  32. A. Semnani, M. Kamyab, and I. T. Rekanos, “Reconstruction of one-dimensional dielectric scatterers using differential evolution and particle swarm optimization,” IEEE Geosci. Remote Sens. Lett. 6, 671–675 (2009).
    [CrossRef]
  33. 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]
  34. A. Semnani, I. T. Rekanos, M. Kamyab, and T. G. Papadopoulos, “Two-dimensional microwave imaging based on hybrid scatterer representation and differential evolution,” IEEE Trans. Antennas Propag. 58, 3289–3298 (2010).
    [CrossRef]
  35. P. Rocca, G. Oliveri, and A. Massa, “Differential evolution as applied to electromagnetics,” IEEE Antennas Propag. Mag. 53(1), 38–49 (2011).
    [CrossRef]
  36. O. Dorn and D. Lesselier, “Level set methods for inverse scattering,” Inverse Probl. 22, R67–R131 (2006).
    [CrossRef]
  37. A. Litman, D. Lesselier, and F. Santosa, “Reconstruction of a two-dimensional binary obstacle by controlled evolution of a level-set,” Inverse Probl. 14, 685–706 (1998).
    [CrossRef]
  38. R. Ferraye, J. Y. Dauvignac, and Ch. Pichot, “Reconstruction of complex and multiple shape object contours using a level set method,” J. Electromagn. Waves Appl. 17, 153–181 (2003).
    [CrossRef]
  39. R. Ferraye, J. Y. Dauvignac, and Ch. Pichot, “An inverse scattering method based on contour deformations by means of a level set method using frequency hopping technique,” IEEE Trans. Antennas Propag. 51, 1100–1113 (2003).
    [CrossRef]
  40. M. R. Hajihashemi and M. El-Shenawee, “Shape reconstruction using the level set method for microwave applications,” IEEE Antennas Wirel. Propag. Lett. 7, 92–96 (2008).
    [CrossRef]
  41. 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]
  42. M. R. Hajihashemi and M. El-Shenawee, “Inverse scattering of three-dimensional PEC objects using the level-set method,” Progr. Electromagn. Res. 116, 23–47 (2011).
    [CrossRef]
  43. M. R. Hajihashemi and M. El-Shenawee, “Level set algorithm for shape reconstruction of nonoverlapping three-dimensional penetrable targets,” IEEE Trans. Geosci. Remote Sens. 50, 75–86 (2012).
    [CrossRef]
  44. D. Colton, H. Haddar, and M. Piana, “The linear sampling method in inverse electromagnetic scattering theory,” Inverse Probl. 19, S105–S137 (2003).
    [CrossRef]
  45. I. Catapano, L. Crocco, and T. Isernia, “On simple methods for shape reconstruction of unknown scatterers,” IEEE Trans. Antennas Propag. 55, 1431–1436 (2007).
    [CrossRef]
  46. R. Aramini, G. Caviglia, A. Massa, and M. Piana, “The linear sampling method and energy conservation,” Inverse Probl. 26, 055004 (2010).
    [CrossRef]
  47. X. Zhang, H. Tortel, S. Ruy, and A. Litman, “Microwave imaging of soil water diffusion using the linear sampling method,” IEEE Geosci. Remote Sens. Lett. 8, 421–425 (2011).
    [CrossRef]
  48. A. Franchois and C. Pichot, “Microwave imaging-complex permittivity reconstruction with a Levenberg–Marquardt method,” IEEE Trans. Antennas Propag. 45, 203–215 (1997).
    [CrossRef]
  49. X. Chen, “Signal-subspace method approach to the intensity-only electromagnetic inverse scattering problem,” J. Opt. Soc. Am. A 25, 2018–2024 (2008).
    [CrossRef]
  50. X. Chen, “Application of signal-subspace and optimization methods in reconstructing extended scatterers,” J. Opt. Soc. Am. A26, 1022–1026 (2009).
    [CrossRef]
  51. 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]
  52. 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]
  53. 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]
  54. G. Oliveri, Y. Zhong, X. Chen, and A. Massa, “Multiresolution subspace-based optimization method for inverse scattering problems,” J. Opt. Soc. Am. A 28, 2057–2069 (2011).
    [CrossRef]
  55. J. De Zaeytijd, A. Franchois, C. Eyraud, and J.-M. Geffrin, “Full-wave three-dimensional microwave imaging with a regularized Gauss-Newton method: theory and experiment,” IEEE Trans. Antennas Propag. 55, 3279–3292 (2007).
    [CrossRef]
  56. C. Gilmore, P. Mojabi, and J. LoVetri, “Comparison of an enhanced distorted Born iterative method and the multiplicative-regularized contrast source inversion method,“ IEEE Trans. Antennas Propag. 57, 2341–2351 (2009).
    [CrossRef]
  57. C. Eyraud, J. Geffrin, and A. Litman, “3D-aggregate quantitative imaging: experimental results and polarization effects,” IEEE Trans. Antennas Propag. 59, 1237–1244 (2011).
    [CrossRef]
  58. O. Bucci, N. Cardace, L. Crocco, and T. Isernia, “Degree of nonlinearity and a new solution procedure in scalar two-dimensional inverse scattering problems,” J. Opt. Soc. Am. A 18, 1832–1843 (2001).
    [CrossRef]
  59. 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]
  60. P. Lobel, L. Blanc-Feraud, C. Pichot, and M. Barlaud, “A new regularization scheme for inverse scattering,” Inverse Probl. 13, 403–410 (1997).
    [CrossRef]
  61. P. Mojabi and J. LoVetri, “Overview and classification of some regularization techniques for the Gauss–Newton inversion method applied to inverse scattering problems,” IEEE Trans. Antennas Propag. 57, 2658–2665 (2009).
    [CrossRef]
  62. R. Autieri, G. Ferraiuolo, and V. Pascazio, “Bayesian regularization in nonlinear imaging: reconstructions from experimental data in nonlinearized microwave tomography,” IEEE Trans. Geosci. Remote Sens. 49, 801–813 (2011).
    [CrossRef]
  63. A. Zakaria and J. LoVetri, “Application of multiplicative regularization to the finite element contrast source inversion method,” IEEE Trans. Antennas Propag. 59, 3495–3498 (2011).
    [CrossRef]
  64. L. Landweber, “An iteration formula for Fredholm integral equations of the first kind,” Am. J. Math. 73, 615–624 (1951).
    [CrossRef]
  65. 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. Imag. 18, 1108–1114 (1999).
    [CrossRef]
  66. C. Estatico, G. Bozza, A. Massa, M. Pastorino, and A. Randazzo, “A two-step iterative inexact-Newton method for electromagnetic imaging of dielectric structures from real data,” Inverse Probl. 21, S81–S94 (2005).
    [CrossRef]
  67. G. Bozza, C. Estatico, M. Pastorino, and A. Randazzo, “An inexact Newton method for microwave reconstruction of strong scatterers,” IEEE Antennas Wirel. Propag. Lett. 5, 61–64 (2006).
    [CrossRef]
  68. G. Bozza, C. Estatico, A. Massa, M. Pastorino, and A. Randazzo, “Short-range image-based method for the inspection of strong scatterers using microwaves,” IEEE Trans. Instrum. Meas. 56, 1181–1188 (2007).
    [CrossRef]
  69. G. Oliveri, L. Lizzi, M. Pastorino, and A. Massa, “A nested multi-scaling inexact-Newton iterative approach for microwave imaging,” IEEE Trans. Antennas Propag. 60, 971–983 (2012).
    [CrossRef]
  70. G. Oliveri, A. Randazzo, M. Pastorino, and A. Massa, “Imaging of separate scatterers by means of a multiscaling multiregion inexact-Newton approach,” Progr. Electromagn. Res. 18, 247–257 (2011).
    [CrossRef]
  71. G. Oliveri, A. Randazzo, M. Pastorino, and A. Massa, “Electromagnetic inversion with the multiscaling inexact Newton method—experimental validation,” Microw. Opt. Technol. Lett. 53, 2834–2838 (2011).
    [CrossRef]
  72. S. Caorsi, M. Donelli, D. Franceschini, and A. Massa, “A new methodology based on an iterative multiscaling for microwave imaging,” IEEE Trans. Microw. Theory Technol. 51, 1162–1173 (2003).
    [CrossRef]
  73. S. Caorsi, M. Donelli, and A. Massa, “Detection, location, and imaging of multiple scatterers by means of the iterative multiscaling method,” IEEE Trans. Microw. Theory Technol. 52, 1217–1228 (2004).
    [CrossRef]
  74. G. Franceschini, D. Franceschini, and A. Massa, “Full-vectorial three-dimensional microwave imaging through the iterative multi-scaling strategy—a preliminary assessment,” IEEE Geosci. Remote Sens. Lett. 2, 428–432 (2005).
    [CrossRef]
  75. O. M. Bucci and G. Franceschetti, “On the degrees of freedom of scattered fields,” IEEE Trans. Antennas Propag. 37, 918–926 (1989).
    [CrossRef]
  76. G. Bozza and M. Pastorino, “An inexact Newton-based approach to microwave imaging within the contrast source formulation,” IEEE Trans. Antennas Propag. 57, 1122–1132 (2009).
    [CrossRef]
  77. A time-dependence ej2πft, f being the working frequency, is assumed and omitted hereinafter.
  78. D. Franceschini, A. Massa, M. Pastorino, and A. Zanetti, “Multi-resolution iterative inversion of real inhomogeneous targets,” Inverse Probl. 21, S51–S64 (2005).
    [CrossRef]
  79. J. H. Richmond, “Scattering by a dielectric cylinder of arbitrary cross shape,” IEEE Trans. Antennas Propag. 13, 334–341 (1965).
    [CrossRef]
  80. K. Belkebir and M. Saillard, Special Section: “Testing inversion algorithms against experimental data,” Inverse Probl. 17, 1565–1571 (2001).
    [CrossRef]

2012 (2)

M. R. Hajihashemi and M. El-Shenawee, “Level set algorithm for shape reconstruction of nonoverlapping three-dimensional penetrable targets,” IEEE Trans. Geosci. Remote Sens. 50, 75–86 (2012).
[CrossRef]

G. Oliveri, L. Lizzi, M. Pastorino, and A. Massa, “A nested multi-scaling inexact-Newton iterative approach for microwave imaging,” IEEE Trans. Antennas Propag. 60, 971–983 (2012).
[CrossRef]

2011 (10)

G. Oliveri, A. Randazzo, M. Pastorino, and A. Massa, “Imaging of separate scatterers by means of a multiscaling multiregion inexact-Newton approach,” Progr. Electromagn. Res. 18, 247–257 (2011).
[CrossRef]

G. Oliveri, A. Randazzo, M. Pastorino, and A. Massa, “Electromagnetic inversion with the multiscaling inexact Newton method—experimental validation,” Microw. Opt. Technol. Lett. 53, 2834–2838 (2011).
[CrossRef]

M. R. Hajihashemi and M. El-Shenawee, “Inverse scattering of three-dimensional PEC objects using the level-set method,” Progr. Electromagn. Res. 116, 23–47 (2011).
[CrossRef]

X. Zhang, H. Tortel, S. Ruy, and A. Litman, “Microwave imaging of soil water diffusion using the linear sampling method,” IEEE Geosci. Remote Sens. Lett. 8, 421–425 (2011).
[CrossRef]

R. Autieri, G. Ferraiuolo, and V. Pascazio, “Bayesian regularization in nonlinear imaging: reconstructions from experimental data in nonlinearized microwave tomography,” IEEE Trans. Geosci. Remote Sens. 49, 801–813 (2011).
[CrossRef]

A. Zakaria and J. LoVetri, “Application of multiplicative regularization to the finite element contrast source inversion method,” IEEE Trans. Antennas Propag. 59, 3495–3498 (2011).
[CrossRef]

G. Bellizzi, O. Bucci, and I. Catapano, “Microwave cancer imaging exploiting magnetic nanoparticles as contrast agent,” IEEE Trans. Biomed. Eng. 58, 2528–2536 (2011).
[CrossRef]

P. Rocca, G. Oliveri, and A. Massa, “Differential evolution as applied to electromagnetics,” IEEE Antennas Propag. Mag. 53(1), 38–49 (2011).
[CrossRef]

C. Eyraud, J. Geffrin, and A. Litman, “3D-aggregate quantitative imaging: experimental results and polarization effects,” IEEE Trans. Antennas Propag. 59, 1237–1244 (2011).
[CrossRef]

G. Oliveri, Y. Zhong, X. Chen, and A. Massa, “Multiresolution subspace-based optimization method for inverse scattering problems,” J. Opt. Soc. Am. A 28, 2057–2069 (2011).
[CrossRef]

2010 (9)

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]

G. Bozza and M. Brignone, “Application of the no-sampling linear sampling method to breast cancer detection,” IEEE Trans. Biomed. Eng. 57, 2525–2534 (2010).
[CrossRef]

M. A. Ali and M. Moghaddam, “3D nonlinear super-resolution microwave inversion technique using time-domain data,” IEEE Trans. Antennas Propag. 58, 2327–2336 (2010).
[CrossRef]

J. D. Shea, P. Kosmas, B. D. Van Veen, and S. C. Hagness, “Contrast-enhanced microwave imaging of breast tumors: a computational study using 3D realistic numerical phantoms,” Inverse Probl. 26, 074009 (2010).
[CrossRef]

O. Dorn and D. Lesselier, “Introduction to the special issue on electromagnetic inverse problems: emerging methods and novel applications,” Inverse Probl. 26, 070201 (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]

A. Semnani, I. T. Rekanos, M. Kamyab, and T. G. Papadopoulos, “Two-dimensional microwave imaging based on hybrid scatterer representation and differential evolution,” IEEE Trans. Antennas Propag. 58, 3289–3298 (2010).
[CrossRef]

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

2009 (11)

X. Chen, “Application of signal-subspace and optimization methods in reconstructing extended scatterers,” J. Opt. Soc. Am. A26, 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. 57, 1122–1132 (2009).
[CrossRef]

P. Mojabi and J. LoVetri, “Overview and classification of some regularization techniques for the Gauss–Newton inversion method applied to inverse scattering problems,” IEEE Trans. Antennas Propag. 57, 2658–2665 (2009).
[CrossRef]

M. El-Shenawee, O. Dorn, and M. Moscoso, “An adjoint-field technique for shape reconstruction of 3-D penetrable object immersed in lossy medium,” IEEE Trans. Antennas Propag. 57, 520–534 (2009).
[CrossRef]

A. Tabatabaeenejad and M. Moghaddam, “Inversion of subsurface properties of layered dielectric structures with random slightly rough interfaces using the method of simulated annealing,” IEEE Trans. Geosci. Remote Sens. 47, 2035–2046 (2009).
[CrossRef]

H. Zhou, T. Takenaka, J. Johnson, and T. Tanaka, “Breast imaging model using microwaves and a time domain three dimensional reconstruction method,” Progr. Electromagn. Res. 93, 57–70 (2009).
[CrossRef]

J. E. Johnson, T. Takenaka, K. Ping, S. Honda, and T. Tanaka, “Advances in the 3-D forward-backward time-stepping (FBTS) inverse scattering technique for breast cancer detection,” IEEE Trans. Biomed. Eng. 56, 2232–2243 (2009).
[CrossRef]

A. Semnani, M. Kamyab, and I. T. Rekanos, “Reconstruction of one-dimensional dielectric scatterers using differential evolution and particle swarm optimization,” IEEE Geosci. Remote Sens. Lett. 6, 671–675 (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]

C. Gilmore, P. Mojabi, and J. LoVetri, “Comparison of an enhanced distorted Born iterative method and the multiplicative-regularized contrast source inversion method,“ IEEE Trans. Antennas Propag. 57, 2341–2351 (2009).
[CrossRef]

2008 (4)

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

I. T. Rekanos, “Shape reconstruction of a perfectly conducting scatterer using differential evolution and particle swarm optimization,” IEEE Trans. Geosci. Remote Sens. 46, 1967–1974 (2008).
[CrossRef]

A. Bréard, G. Perrusson, and D. Lesselier, “Hybrid differential evolution and retrieval of buried spheres in subsoil,” IEEE Geosci. Remote Sens. Lett. 5, 788–792 (2008).
[CrossRef]

M. R. Hajihashemi and M. El-Shenawee, “Shape reconstruction using the level set method for microwave applications,” IEEE Antennas Wirel. Propag. Lett. 7, 92–96 (2008).
[CrossRef]

2007 (7)

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

J. De Zaeytijd, A. Franchois, C. Eyraud, and J.-M. Geffrin, “Full-wave three-dimensional microwave imaging with a regularized Gauss-Newton method: theory and experiment,” IEEE Trans. Antennas Propag. 55, 3279–3292 (2007).
[CrossRef]

G. Bozza, C. Estatico, A. Massa, M. Pastorino, and A. Randazzo, “Short-range image-based method for the inspection of strong scatterers using microwaves,” IEEE Trans. Instrum. Meas. 56, 1181–1188 (2007).
[CrossRef]

T. Rubk, P. M. Meaney, P. Meincke, and K. D. Paulsen, “Nonlinear microwave imaging for breast-cancer screening using Gauss–Newton’s method and the CGLS inversion algorithm,” IEEE Trans. Antennas Propag. 55, 2320–2331 (2007).
[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,” 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(2), 26–38 (2007).
[CrossRef]

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

2006 (4)

O. Dorn and D. Lesselier, “Level set methods for inverse scattering,” Inverse Probl. 22, R67–R131 (2006).
[CrossRef]

C.-H. Kuo and M. Moghaddam, “Electromagnetic scattering from a buried cylinder in layered media with rough interfaces,” IEEE Trans. Antennas Propag. 54, 2392–2401 (2006).
[CrossRef]

M. El-Shenawee and E. Miller, “Spherical harmonics microwave algorithm for shape and location reconstruction of breast cancer tumors,” IEEE Trans. Med. Imag. 25, 1258–1271(2006).
[CrossRef]

G. Bozza, C. Estatico, M. Pastorino, and A. Randazzo, “An inexact Newton method for microwave reconstruction of strong scatterers,” IEEE Antennas Wirel. Propag. Lett. 5, 61–64 (2006).
[CrossRef]

2005 (3)

C. Estatico, G. Bozza, A. Massa, M. Pastorino, and A. Randazzo, “A two-step iterative inexact-Newton method for electromagnetic imaging of dielectric structures from real data,” Inverse Probl. 21, S81–S94 (2005).
[CrossRef]

D. Franceschini, A. Massa, M. Pastorino, and A. Zanetti, “Multi-resolution iterative inversion of real inhomogeneous targets,” Inverse Probl. 21, S51–S64 (2005).
[CrossRef]

G. Franceschini, D. Franceschini, and A. Massa, “Full-vectorial three-dimensional microwave imaging through the iterative multi-scaling strategy—a preliminary assessment,” IEEE Geosci. Remote Sens. Lett. 2, 428–432 (2005).
[CrossRef]

2004 (5)

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

Z. Q. Zhang and Q. H. Liu, “Three-dimensional nonlinear image reconstruction for microwave biomedical imaging,” IEEE Trans. Biomed. Eng. 51, 544–548 (2004).
[CrossRef]

A. Baussard, E. L. Miller, and D. Lesselier, “Adaptive multiscale reconstruction of buried objects,” Inverse Probl. 20, S1–S15 (2004).
[CrossRef]

A. Massa, M. Pastorino, and A. Randazzo, “Reconstruction of two-dimensional buried objects by a hybrid differential evolution method,” Inverse Probl. 20, S135–S150 (2004).
[CrossRef]

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

2003 (6)

R. Ferraye, J. Y. Dauvignac, and Ch. Pichot, “Reconstruction of complex and multiple shape object contours using a level set method,” J. Electromagn. Waves Appl. 17, 153–181 (2003).
[CrossRef]

R. Ferraye, J. Y. Dauvignac, and Ch. Pichot, “An inverse scattering method based on contour deformations by means of a level set method using frequency hopping technique,” IEEE Trans. Antennas Propag. 51, 1100–1113 (2003).
[CrossRef]

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

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

D. Colton, H. Haddar, and M. Piana, “The linear sampling method in inverse electromagnetic scattering theory,” Inverse Probl. 19, S105–S137 (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 (2002).
[CrossRef]

2001 (4)

P. M. van Den Berg and A. Abubakar, “Contrast source inversion method: state of the art,” Progr. Electromagn. Res. 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]

K. Belkebir and M. Saillard, Special Section: “Testing inversion algorithms against experimental data,” Inverse Probl. 17, 1565–1571 (2001).
[CrossRef]

O. Bucci, N. Cardace, L. Crocco, and T. Isernia, “Degree of nonlinearity and a new solution procedure in scalar two-dimensional inverse scattering problems,” J. Opt. Soc. Am. A 18, 1832–1843 (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. Microw. Theory Technol. 48, 1841–1853 (2000).
[CrossRef]

S. Caorsi, A. Massa, and M. Pastorino, “Numerical assessment concerning a focused microwave diagnostic method for medical applications,” IEEE Trans. Microw. Theory Technol. 48, 1815–1830 (2000).
[CrossRef]

1999 (2)

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

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. Imag. 18, 1108–1114 (1999).
[CrossRef]

1998 (1)

A. Litman, D. Lesselier, and F. Santosa, “Reconstruction of a two-dimensional binary obstacle by controlled evolution of a level-set,” Inverse Probl. 14, 685–706 (1998).
[CrossRef]

1997 (2)

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

A. Franchois and C. Pichot, “Microwave imaging-complex permittivity reconstruction with a Levenberg–Marquardt method,” IEEE Trans. Antennas Propag. 45, 203–215 (1997).
[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. 43, 784–792 (1995).
[CrossRef]

1989 (1)

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

1965 (1)

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

1951 (1)

L. Landweber, “An iteration formula for Fredholm integral equations of the first kind,” Am. J. Math. 73, 615–624 (1951).
[CrossRef]

Abubakar, A.

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

P. M. van Den Berg and A. Abubakar, “Contrast source inversion method: state of the art,” Progr. Electromagn. Res. 34, 189–218 (2001).
[CrossRef]

Agarwal, K.

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]

Ali, M. A.

M. A. Ali and M. Moghaddam, “3D nonlinear super-resolution microwave inversion technique using time-domain data,” IEEE Trans. Antennas Propag. 58, 2327–2336 (2010).
[CrossRef]

Aramini, R.

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

Autieri, R.

R. Autieri, G. Ferraiuolo, and V. Pascazio, “Bayesian regularization in nonlinear imaging: reconstructions from experimental data in nonlinearized microwave tomography,” IEEE Trans. Geosci. Remote Sens. 49, 801–813 (2011).
[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]

Baussard, A.

A. Baussard, E. L. Miller, and D. Lesselier, “Adaptive multiscale reconstruction of buried objects,” Inverse Probl. 20, S1–S15 (2004).
[CrossRef]

Belkebir, K.

K. Belkebir and M. Saillard, Special Section: “Testing inversion algorithms against experimental data,” Inverse Probl. 17, 1565–1571 (2001).
[CrossRef]

Bellizzi, G.

G. Bellizzi, O. Bucci, and I. Catapano, “Microwave cancer imaging exploiting magnetic nanoparticles as contrast agent,” IEEE Trans. Biomed. Eng. 58, 2528–2536 (2011).
[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]

Bermani, E.

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

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]

Boni, A.

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

Bowler, J.

D. Lesselier and J. Bowler, “Foreword to the special section on electromagnetic and ultrasonic nondestructive evaluation,” Inverse Probl. 18 (2002).
[CrossRef]

Bozza, G.

G. Bozza and M. Brignone, “Application of the no-sampling linear sampling method to breast cancer detection,” IEEE Trans. Biomed. Eng. 57, 2525–2534 (2010).
[CrossRef]

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

G. Bozza, C. Estatico, A. Massa, M. Pastorino, and A. Randazzo, “Short-range image-based method for the inspection of strong scatterers using microwaves,” IEEE Trans. Instrum. Meas. 56, 1181–1188 (2007).
[CrossRef]

G. Bozza, C. Estatico, M. Pastorino, and A. Randazzo, “An inexact Newton method for microwave reconstruction of strong scatterers,” IEEE Antennas Wirel. Propag. Lett. 5, 61–64 (2006).
[CrossRef]

C. Estatico, G. Bozza, A. Massa, M. Pastorino, and A. Randazzo, “A two-step iterative inexact-Newton method for electromagnetic imaging of dielectric structures from real data,” Inverse Probl. 21, S81–S94 (2005).
[CrossRef]

Bréard, A.

A. Bréard, G. Perrusson, and D. Lesselier, “Hybrid differential evolution and retrieval of buried spheres in subsoil,” IEEE Geosci. Remote Sens. Lett. 5, 788–792 (2008).
[CrossRef]

Brignone, M.

G. Bozza and M. Brignone, “Application of the no-sampling linear sampling method to breast cancer detection,” IEEE Trans. Biomed. Eng. 57, 2525–2534 (2010).
[CrossRef]

Bucci, O.

G. Bellizzi, O. Bucci, and I. Catapano, “Microwave cancer imaging exploiting magnetic nanoparticles as contrast agent,” IEEE Trans. Biomed. Eng. 58, 2528–2536 (2011).
[CrossRef]

O. Bucci, N. Cardace, L. Crocco, and T. Isernia, “Degree of nonlinearity and a new solution procedure in scalar two-dimensional inverse scattering problems,” J. Opt. Soc. Am. A 18, 1832–1843 (2001).
[CrossRef]

Bucci, O. M.

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

Caorsi, S.

S. Caorsi, M. Donelli, and A. Massa, “Detection, location, and imaging of multiple scatterers by means of the iterative multiscaling method,” IEEE Trans. Microw. Theory Technol. 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. Microw. Theory Technol. 51, 1162–1173 (2003).
[CrossRef]

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

S. Caorsi, A. Massa, and M. Pastorino, “Numerical assessment concerning a focused microwave diagnostic method for medical applications,” IEEE Trans. Microw. Theory Technol. 48, 1815–1830 (2000).
[CrossRef]

Cardace, N.

Catapano, I.

G. Bellizzi, O. Bucci, and I. Catapano, “Microwave cancer imaging exploiting magnetic nanoparticles as contrast agent,” IEEE Trans. Biomed. Eng. 58, 2528–2536 (2011).
[CrossRef]

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

Caviglia, G.

R. Aramini, G. Caviglia, A. Massa, and M. Piana, “The linear sampling method and energy conservation,” Inverse Probl. 26, 055004 (2010).
[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,” IEEE Trans. Geosci. Remote Sens. 45, 2419–2421 (2007).
[CrossRef]

Chen, X.

G. Oliveri, Y. Zhong, X. Chen, and A. Massa, “Multiresolution subspace-based optimization method for inverse scattering problems,” J. Opt. Soc. Am. A 28, 2057–2069 (2011).
[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]

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, “Application of signal-subspace and optimization methods in reconstructing extended scatterers,” J. Opt. Soc. Am. A26, 1022–1026 (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]

Chiwdhury, S.

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

Colton, D.

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

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

Crocco, L.

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

O. Bucci, N. Cardace, L. Crocco, and T. Isernia, “Degree of nonlinearity and a new solution procedure in scalar two-dimensional inverse scattering problems,” J. Opt. Soc. Am. A 18, 1832–1843 (2001).
[CrossRef]

Dauvignac, J. Y.

R. Ferraye, J. Y. Dauvignac, and Ch. Pichot, “Reconstruction of complex and multiple shape object contours using a level set method,” J. Electromagn. Waves Appl. 17, 153–181 (2003).
[CrossRef]

R. Ferraye, J. Y. Dauvignac, and Ch. Pichot, “An inverse scattering method based on contour deformations by means of a level set method using frequency hopping technique,” IEEE Trans. Antennas Propag. 51, 1100–1113 (2003).
[CrossRef]

Davros, W.

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

De Zaeytijd, J.

J. De Zaeytijd, A. Franchois, C. Eyraud, and J.-M. Geffrin, “Full-wave three-dimensional microwave imaging with a regularized Gauss-Newton method: theory and experiment,” IEEE Trans. Antennas Propag. 55, 3279–3292 (2007).
[CrossRef]

Donelli, M.

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, and A. Massa, “Detection, location, and imaging of multiple scatterers by means of the iterative multiscaling method,” IEEE Trans. Microw. Theory Technol. 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. Microw. Theory Technol. 51, 1162–1173 (2003).
[CrossRef]

Dorn, O.

O. Dorn and D. Lesselier, “Introduction to the special issue on electromagnetic inverse problems: emerging methods and novel applications,” Inverse Probl. 26, 070201 (2010).
[CrossRef]

M. El-Shenawee, O. Dorn, and M. Moscoso, “An adjoint-field technique for shape reconstruction of 3-D penetrable object immersed in lossy medium,” IEEE Trans. Antennas Propag. 57, 520–534 (2009).
[CrossRef]

O. Dorn and D. Lesselier, “Level set methods for inverse scattering,” Inverse Probl. 22, R67–R131 (2006).
[CrossRef]

El-Shenawee, M.

M. R. Hajihashemi and M. El-Shenawee, “Level set algorithm for shape reconstruction of nonoverlapping three-dimensional penetrable targets,” IEEE Trans. Geosci. Remote Sens. 50, 75–86 (2012).
[CrossRef]

M. R. Hajihashemi and M. El-Shenawee, “Inverse scattering of three-dimensional PEC objects using the level-set method,” Progr. Electromagn. Res. 116, 23–47 (2011).
[CrossRef]

M. El-Shenawee, O. Dorn, and M. Moscoso, “An adjoint-field technique for shape reconstruction of 3-D penetrable object immersed in lossy medium,” IEEE Trans. Antennas Propag. 57, 520–534 (2009).
[CrossRef]

M. R. Hajihashemi and M. El-Shenawee, “Shape reconstruction using the level set method for microwave applications,” IEEE Antennas Wirel. Propag. Lett. 7, 92–96 (2008).
[CrossRef]

M. El-Shenawee and E. Miller, “Spherical harmonics microwave algorithm for shape and location reconstruction of breast cancer tumors,” IEEE Trans. Med. Imag. 25, 1258–1271(2006).
[CrossRef]

Estatico, C.

G. Bozza, C. Estatico, A. Massa, M. Pastorino, and A. Randazzo, “Short-range image-based method for the inspection of strong scatterers using microwaves,” IEEE Trans. Instrum. Meas. 56, 1181–1188 (2007).
[CrossRef]

G. Bozza, C. Estatico, M. Pastorino, and A. Randazzo, “An inexact Newton method for microwave reconstruction of strong scatterers,” IEEE Antennas Wirel. Propag. Lett. 5, 61–64 (2006).
[CrossRef]

C. Estatico, G. Bozza, A. Massa, M. Pastorino, and A. Randazzo, “A two-step iterative inexact-Newton method for electromagnetic imaging of dielectric structures from real data,” Inverse Probl. 21, S81–S94 (2005).
[CrossRef]

Eyraud, C.

C. Eyraud, J. Geffrin, and A. Litman, “3D-aggregate quantitative imaging: experimental results and polarization effects,” IEEE Trans. Antennas Propag. 59, 1237–1244 (2011).
[CrossRef]

J. De Zaeytijd, A. Franchois, C. Eyraud, and J.-M. Geffrin, “Full-wave three-dimensional microwave imaging with a regularized Gauss-Newton method: theory and experiment,” IEEE Trans. Antennas Propag. 55, 3279–3292 (2007).
[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. Microw. Theory Technol. 48, 1841–1853 (2000).
[CrossRef]

Ferraiuolo, G.

R. Autieri, G. Ferraiuolo, and V. Pascazio, “Bayesian regularization in nonlinear imaging: reconstructions from experimental data in nonlinearized microwave tomography,” IEEE Trans. Geosci. Remote Sens. 49, 801–813 (2011).
[CrossRef]

Ferraye, R.

R. Ferraye, J. Y. Dauvignac, and Ch. Pichot, “Reconstruction of complex and multiple shape object contours using a level set method,” J. Electromagn. Waves Appl. 17, 153–181 (2003).
[CrossRef]

R. Ferraye, J. Y. Dauvignac, and Ch. Pichot, “An inverse scattering method based on contour deformations by means of a level set method using frequency hopping technique,” IEEE Trans. Antennas Propag. 51, 1100–1113 (2003).
[CrossRef]

Franceschetti, G.

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

Franceschini, D.

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]

D. Franceschini, A. Massa, M. Pastorino, and A. Zanetti, “Multi-resolution iterative inversion of real inhomogeneous targets,” Inverse Probl. 21, S51–S64 (2005).
[CrossRef]

G. Franceschini, D. Franceschini, and A. Massa, “Full-vectorial three-dimensional microwave imaging through the iterative multi-scaling strategy—a preliminary assessment,” IEEE Geosci. Remote Sens. Lett. 2, 428–432 (2005).
[CrossRef]

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

Franceschini, G.

G. Franceschini, D. Franceschini, and A. Massa, “Full-vectorial three-dimensional microwave imaging through the iterative multi-scaling strategy—a preliminary assessment,” IEEE Geosci. Remote Sens. Lett. 2, 428–432 (2005).
[CrossRef]

Franchois, A.

J. De Zaeytijd, A. Franchois, C. Eyraud, and J.-M. Geffrin, “Full-wave three-dimensional microwave imaging with a regularized Gauss-Newton method: theory and experiment,” IEEE Trans. Antennas Propag. 55, 3279–3292 (2007).
[CrossRef]

A. Franchois and C. Pichot, “Microwave imaging-complex permittivity reconstruction with a Levenberg–Marquardt method,” IEEE Trans. Antennas Propag. 45, 203–215 (1997).
[CrossRef]

Geffrin, J.

C. Eyraud, J. Geffrin, and A. Litman, “3D-aggregate quantitative imaging: experimental results and polarization effects,” IEEE Trans. Antennas Propag. 59, 1237–1244 (2011).
[CrossRef]

Geffrin, J.-M.

J. De Zaeytijd, A. Franchois, C. Eyraud, and J.-M. Geffrin, “Full-wave three-dimensional microwave imaging with a regularized Gauss-Newton method: theory and experiment,” IEEE Trans. Antennas Propag. 55, 3279–3292 (2007).
[CrossRef]

Giakos, G. C.

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

Gilmore, C.

C. Gilmore, P. Mojabi, and J. LoVetri, “Comparison of an enhanced distorted Born iterative method and the multiplicative-regularized contrast source inversion method,“ IEEE Trans. Antennas Propag. 57, 2341–2351 (2009).
[CrossRef]

Habashy, T. M.

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

Haddar, H.

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

Hagness, S. C.

J. D. Shea, P. Kosmas, B. D. Van Veen, and S. C. Hagness, “Contrast-enhanced microwave imaging of breast tumors: a computational study using 3D realistic numerical phantoms,” Inverse Probl. 26, 074009 (2010).
[CrossRef]

Hajihashemi, M. R.

M. R. Hajihashemi and M. El-Shenawee, “Level set algorithm for shape reconstruction of nonoverlapping three-dimensional penetrable targets,” IEEE Trans. Geosci. Remote Sens. 50, 75–86 (2012).
[CrossRef]

M. R. Hajihashemi and M. El-Shenawee, “Inverse scattering of three-dimensional PEC objects using the level-set method,” Progr. Electromagn. Res. 116, 23–47 (2011).
[CrossRef]

M. R. Hajihashemi and M. El-Shenawee, “Shape reconstruction using the level set method for microwave applications,” IEEE Antennas Wirel. Propag. Lett. 7, 92–96 (2008).
[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. 43, 784–792 (1995).
[CrossRef]

Honda, S.

J. E. Johnson, T. Takenaka, K. Ping, S. Honda, and T. Tanaka, “Advances in the 3-D forward-backward time-stepping (FBTS) inverse scattering technique for breast cancer detection,” IEEE Trans. Biomed. Eng. 56, 2232–2243 (2009).
[CrossRef]

Isernia, T.

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

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. Bucci, N. Cardace, L. Crocco, and T. Isernia, “Degree of nonlinearity and a new solution procedure in scalar two-dimensional inverse scattering problems,” J. Opt. Soc. Am. A 18, 1832–1843 (2001).
[CrossRef]

Johnson, J.

H. Zhou, T. Takenaka, J. Johnson, and T. Tanaka, “Breast imaging model using microwaves and a time domain three dimensional reconstruction method,” Progr. Electromagn. Res. 93, 57–70 (2009).
[CrossRef]

Johnson, J. E.

J. E. Johnson, T. Takenaka, K. Ping, S. Honda, and T. Tanaka, “Advances in the 3-D forward-backward time-stepping (FBTS) inverse scattering technique for breast cancer detection,” IEEE Trans. Biomed. Eng. 56, 2232–2243 (2009).
[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,” IEEE Trans. Geosci. Remote Sens. 45, 2419–2421 (2007).
[CrossRef]

Kamyab, M.

A. Semnani, I. T. Rekanos, M. Kamyab, and T. G. Papadopoulos, “Two-dimensional microwave imaging based on hybrid scatterer representation and differential evolution,” IEEE Trans. Antennas Propag. 58, 3289–3298 (2010).
[CrossRef]

A. Semnani, M. Kamyab, and I. T. Rekanos, “Reconstruction of one-dimensional dielectric scatterers using differential evolution and particle swarm optimization,” IEEE Geosci. Remote Sens. Lett. 6, 671–675 (2009).
[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(2), 26–38 (2007).
[CrossRef]

Kosmas, P.

J. D. Shea, P. Kosmas, B. D. Van Veen, and S. C. Hagness, “Contrast-enhanced microwave imaging of breast tumors: a computational study using 3D realistic numerical phantoms,” Inverse Probl. 26, 074009 (2010).
[CrossRef]

Kress, R.

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

Kuo, C.-H.

C.-H. Kuo and M. Moghaddam, “Electromagnetic scattering from a buried cylinder in layered media with rough interfaces,” IEEE Trans. Antennas Propag. 54, 2392–2401 (2006).
[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]

Landweber, L.

L. Landweber, “An iteration formula for Fredholm integral equations of the first kind,” Am. J. Math. 73, 615–624 (1951).
[CrossRef]

Lesselier, D.

O. Dorn and D. Lesselier, “Introduction to the special issue on electromagnetic inverse problems: emerging methods and novel applications,” Inverse Probl. 26, 070201 (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]

A. Bréard, G. Perrusson, and D. Lesselier, “Hybrid differential evolution and retrieval of buried spheres in subsoil,” IEEE Geosci. Remote Sens. Lett. 5, 788–792 (2008).
[CrossRef]

O. Dorn and D. Lesselier, “Level set methods for inverse scattering,” Inverse Probl. 22, R67–R131 (2006).
[CrossRef]

A. Baussard, E. L. Miller, and D. Lesselier, “Adaptive multiscale reconstruction of buried objects,” Inverse Probl. 20, S1–S15 (2004).
[CrossRef]

D. Lesselier and J. Bowler, “Foreword to the special section on electromagnetic and ultrasonic nondestructive evaluation,” Inverse Probl. 18 (2002).
[CrossRef]

A. Litman, D. Lesselier, and F. Santosa, “Reconstruction of a two-dimensional binary obstacle by controlled evolution of a level-set,” Inverse Probl. 14, 685–706 (1998).
[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. Microw. Theory Technol. 48, 1841–1853 (2000).
[CrossRef]

Litman, A.

C. Eyraud, J. Geffrin, and A. Litman, “3D-aggregate quantitative imaging: experimental results and polarization effects,” IEEE Trans. Antennas Propag. 59, 1237–1244 (2011).
[CrossRef]

X. Zhang, H. Tortel, S. Ruy, and A. Litman, “Microwave imaging of soil water diffusion using the linear sampling method,” IEEE Geosci. Remote Sens. Lett. 8, 421–425 (2011).
[CrossRef]

A. Litman, D. Lesselier, and F. Santosa, “Reconstruction of a two-dimensional binary obstacle by controlled evolution of a level-set,” Inverse Probl. 14, 685–706 (1998).
[CrossRef]

Liu, Q. H.

Z. Q. Zhang and Q. H. Liu, “Three-dimensional nonlinear image reconstruction for microwave biomedical imaging,” IEEE Trans. Biomed. Eng. 51, 544–548 (2004).
[CrossRef]

Lizzi, L.

G. Oliveri, L. Lizzi, M. Pastorino, and A. Massa, “A nested multi-scaling inexact-Newton iterative approach for microwave imaging,” IEEE Trans. Antennas Propag. 60, 971–983 (2012).
[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]

LoVetri, J.

A. Zakaria and J. LoVetri, “Application of multiplicative regularization to the finite element contrast source inversion method,” IEEE Trans. Antennas Propag. 59, 3495–3498 (2011).
[CrossRef]

C. Gilmore, P. Mojabi, and J. LoVetri, “Comparison of an enhanced distorted Born iterative method and the multiplicative-regularized contrast source inversion method,“ IEEE Trans. Antennas Propag. 57, 2341–2351 (2009).
[CrossRef]

P. Mojabi and J. LoVetri, “Overview and classification of some regularization techniques for the Gauss–Newton inversion method applied to inverse scattering problems,” IEEE Trans. Antennas Propag. 57, 2658–2665 (2009).
[CrossRef]

Massa, A.

G. Oliveri, L. Lizzi, M. Pastorino, and A. Massa, “A nested multi-scaling inexact-Newton iterative approach for microwave imaging,” IEEE Trans. Antennas Propag. 60, 971–983 (2012).
[CrossRef]

G. Oliveri, Y. Zhong, X. Chen, and A. Massa, “Multiresolution subspace-based optimization method for inverse scattering problems,” J. Opt. Soc. Am. A 28, 2057–2069 (2011).
[CrossRef]

G. Oliveri, A. Randazzo, M. Pastorino, and A. Massa, “Electromagnetic inversion with the multiscaling inexact Newton method—experimental validation,” Microw. Opt. Technol. Lett. 53, 2834–2838 (2011).
[CrossRef]

P. Rocca, G. Oliveri, and A. Massa, “Differential evolution as applied to electromagnetics,” IEEE Antennas Propag. Mag. 53(1), 38–49 (2011).
[CrossRef]

G. Oliveri, A. Randazzo, M. Pastorino, and A. Massa, “Imaging of separate scatterers by means of a multiscaling multiregion inexact-Newton approach,” Progr. Electromagn. Res. 18, 247–257 (2011).
[CrossRef]

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

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]

G. Bozza, C. Estatico, A. Massa, M. Pastorino, and A. Randazzo, “Short-range image-based method for the inspection of strong scatterers using microwaves,” IEEE Trans. Instrum. Meas. 56, 1181–1188 (2007).
[CrossRef]

G. Franceschini, D. Franceschini, and A. Massa, “Full-vectorial three-dimensional microwave imaging through the iterative multi-scaling strategy—a preliminary assessment,” IEEE Geosci. Remote Sens. Lett. 2, 428–432 (2005).
[CrossRef]

D. Franceschini, A. Massa, M. Pastorino, and A. Zanetti, “Multi-resolution iterative inversion of real inhomogeneous targets,” Inverse Probl. 21, S51–S64 (2005).
[CrossRef]

C. Estatico, G. Bozza, A. Massa, M. Pastorino, and A. Randazzo, “A two-step iterative inexact-Newton method for electromagnetic imaging of dielectric structures from real data,” Inverse Probl. 21, S81–S94 (2005).
[CrossRef]

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

A. Massa, M. Pastorino, and A. Randazzo, “Reconstruction of two-dimensional buried objects by a hybrid differential evolution method,” Inverse Probl. 20, S135–S150 (2004).
[CrossRef]

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

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

S. Caorsi, A. Massa, and M. Pastorino, “Numerical assessment concerning a focused microwave diagnostic method for medical applications,” IEEE Trans. Microw. Theory Technol. 48, 1815–1830 (2000).
[CrossRef]

Meaney, P. M.

T. Rubk, P. M. Meaney, P. Meincke, and K. D. Paulsen, “Nonlinear microwave imaging for breast-cancer screening using Gauss–Newton’s method and the CGLS inversion algorithm,” IEEE Trans. Antennas Propag. 55, 2320–2331 (2007).
[CrossRef]

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. Microw. Theory Technol. 48, 1841–1853 (2000).
[CrossRef]

Meincke, P.

T. Rubk, P. M. Meaney, P. Meincke, and K. D. Paulsen, “Nonlinear microwave imaging for breast-cancer screening using Gauss–Newton’s method and the CGLS inversion algorithm,” IEEE Trans. Antennas Propag. 55, 2320–2331 (2007).
[CrossRef]

Miller, E.

M. El-Shenawee and E. Miller, “Spherical harmonics microwave algorithm for shape and location reconstruction of breast cancer tumors,” IEEE Trans. Med. Imag. 25, 1258–1271(2006).
[CrossRef]

Miller, E. L.

A. Baussard, E. L. Miller, and D. Lesselier, “Adaptive multiscale reconstruction of buried objects,” Inverse Probl. 20, S1–S15 (2004).
[CrossRef]

Moghaddam, M.

M. A. Ali and M. Moghaddam, “3D nonlinear super-resolution microwave inversion technique using time-domain data,” IEEE Trans. Antennas Propag. 58, 2327–2336 (2010).
[CrossRef]

A. Tabatabaeenejad and M. Moghaddam, “Inversion of subsurface properties of layered dielectric structures with random slightly rough interfaces using the method of simulated annealing,” IEEE Trans. Geosci. Remote Sens. 47, 2035–2046 (2009).
[CrossRef]

C.-H. Kuo and M. Moghaddam, “Electromagnetic scattering from a buried cylinder in layered media with rough interfaces,” IEEE Trans. Antennas Propag. 54, 2392–2401 (2006).
[CrossRef]

Mojabi, P.

P. Mojabi and J. LoVetri, “Overview and classification of some regularization techniques for the Gauss–Newton inversion method applied to inverse scattering problems,” IEEE Trans. Antennas Propag. 57, 2658–2665 (2009).
[CrossRef]

C. Gilmore, P. Mojabi, and J. LoVetri, “Comparison of an enhanced distorted Born iterative method and the multiplicative-regularized contrast source inversion method,“ IEEE Trans. Antennas Propag. 57, 2341–2351 (2009).
[CrossRef]

Moscoso, M.

M. El-Shenawee, O. Dorn, and M. Moscoso, “An adjoint-field technique for shape reconstruction of 3-D penetrable object immersed in lossy medium,” IEEE Trans. Antennas Propag. 57, 520–534 (2009).
[CrossRef]

Oliveri, G.

G. Oliveri, L. Lizzi, M. Pastorino, and A. Massa, “A nested multi-scaling inexact-Newton iterative approach for microwave imaging,” IEEE Trans. Antennas Propag. 60, 971–983 (2012).
[CrossRef]

G. Oliveri, Y. Zhong, X. Chen, and A. Massa, “Multiresolution subspace-based optimization method for inverse scattering problems,” J. Opt. Soc. Am. A 28, 2057–2069 (2011).
[CrossRef]

G. Oliveri, A. Randazzo, M. Pastorino, and A. Massa, “Electromagnetic inversion with the multiscaling inexact Newton method—experimental validation,” Microw. Opt. Technol. Lett. 53, 2834–2838 (2011).
[CrossRef]

P. Rocca, G. Oliveri, and A. Massa, “Differential evolution as applied to electromagnetics,” IEEE Antennas Propag. Mag. 53(1), 38–49 (2011).
[CrossRef]

G. Oliveri, A. Randazzo, M. Pastorino, and A. Massa, “Imaging of separate scatterers by means of a multiscaling multiregion inexact-Newton approach,” Progr. Electromagn. Res. 18, 247–257 (2011).
[CrossRef]

Pan, L.

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]

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]

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. Imag. 18, 1108–1114 (1999).
[CrossRef]

Papadopoulos, T. G.

A. Semnani, I. T. Rekanos, M. Kamyab, and T. G. Papadopoulos, “Two-dimensional microwave imaging based on hybrid scatterer representation and differential evolution,” IEEE Trans. Antennas Propag. 58, 3289–3298 (2010).
[CrossRef]

Pascazio, V.

R. Autieri, G. Ferraiuolo, and V. Pascazio, “Bayesian regularization in nonlinear imaging: reconstructions from experimental data in nonlinearized microwave tomography,” IEEE Trans. Geosci. Remote Sens. 49, 801–813 (2011).
[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]

Pastorino, M.

G. Oliveri, L. Lizzi, M. Pastorino, and A. Massa, “A nested multi-scaling inexact-Newton iterative approach for microwave imaging,” IEEE Trans. Antennas Propag. 60, 971–983 (2012).
[CrossRef]

G. Oliveri, A. Randazzo, M. Pastorino, and A. Massa, “Electromagnetic inversion with the multiscaling inexact Newton method—experimental validation,” Microw. Opt. Technol. Lett. 53, 2834–2838 (2011).
[CrossRef]

G. Oliveri, A. Randazzo, M. Pastorino, and A. Massa, “Imaging of separate scatterers by means of a multiscaling multiregion inexact-Newton approach,” Progr. Electromagn. Res. 18, 247–257 (2011).
[CrossRef]

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

G. Bozza, C. Estatico, A. Massa, M. Pastorino, and A. Randazzo, “Short-range image-based method for the inspection of strong scatterers using microwaves,” IEEE Trans. Instrum. Meas. 56, 1181–1188 (2007).
[CrossRef]

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

G. Bozza, C. Estatico, M. Pastorino, and A. Randazzo, “An inexact Newton method for microwave reconstruction of strong scatterers,” IEEE Antennas Wirel. Propag. Lett. 5, 61–64 (2006).
[CrossRef]

C. Estatico, G. Bozza, A. Massa, M. Pastorino, and A. Randazzo, “A two-step iterative inexact-Newton method for electromagnetic imaging of dielectric structures from real data,” Inverse Probl. 21, S81–S94 (2005).
[CrossRef]

D. Franceschini, A. Massa, M. Pastorino, and A. Zanetti, “Multi-resolution iterative inversion of real inhomogeneous targets,” Inverse Probl. 21, S51–S64 (2005).
[CrossRef]

A. Massa, M. Pastorino, and A. Randazzo, “Reconstruction of two-dimensional buried objects by a hybrid differential evolution method,” Inverse Probl. 20, S135–S150 (2004).
[CrossRef]

S. Caorsi, A. Massa, and M. Pastorino, “Numerical assessment concerning a focused microwave diagnostic method for medical applications,” IEEE Trans. Microw. Theory Technol. 48, 1815–1830 (2000).
[CrossRef]

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

Paulsen, K. D.

T. Rubk, P. M. Meaney, P. Meincke, and K. D. Paulsen, “Nonlinear microwave imaging for breast-cancer screening using Gauss–Newton’s method and the CGLS inversion algorithm,” IEEE Trans. Antennas Propag. 55, 2320–2331 (2007).
[CrossRef]

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. Microw. Theory Technol. 48, 1841–1853 (2000).
[CrossRef]

Perrusson, G.

A. Bréard, G. Perrusson, and D. Lesselier, “Hybrid differential evolution and retrieval of buried spheres in subsoil,” IEEE Geosci. Remote Sens. Lett. 5, 788–792 (2008).
[CrossRef]

Piana, M.

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

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

Pichot, C.

A. Franchois and C. Pichot, “Microwave imaging-complex permittivity reconstruction with a Levenberg–Marquardt method,” IEEE Trans. Antennas Propag. 45, 203–215 (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]

Pichot, Ch.

R. Ferraye, J. Y. Dauvignac, and Ch. Pichot, “An inverse scattering method based on contour deformations by means of a level set method using frequency hopping technique,” IEEE Trans. Antennas Propag. 51, 1100–1113 (2003).
[CrossRef]

R. Ferraye, J. Y. Dauvignac, and Ch. Pichot, “Reconstruction of complex and multiple shape object contours using a level set method,” J. Electromagn. Waves Appl. 17, 153–181 (2003).
[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]

Ping, K.

J. E. Johnson, T. Takenaka, K. Ping, S. Honda, and T. Tanaka, “Advances in the 3-D forward-backward time-stepping (FBTS) inverse scattering technique for breast cancer detection,” IEEE Trans. Biomed. Eng. 56, 2232–2243 (2009).
[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. Microw. Theory Technol. 48, 1841–1853 (2000).
[CrossRef]

Randazzo, A.

G. Oliveri, A. Randazzo, M. Pastorino, and A. Massa, “Imaging of separate scatterers by means of a multiscaling multiregion inexact-Newton approach,” Progr. Electromagn. Res. 18, 247–257 (2011).
[CrossRef]

G. Oliveri, A. Randazzo, M. Pastorino, and A. Massa, “Electromagnetic inversion with the multiscaling inexact Newton method—experimental validation,” Microw. Opt. Technol. Lett. 53, 2834–2838 (2011).
[CrossRef]

G. Bozza, C. Estatico, A. Massa, M. Pastorino, and A. Randazzo, “Short-range image-based method for the inspection of strong scatterers using microwaves,” IEEE Trans. Instrum. Meas. 56, 1181–1188 (2007).
[CrossRef]

G. Bozza, C. Estatico, M. Pastorino, and A. Randazzo, “An inexact Newton method for microwave reconstruction of strong scatterers,” IEEE Antennas Wirel. Propag. Lett. 5, 61–64 (2006).
[CrossRef]

C. Estatico, G. Bozza, A. Massa, M. Pastorino, and A. Randazzo, “A two-step iterative inexact-Newton method for electromagnetic imaging of dielectric structures from real data,” Inverse Probl. 21, S81–S94 (2005).
[CrossRef]

A. Massa, M. Pastorino, and A. Randazzo, “Reconstruction of two-dimensional buried objects by a hybrid differential evolution method,” Inverse Probl. 20, S135–S150 (2004).
[CrossRef]

Rekanos, I. T.

A. Semnani, I. T. Rekanos, M. Kamyab, and T. G. Papadopoulos, “Two-dimensional microwave imaging based on hybrid scatterer representation and differential evolution,” IEEE Trans. Antennas Propag. 58, 3289–3298 (2010).
[CrossRef]

A. Semnani, M. Kamyab, and I. T. Rekanos, “Reconstruction of one-dimensional dielectric scatterers using differential evolution and particle swarm optimization,” IEEE Geosci. Remote Sens. Lett. 6, 671–675 (2009).
[CrossRef]

I. T. Rekanos, “Shape reconstruction of a perfectly conducting scatterer using differential evolution and particle swarm optimization,” IEEE Trans. Geosci. Remote Sens. 46, 1967–1974 (2008).
[CrossRef]

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. Imag. 18, 1108–1114 (1999).
[CrossRef]

Richmond, J. H.

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

Rocca, P.

P. Rocca, G. Oliveri, and A. Massa, “Differential evolution as applied to electromagnetics,” IEEE Antennas Propag. Mag. 53(1), 38–49 (2011).
[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]

Rubk, T.

T. Rubk, P. M. Meaney, P. Meincke, and K. D. Paulsen, “Nonlinear microwave imaging for breast-cancer screening using Gauss–Newton’s method and the CGLS inversion algorithm,” IEEE Trans. Antennas Propag. 55, 2320–2331 (2007).
[CrossRef]

Russo, F.

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

Ruy, S.

X. Zhang, H. Tortel, S. Ruy, and A. Litman, “Microwave imaging of soil water diffusion using the linear sampling method,” IEEE Geosci. Remote Sens. Lett. 8, 421–425 (2011).
[CrossRef]

Saillard, M.

K. Belkebir and M. Saillard, Special Section: “Testing inversion algorithms against experimental data,” Inverse Probl. 17, 1565–1571 (2001).
[CrossRef]

Santosa, F.

A. Litman, D. Lesselier, and F. Santosa, “Reconstruction of a two-dimensional binary obstacle by controlled evolution of a level-set,” Inverse Probl. 14, 685–706 (1998).
[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,” IEEE Trans. Geosci. Remote Sens. 45, 2419–2421 (2007).
[CrossRef]

Semnani, A.

A. Semnani, I. T. Rekanos, M. Kamyab, and T. G. Papadopoulos, “Two-dimensional microwave imaging based on hybrid scatterer representation and differential evolution,” IEEE Trans. Antennas Propag. 58, 3289–3298 (2010).
[CrossRef]

A. Semnani, M. Kamyab, and I. T. Rekanos, “Reconstruction of one-dimensional dielectric scatterers using differential evolution and particle swarm optimization,” IEEE Geosci. Remote Sens. Lett. 6, 671–675 (2009).
[CrossRef]

Shah, N.

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

Shea, J. D.

J. D. Shea, P. Kosmas, B. D. Van Veen, and S. C. Hagness, “Contrast-enhanced microwave imaging of breast tumors: a computational study using 3D realistic numerical phantoms,” Inverse Probl. 26, 074009 (2010).
[CrossRef]

Tabatabaeenejad, A.

A. Tabatabaeenejad and M. Moghaddam, “Inversion of subsurface properties of layered dielectric structures with random slightly rough interfaces using the method of simulated annealing,” IEEE Trans. Geosci. Remote Sens. 47, 2035–2046 (2009).
[CrossRef]

Takenaka, T.

J. E. Johnson, T. Takenaka, K. Ping, S. Honda, and T. Tanaka, “Advances in the 3-D forward-backward time-stepping (FBTS) inverse scattering technique for breast cancer detection,” IEEE Trans. Biomed. Eng. 56, 2232–2243 (2009).
[CrossRef]

H. Zhou, T. Takenaka, J. Johnson, and T. Tanaka, “Breast imaging model using microwaves and a time domain three dimensional reconstruction method,” Progr. Electromagn. Res. 93, 57–70 (2009).
[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]

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

Tanaka, T.

H. Zhou, T. Takenaka, J. Johnson, and T. Tanaka, “Breast imaging model using microwaves and a time domain three dimensional reconstruction method,” Progr. Electromagn. Res. 93, 57–70 (2009).
[CrossRef]

J. E. Johnson, T. Takenaka, K. Ping, S. Honda, and T. Tanaka, “Advances in the 3-D forward-backward time-stepping (FBTS) inverse scattering technique for breast cancer detection,” IEEE Trans. Biomed. Eng. 56, 2232–2243 (2009).
[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]

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

Tortel, H.

X. Zhang, H. Tortel, S. Ruy, and A. Litman, “Microwave imaging of soil water diffusion using the linear sampling method,” IEEE Geosci. Remote Sens. Lett. 8, 421–425 (2011).
[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. Imag. 18, 1108–1114 (1999).
[CrossRef]

van Den Berg, P. M.

P. M. van Den Berg and A. Abubakar, “Contrast source inversion method: state of the art,” Progr. Electromagn. Res. 34, 189–218 (2001).
[CrossRef]

Van Veen, B. D.

J. D. Shea, P. Kosmas, B. D. Van Veen, and S. C. Hagness, “Contrast-enhanced microwave imaging of breast tumors: a computational study using 3D realistic numerical phantoms,” Inverse Probl. 26, 074009 (2010).
[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. 43, 784–792 (1995).
[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,” IEEE Trans. Geosci. Remote Sens. 45, 2419–2421 (2007).
[CrossRef]

Yeo, S.

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]

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]

Zakaria, A.

A. Zakaria and J. LoVetri, “Application of multiplicative regularization to the finite element contrast source inversion method,” IEEE Trans. Antennas Propag. 59, 3495–3498 (2011).
[CrossRef]

Zanetti, A.

D. Franceschini, A. Massa, M. Pastorino, and A. Zanetti, “Multi-resolution iterative inversion of real inhomogeneous targets,” Inverse Probl. 21, S51–S64 (2005).
[CrossRef]

Zhang, X.

X. Zhang, H. Tortel, S. Ruy, and A. Litman, “Microwave imaging of soil water diffusion using the linear sampling method,” IEEE Geosci. Remote Sens. Lett. 8, 421–425 (2011).
[CrossRef]

Zhang, Z. Q.

Z. Q. Zhang and Q. H. Liu, “Three-dimensional nonlinear image reconstruction for microwave biomedical imaging,” IEEE Trans. Biomed. Eng. 51, 544–548 (2004).
[CrossRef]

Zhong, Y.

G. Oliveri, Y. Zhong, X. Chen, and A. Massa, “Multiresolution subspace-based optimization method for inverse scattering problems,” J. Opt. Soc. Am. A 28, 2057–2069 (2011).
[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]

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]

Zhou, H.

H. Zhou, T. Takenaka, J. Johnson, and T. Tanaka, “Breast imaging model using microwaves and a time domain three dimensional reconstruction method,” Progr. Electromagn. Res. 93, 57–70 (2009).
[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]

Zoughi, R.

S. Kharkovsky and R. Zoughi, “Microwave and millimeter wave nondestructive testing and evaluation—overview and recent advances,” IEEE Instrum. Meas. Mag. 10(2), 26–38 (2007).
[CrossRef]

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

Am. J. Math. (1)

L. Landweber, “An iteration formula for Fredholm integral equations of the first kind,” Am. J. Math. 73, 615–624 (1951).
[CrossRef]

IEEE Antennas Propag. Mag. (1)

P. Rocca, G. Oliveri, and A. Massa, “Differential evolution as applied to electromagnetics,” IEEE Antennas Propag. Mag. 53(1), 38–49 (2011).
[CrossRef]

IEEE Antennas Wirel. Propag. Lett. (2)

G. Bozza, C. Estatico, M. Pastorino, and A. Randazzo, “An inexact Newton method for microwave reconstruction of strong scatterers,” IEEE Antennas Wirel. Propag. Lett. 5, 61–64 (2006).
[CrossRef]

M. R. Hajihashemi and M. El-Shenawee, “Shape reconstruction using the level set method for microwave applications,” IEEE Antennas Wirel. Propag. Lett. 7, 92–96 (2008).
[CrossRef]

IEEE Geosci. Remote Sens. Lett. (4)

A. Semnani, M. Kamyab, and I. T. Rekanos, “Reconstruction of one-dimensional dielectric scatterers using differential evolution and particle swarm optimization,” IEEE Geosci. Remote Sens. Lett. 6, 671–675 (2009).
[CrossRef]

X. Zhang, H. Tortel, S. Ruy, and A. Litman, “Microwave imaging of soil water diffusion using the linear sampling method,” IEEE Geosci. Remote Sens. Lett. 8, 421–425 (2011).
[CrossRef]

G. Franceschini, D. Franceschini, and A. Massa, “Full-vectorial three-dimensional microwave imaging through the iterative multi-scaling strategy—a preliminary assessment,” IEEE Geosci. Remote Sens. Lett. 2, 428–432 (2005).
[CrossRef]

A. Bréard, G. Perrusson, and D. Lesselier, “Hybrid differential evolution and retrieval of buried spheres in subsoil,” IEEE Geosci. Remote Sens. Lett. 5, 788–792 (2008).
[CrossRef]

IEEE Instrum. Meas. Mag. (2)

S. Kharkovsky and R. Zoughi, “Microwave and millimeter wave nondestructive testing and evaluation—overview and recent advances,” IEEE Instrum. Meas. Mag. 10(2), 26–38 (2007).
[CrossRef]

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

IEEE Trans. Antennas Propag. (19)

M. El-Shenawee, O. Dorn, and M. Moscoso, “An adjoint-field technique for shape reconstruction of 3-D penetrable object immersed in lossy medium,” IEEE Trans. Antennas Propag. 57, 520–534 (2009).
[CrossRef]

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

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

T. Rubk, P. M. Meaney, P. Meincke, and K. D. Paulsen, “Nonlinear microwave imaging for breast-cancer screening using Gauss–Newton’s method and the CGLS inversion algorithm,” IEEE Trans. Antennas Propag. 55, 2320–2331 (2007).
[CrossRef]

M. A. Ali and M. Moghaddam, “3D nonlinear super-resolution microwave inversion technique using time-domain data,” IEEE Trans. Antennas Propag. 58, 2327–2336 (2010).
[CrossRef]

C.-H. Kuo and M. Moghaddam, “Electromagnetic scattering from a buried cylinder in layered media with rough interfaces,” IEEE Trans. Antennas Propag. 54, 2392–2401 (2006).
[CrossRef]

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

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

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

G. Oliveri, L. Lizzi, M. Pastorino, and A. Massa, “A nested multi-scaling inexact-Newton iterative approach for microwave imaging,” IEEE Trans. Antennas Propag. 60, 971–983 (2012).
[CrossRef]

A. Zakaria and J. LoVetri, “Application of multiplicative regularization to the finite element contrast source inversion method,” IEEE Trans. Antennas Propag. 59, 3495–3498 (2011).
[CrossRef]

A. Franchois and C. Pichot, “Microwave imaging-complex permittivity reconstruction with a Levenberg–Marquardt method,” IEEE Trans. Antennas Propag. 45, 203–215 (1997).
[CrossRef]

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

P. Mojabi and J. LoVetri, “Overview and classification of some regularization techniques for the Gauss–Newton inversion method applied to inverse scattering problems,” IEEE Trans. Antennas Propag. 57, 2658–2665 (2009).
[CrossRef]

A. Semnani, I. T. Rekanos, M. Kamyab, and T. G. Papadopoulos, “Two-dimensional microwave imaging based on hybrid scatterer representation and differential evolution,” IEEE Trans. Antennas Propag. 58, 3289–3298 (2010).
[CrossRef]

R. Ferraye, J. Y. Dauvignac, and Ch. Pichot, “An inverse scattering method based on contour deformations by means of a level set method using frequency hopping technique,” IEEE Trans. Antennas Propag. 51, 1100–1113 (2003).
[CrossRef]

J. De Zaeytijd, A. Franchois, C. Eyraud, and J.-M. Geffrin, “Full-wave three-dimensional microwave imaging with a regularized Gauss-Newton method: theory and experiment,” IEEE Trans. Antennas Propag. 55, 3279–3292 (2007).
[CrossRef]

C. Gilmore, P. Mojabi, and J. LoVetri, “Comparison of an enhanced distorted Born iterative method and the multiplicative-regularized contrast source inversion method,“ IEEE Trans. Antennas Propag. 57, 2341–2351 (2009).
[CrossRef]

C. Eyraud, J. Geffrin, and A. Litman, “3D-aggregate quantitative imaging: experimental results and polarization effects,” IEEE Trans. Antennas Propag. 59, 1237–1244 (2011).
[CrossRef]

IEEE Trans. Biomed. Eng. (4)

G. Bellizzi, O. Bucci, and I. Catapano, “Microwave cancer imaging exploiting magnetic nanoparticles as contrast agent,” IEEE Trans. Biomed. Eng. 58, 2528–2536 (2011).
[CrossRef]

J. E. Johnson, T. Takenaka, K. Ping, S. Honda, and T. Tanaka, “Advances in the 3-D forward-backward time-stepping (FBTS) inverse scattering technique for breast cancer detection,” IEEE Trans. Biomed. Eng. 56, 2232–2243 (2009).
[CrossRef]

G. Bozza and M. Brignone, “Application of the no-sampling linear sampling method to breast cancer detection,” IEEE Trans. Biomed. Eng. 57, 2525–2534 (2010).
[CrossRef]

Z. Q. Zhang and Q. H. Liu, “Three-dimensional nonlinear image reconstruction for microwave biomedical imaging,” IEEE Trans. Biomed. Eng. 51, 544–548 (2004).
[CrossRef]

IEEE Trans. Geosci. Remote Sens. (9)

A. Tabatabaeenejad and M. Moghaddam, “Inversion of subsurface properties of layered dielectric structures with random slightly rough interfaces using the method of simulated annealing,” IEEE Trans. Geosci. Remote Sens. 47, 2035–2046 (2009).
[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,” IEEE Trans. Geosci. Remote Sens. 45, 2419–2421 (2007).
[CrossRef]

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

I. T. Rekanos, “Shape reconstruction of a perfectly conducting scatterer using differential evolution and particle swarm optimization,” IEEE Trans. Geosci. Remote Sens. 46, 1967–1974 (2008).
[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]

M. R. Hajihashemi and M. El-Shenawee, “Level set algorithm for shape reconstruction of nonoverlapping three-dimensional penetrable targets,” IEEE Trans. Geosci. Remote Sens. 50, 75–86 (2012).
[CrossRef]

R. Autieri, G. Ferraiuolo, and V. Pascazio, “Bayesian regularization in nonlinear imaging: reconstructions from experimental data in nonlinearized microwave tomography,” IEEE Trans. Geosci. Remote Sens. 49, 801–813 (2011).
[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]

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]

IEEE Trans. Instrum. Meas. (1)

G. Bozza, C. Estatico, A. Massa, M. Pastorino, and A. Randazzo, “Short-range image-based method for the inspection of strong scatterers using microwaves,” IEEE Trans. Instrum. Meas. 56, 1181–1188 (2007).
[CrossRef]

IEEE Trans. Med. Imag. (2)

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. Imag. 18, 1108–1114 (1999).
[CrossRef]

M. El-Shenawee and E. Miller, “Spherical harmonics microwave algorithm for shape and location reconstruction of breast cancer tumors,” IEEE Trans. Med. Imag. 25, 1258–1271(2006).
[CrossRef]

IEEE Trans. Microw. Theory Technol. (4)

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. Microw. Theory Technol. 48, 1841–1853 (2000).
[CrossRef]

S. Caorsi, A. Massa, and M. Pastorino, “Numerical assessment concerning a focused microwave diagnostic method for medical applications,” IEEE Trans. Microw. Theory Technol. 48, 1815–1830 (2000).
[CrossRef]

S. Caorsi, M. Donelli, D. Franceschini, and A. Massa, “A new methodology based on an iterative multiscaling for microwave imaging,” IEEE Trans. Microw. Theory Technol. 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. Microw. Theory Technol. 52, 1217–1228 (2004).
[CrossRef]

Inverse Probl. (14)

D. Franceschini, A. Massa, M. Pastorino, and A. Zanetti, “Multi-resolution iterative inversion of real inhomogeneous targets,” Inverse Probl. 21, S51–S64 (2005).
[CrossRef]

O. Dorn and D. Lesselier, “Introduction to the special issue on electromagnetic inverse problems: emerging methods and novel applications,” Inverse Probl. 26, 070201 (2010).
[CrossRef]

A. Baussard, E. L. Miller, and D. Lesselier, “Adaptive multiscale reconstruction of buried objects,” Inverse Probl. 20, S1–S15 (2004).
[CrossRef]

A. Massa, M. Pastorino, and A. Randazzo, “Reconstruction of two-dimensional buried objects by a hybrid differential evolution method,” Inverse Probl. 20, S135–S150 (2004).
[CrossRef]

D. Lesselier and J. Bowler, “Foreword to the special section on electromagnetic and ultrasonic nondestructive evaluation,” Inverse Probl. 18 (2002).
[CrossRef]

O. Dorn and D. Lesselier, “Level set methods for inverse scattering,” Inverse Probl. 22, R67–R131 (2006).
[CrossRef]

A. Litman, D. Lesselier, and F. Santosa, “Reconstruction of a two-dimensional binary obstacle by controlled evolution of a level-set,” Inverse Probl. 14, 685–706 (1998).
[CrossRef]

J. D. Shea, P. Kosmas, B. D. Van Veen, and S. C. Hagness, “Contrast-enhanced microwave imaging of breast tumors: a computational study using 3D realistic numerical phantoms,” Inverse Probl. 26, 074009 (2010).
[CrossRef]

C. Estatico, G. Bozza, A. Massa, M. Pastorino, and A. Randazzo, “A two-step iterative inexact-Newton method for electromagnetic imaging of dielectric structures from real data,” Inverse Probl. 21, S81–S94 (2005).
[CrossRef]

K. Belkebir and M. Saillard, Special Section: “Testing inversion algorithms against experimental data,” Inverse Probl. 17, 1565–1571 (2001).
[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]

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

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

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]

J. Electromagn. Waves Appl. (1)

R. Ferraye, J. Y. Dauvignac, and Ch. Pichot, “Reconstruction of complex and multiple shape object contours using a level set method,” J. Electromagn. Waves Appl. 17, 153–181 (2003).
[CrossRef]

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

Microw. Opt. Technol. Lett. (1)

G. Oliveri, A. Randazzo, M. Pastorino, and A. Massa, “Electromagnetic inversion with the multiscaling inexact Newton method—experimental validation,” Microw. Opt. Technol. Lett. 53, 2834–2838 (2011).
[CrossRef]

Progr. Electromagn. Res. (5)

G. Oliveri, A. Randazzo, M. Pastorino, and A. Massa, “Imaging of separate scatterers by means of a multiscaling multiregion inexact-Newton approach,” Progr. Electromagn. Res. 18, 247–257 (2011).
[CrossRef]

M. R. Hajihashemi and M. El-Shenawee, “Inverse scattering of three-dimensional PEC objects using the level-set method,” Progr. Electromagn. Res. 116, 23–47 (2011).
[CrossRef]

P. M. van Den Berg and A. Abubakar, “Contrast source inversion method: state of the art,” Progr. Electromagn. Res. 34, 189–218 (2001).
[CrossRef]

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

H. Zhou, T. Takenaka, J. Johnson, and T. Tanaka, “Breast imaging model using microwaves and a time domain three dimensional reconstruction method,” Progr. Electromagn. Res. 93, 57–70 (2009).
[CrossRef]

Subspace-based optimization method for reconstructing extended scatterers: transverse electric case (1)

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]

Other (3)

A time-dependence ej2πft, f being the working frequency, is assumed and omitted hereinafter.

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

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

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Figures (11)

Fig. 1.
Fig. 1.

L-shaped cylinder ( τ = 0.5 , V = 24 , M = 360 , noiseless data)—actual contrast. (a) Reconstructed profile with IMSA–IN–CSI at (b)  s = 1 , (c)  s = 2 , (d)  s = 3 , (e)  s = 4 , and (f)  s = S opt = 5 .

Fig. 2.
Fig. 2.

L-shaped cylinder ( τ = 0.5 , V = 24 , M = 360 , noiseless data). Behavior of the residual and the reconstruction error versus the iteration number.

Fig. 3.
Fig. 3.

L-shaped cylinder ( τ = 0.5 , V = 24 , M = 360 , SNR = 20 dB ). Behavior of the residual and the reconstruction error versus the iteration number (a) and reconstructed profiles when applying (b) the BARE–IN–CSI and (c) the IMSA–IN–CSI.

Fig. 4.
Fig. 4.

L-shaped cylinder ( τ = 0.5 , V = 24 , M = 360 , SNR = 10 dB ). Behavior of the reconstruction error versus the SNR (a) and retrieved contrast when applying the (b) BARE–IN–CSI and (c) IMSA–IN–CSI.

Fig. 5.
Fig. 5.

Multiple separated cylinders ( τ = 0.5 , V = 24 , M = 360 , SNR = 20 dB ). Actual contrast (a) and retrieved profiles when applying the (b) BARE–IN–CFI, (c) BARE–IN–CSI, (d) IMSA–IN–CFI, and (e) IMSA–IN–CSI.

Fig. 6.
Fig. 6.

Multiple separate cylinders ( V = 24 , M = 360 ). Behavior of the reconstruction error versus the (a) SNR ( τ = 0.5 ) and (b) scatterer contrast ( SNR = 20 dB ).

Fig. 7.
Fig. 7.

Inhomogeneous cylinder ( τ in = 1.5 , τ ext = 1.0 , V = 24 , M = 360 , SNR = 20 dB ). Actual contrast (a) and retrieved profiles with the (b) BARE–IN–CFI, (c) BARE–IN–CSI, (d) IMSA–IN–CFI, and (e) IMSA–IN–CSI.

Fig. 8.
Fig. 8.

Inhomogeneous cylinder ( τ in = 1.5 , τ ext = 1.0 , V = 24 , SNR = 20 dB ). Behavior of the reconstruction error versus M (a) and samples ( M = 24 ) of the dielectric distributions retrieved with the (b) BARE–IN–CFI, (c) BARE–IN–CSI, (d) IMSA–IN–CFI, and (e) IMSA–IN–CSI.

Fig. 9.
Fig. 9.

Experimental results (“FoamDielExt” scenario, f = 4 GHz ). Sketch of the actual scatterer (a) and retrieved contrasts with the (b) BARE–IN–CFI, (c) BARE–IN–CSI, (d) IMSA–IN–CFI, and (e) IMSA–IN–CSI.

Fig. 10.
Fig. 10.

Experimental results (“FoamDielInt” scenario, f = 4 GHz ). Sketch of the actual scatterer (a) and retrieved contrasts with the (b) BARE–IN–CFI, (c) BARE–IN–CSI, (d) IMSA–IN–CFI, and (e) IMSA–IN–CSI.

Fig. 11.
Fig. 11.

Experimental results (“FoamTwinDiel” scenario, f = 4 GHz ). Sketch of the actual scatterer (a) and retrieved contrasts with the (b) BARE–IN–CFI, (c) BARE–IN–CSI, (d) IMSA–IN–CFI, and (e) IMSA–IN–CSI.

Tables (1)

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Table 1. Inhomogeneous Cylinder ( τ int = 1.0 , τ ext = 0.5 ; V = 24 , SNR = 20 dB )—Error Values and Computational Indices

Equations (11)

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e scatt ( v ) ( r ) = G ext J ( v ) ( r ) , r D meas ( v ) ,
0 = J ( v ) ( r ) { τ ( r ) e inc ( v ) ( r ) + τ ( r ) G int J ( v ) ( r ) } , r D inv
G ( x ) = [ G ext J ( 1 ) G ext J ( V ) J ( 1 ) τ e inc ( 1 ) τ G int J ( 1 ) J ( V ) τ e inc ( V ) τ G int J ( V ) ] .
[ e scatt ( 1 ) e scatt ( V ) 0 0 ] = [ G ext ( 1 ) J ( 1 ) G ext ( V ) J ( V ) J ( 1 ) diag ( τ ) e inc ( 1 ) diag ( τ ) G int J ( 1 ) J ( V ) diag ( τ ) e inc ( V ) diag ( τ ) G int J ( V ) ] ,
y = G ( x ) ,
G k | ( s ) h k | ( s ) = e k | ( s ) ,
G k | ( s ) = [ 0 A ( 1 ) | ( s ) 0 0 0 0 A ( 2 ) | ( s ) 0 0 0 0 A ( V ) | ( s ) B ( 1 ) | ( s ) C | ( s ) 0 0 B ( 2 ) | ( s ) 0 C | ( s ) 0 B ( V ) | ( s ) 0 0 C | ( s ) ] ,
h k , i + 1 | ( s ) = h k , i | ( s ) β k | ( s ) G k * | ( s ) ( G k | ( s ) h k , i | ( s ) e k | ( s ) ) ,
ξ D inv | τ ˜ ( r ) τ ( r ) | d r area ( D inv ) × D inv | τ ( r ) + 1 | d r ,
ξ IMSA IN CSI | M = 24 ξ IMSA IN CSI | M = 360 4.2
ξ IMSA IN CFI | M = 24 ξ IMSA IN CFI | M = 360 7.9

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