Abstract

Iterative techniques are presented for two-dimensional inverse scattering from electrically large regions. The region is illuminated by transmitters with arbitrary profiles; this is an escalation in complexity from the line-source and the plane-wave excitations considered in many previous inverse-scattering studies. Imaging algorithms require an accurate and efficient forward model. Here a Gaussian-beam algorithm is utilized as a forward solver and is incorporated into an iterative-Born inversion scheme. General antenna profiles are incorporated into the algorithm by use of the matched-pursuits technique, by which the aperture fields are matched to the beam-tracing algorithm. Results are presented for several cases in which the simple Born approximation fails. Issues addressed include the types of profiles that can be successfully imaged, suitable antenna distributions, and the range of parameters over which the scheme is effective. Performance of the algorithm in the presence of noisy data is also tested.

© 1999 Optical Society of America

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References

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  1. B. Rao, L. Carin, “Inverse scattering for electrically large regions with a gaussian-beam forward model,” IEEE Trans. Antennas Propag. (to be published).
  2. V. Červený, M. M. Popov, I. Pšenčik, “Computation of wave fields in inhomogeneous media—Gaussian beam approach,” Geophys. J. R. Astron. Soc. 70, 109–128 (1982).
    [CrossRef]
  3. M. B. Porter, H. P. Bucker, “Gaussian beam tracing for computing ocean acoustic fields,” J. Acoust. Soc. Am. 82, 1349–1359 (1987).
    [CrossRef]
  4. Y. M. Wang, W. C. Chew, “An iterative solution of the two-dimensional electromagnetic inverse scattering problem,” Int. J. Imaging Syst. Technol. 1, 100–108 (1989).
    [CrossRef]
  5. W. C. Chew, Y. M. Wang, “Reconstruction of two-dimensional permittivity distribution using the distorted Born iterative method,” IEEE Trans. Med. Imaging 9, 218–225 (1990).
    [CrossRef] [PubMed]
  6. A. J. Tijhuis, “Iterative determination of permittivity and conductivity profiles of a dielectric slab in time domain,” IEEE Trans. Antennas Propag. 29, 239–245 (1981).
    [CrossRef]
  7. A. Franchois, C. Pichot, “Microwave imaging—complex permittivity reconstruction with a Levenberg–Marquardt method,” IEEE Trans. Antennas Propag. 45, 203–215 (1997).
    [CrossRef]
  8. E. L. Miller, A. S. Willsky, “A multiscale, statistically based inversion scheme for linearized inverse scattering problems,” IEEE Trans. Geoscience Remote Sens. 34, 346–357 (1995).
    [CrossRef]
  9. S. G. Mallat, Z. Zhang, “Matching pursuits with a wave-based dictionary,” IEEE Trans. Signal Process. 45, 2912–2927 (1997).
    [CrossRef]
  10. D. T. Borup, O. P. Gandhi, “Calculation of high resolution SAR distributions in biological bodies using the FFT algorithm and conjugate gradient method,” IEEE Trans. Microwave Theory Tech. MTT-33, 417–419 (1985).
    [CrossRef]
  11. R. F. Harrington, Field Computation by Moment Methods (Kreiger, Malabar, Fla., 1985).
  12. A. J. Devaney, “A computer simulation study of diffraction tomography,” IEEE Trans. Biomed. Eng. 30, 377–386 (1983).
    [CrossRef] [PubMed]
  13. A. J. Devaney, “A filtered backpropagation algorithm for diffraction tomography,” Ultrason. Imaging 4, 336–360 (1982).
    [CrossRef] [PubMed]
  14. A. J. Devaney, “Inverse-scattering theory within the Rytov approximation,” Opt. Lett. 6, 374–376 (1981).
    [CrossRef] [PubMed]
  15. W. Tabbara, B. Duchene, Ch. Pichot, D. Lesselier, L. Chomeloux, N. Joachimowicz, “Diffraction tomography: contribution to the analysis of applications in microwaves and ultrasonics,” Inverse Probl. 4, 305–331 (1988).
    [CrossRef]
  16. M. H. Reilly, E. L. Strobel, “Efficient ray tracing through a realistic ionosphere,” Radio Sci. 23, 247–256 (1988).
    [CrossRef]
  17. F. B. Jensen, W. A. Kuperman, M. B. Porter, H. Schmidt, eds., Computational Ocean Acoustics (American Institute of Physics, New York, 1994), Chap. 3.
  18. L. B. Felsen, N. Marcuvitz, Radiation and Scattering of Waves (Prentice-Hall, Englewood Cliffs, N.J., 1973), Chap. 4 (republished by the Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1994).
  19. B. Rao, “Gabor based gaussian beam tracing algorithm for wave propagation through large inhomogeneous regions,” M.S. thesis (Duke University, Durham, N.C., 1997).
  20. D. Gabor, “Theory of communication,” J. Inst. Elect. Eng. 93, 429–457 (1946).
  21. J. J. Maciel, L. B. Felsen, “Systematic study of fields due to extended apertures by Gaussian beam discretization,” IEEE Trans. Antennas Propag. 37, 884–892 (1989).
    [CrossRef]
  22. J. J. Maciel, L. B. Felsen, “Gaussian beam analysis of propagation from an extended plane aperture distribution through dielectric layers. I. Plane layer; II. Circular cylindrical layer,” IEEE Trans. Antennas Propag. 38, 1608–1624 (1990).
  23. B. Rao, L. Carin, “A hybrid (parabolic equation)-(gaussian beam) algorithm for wave propagation through large inhomogeneous regions,” IEEE Trans. Antennas Propag. 46, 700–709 (1998).
    [CrossRef]
  24. C. T. H. Baker, The Numerical Treatment of Integral Equations (Clarendon, Oxford, 1977).
  25. A. N. Tikhonov, V. Y. Arsenin, Solution of Ill-Posed Problems (Winston, Washington D.C., 1977).
  26. K. S. Kunz, R. J. Luebbers, The Finite Difference Time Domain Method for Electromagnetics (CRC Press, Boca Raton, Fla., 1993).
  27. M. Moghaddam, W. Chew, “Nonlinear two-dimensional velocity profile inversion using time-domain data,” IEEE Trans. Geosci. Remote Sens. 30, 147–156 (1992).
    [CrossRef]
  28. P. G. Petropoulos, “Phase error control for FDTD methods of second and fourth order accuracy,” IEEE Trans. Antennas Propag. 42, 859–862 (1994).
    [CrossRef]
  29. B. Rao, “Imaging algorithms for electrically large targets,” Ph.D. dissertation (Duke University, Durham, N.C., 1999).

1998 (1)

B. Rao, L. Carin, “A hybrid (parabolic equation)-(gaussian beam) algorithm for wave propagation through large inhomogeneous regions,” IEEE Trans. Antennas Propag. 46, 700–709 (1998).
[CrossRef]

1997 (2)

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

S. G. Mallat, Z. Zhang, “Matching pursuits with a wave-based dictionary,” IEEE Trans. Signal Process. 45, 2912–2927 (1997).
[CrossRef]

1995 (1)

E. L. Miller, A. S. Willsky, “A multiscale, statistically based inversion scheme for linearized inverse scattering problems,” IEEE Trans. Geoscience Remote Sens. 34, 346–357 (1995).
[CrossRef]

1994 (1)

P. G. Petropoulos, “Phase error control for FDTD methods of second and fourth order accuracy,” IEEE Trans. Antennas Propag. 42, 859–862 (1994).
[CrossRef]

1992 (1)

M. Moghaddam, W. Chew, “Nonlinear two-dimensional velocity profile inversion using time-domain data,” IEEE Trans. Geosci. Remote Sens. 30, 147–156 (1992).
[CrossRef]

1990 (2)

W. C. Chew, Y. M. Wang, “Reconstruction of two-dimensional permittivity distribution using the distorted Born iterative method,” IEEE Trans. Med. Imaging 9, 218–225 (1990).
[CrossRef] [PubMed]

J. J. Maciel, L. B. Felsen, “Gaussian beam analysis of propagation from an extended plane aperture distribution through dielectric layers. I. Plane layer; II. Circular cylindrical layer,” IEEE Trans. Antennas Propag. 38, 1608–1624 (1990).

1989 (2)

Y. M. Wang, W. C. Chew, “An iterative solution of the two-dimensional electromagnetic inverse scattering problem,” Int. J. Imaging Syst. Technol. 1, 100–108 (1989).
[CrossRef]

J. J. Maciel, L. B. Felsen, “Systematic study of fields due to extended apertures by Gaussian beam discretization,” IEEE Trans. Antennas Propag. 37, 884–892 (1989).
[CrossRef]

1988 (2)

W. Tabbara, B. Duchene, Ch. Pichot, D. Lesselier, L. Chomeloux, N. Joachimowicz, “Diffraction tomography: contribution to the analysis of applications in microwaves and ultrasonics,” Inverse Probl. 4, 305–331 (1988).
[CrossRef]

M. H. Reilly, E. L. Strobel, “Efficient ray tracing through a realistic ionosphere,” Radio Sci. 23, 247–256 (1988).
[CrossRef]

1987 (1)

M. B. Porter, H. P. Bucker, “Gaussian beam tracing for computing ocean acoustic fields,” J. Acoust. Soc. Am. 82, 1349–1359 (1987).
[CrossRef]

1985 (1)

D. T. Borup, O. P. Gandhi, “Calculation of high resolution SAR distributions in biological bodies using the FFT algorithm and conjugate gradient method,” IEEE Trans. Microwave Theory Tech. MTT-33, 417–419 (1985).
[CrossRef]

1983 (1)

A. J. Devaney, “A computer simulation study of diffraction tomography,” IEEE Trans. Biomed. Eng. 30, 377–386 (1983).
[CrossRef] [PubMed]

1982 (2)

A. J. Devaney, “A filtered backpropagation algorithm for diffraction tomography,” Ultrason. Imaging 4, 336–360 (1982).
[CrossRef] [PubMed]

V. Červený, M. M. Popov, I. Pšenčik, “Computation of wave fields in inhomogeneous media—Gaussian beam approach,” Geophys. J. R. Astron. Soc. 70, 109–128 (1982).
[CrossRef]

1981 (2)

A. J. Tijhuis, “Iterative determination of permittivity and conductivity profiles of a dielectric slab in time domain,” IEEE Trans. Antennas Propag. 29, 239–245 (1981).
[CrossRef]

A. J. Devaney, “Inverse-scattering theory within the Rytov approximation,” Opt. Lett. 6, 374–376 (1981).
[CrossRef] [PubMed]

1946 (1)

D. Gabor, “Theory of communication,” J. Inst. Elect. Eng. 93, 429–457 (1946).

Arsenin, V. Y.

A. N. Tikhonov, V. Y. Arsenin, Solution of Ill-Posed Problems (Winston, Washington D.C., 1977).

Baker, C. T. H.

C. T. H. Baker, The Numerical Treatment of Integral Equations (Clarendon, Oxford, 1977).

Borup, D. T.

D. T. Borup, O. P. Gandhi, “Calculation of high resolution SAR distributions in biological bodies using the FFT algorithm and conjugate gradient method,” IEEE Trans. Microwave Theory Tech. MTT-33, 417–419 (1985).
[CrossRef]

Bucker, H. P.

M. B. Porter, H. P. Bucker, “Gaussian beam tracing for computing ocean acoustic fields,” J. Acoust. Soc. Am. 82, 1349–1359 (1987).
[CrossRef]

Carin, L.

B. Rao, L. Carin, “A hybrid (parabolic equation)-(gaussian beam) algorithm for wave propagation through large inhomogeneous regions,” IEEE Trans. Antennas Propag. 46, 700–709 (1998).
[CrossRef]

B. Rao, L. Carin, “Inverse scattering for electrically large regions with a gaussian-beam forward model,” IEEE Trans. Antennas Propag. (to be published).

Cervený, V.

V. Červený, M. M. Popov, I. Pšenčik, “Computation of wave fields in inhomogeneous media—Gaussian beam approach,” Geophys. J. R. Astron. Soc. 70, 109–128 (1982).
[CrossRef]

Chew, W.

M. Moghaddam, W. Chew, “Nonlinear two-dimensional velocity profile inversion using time-domain data,” IEEE Trans. Geosci. Remote Sens. 30, 147–156 (1992).
[CrossRef]

Chew, W. C.

W. C. Chew, Y. M. Wang, “Reconstruction of two-dimensional permittivity distribution using the distorted Born iterative method,” IEEE Trans. Med. Imaging 9, 218–225 (1990).
[CrossRef] [PubMed]

Y. M. Wang, W. C. Chew, “An iterative solution of the two-dimensional electromagnetic inverse scattering problem,” Int. J. Imaging Syst. Technol. 1, 100–108 (1989).
[CrossRef]

Chomeloux, L.

W. Tabbara, B. Duchene, Ch. Pichot, D. Lesselier, L. Chomeloux, N. Joachimowicz, “Diffraction tomography: contribution to the analysis of applications in microwaves and ultrasonics,” Inverse Probl. 4, 305–331 (1988).
[CrossRef]

Devaney, A. J.

A. J. Devaney, “A computer simulation study of diffraction tomography,” IEEE Trans. Biomed. Eng. 30, 377–386 (1983).
[CrossRef] [PubMed]

A. J. Devaney, “A filtered backpropagation algorithm for diffraction tomography,” Ultrason. Imaging 4, 336–360 (1982).
[CrossRef] [PubMed]

A. J. Devaney, “Inverse-scattering theory within the Rytov approximation,” Opt. Lett. 6, 374–376 (1981).
[CrossRef] [PubMed]

Duchene, B.

W. Tabbara, B. Duchene, Ch. Pichot, D. Lesselier, L. Chomeloux, N. Joachimowicz, “Diffraction tomography: contribution to the analysis of applications in microwaves and ultrasonics,” Inverse Probl. 4, 305–331 (1988).
[CrossRef]

Felsen, L. B.

J. J. Maciel, L. B. Felsen, “Gaussian beam analysis of propagation from an extended plane aperture distribution through dielectric layers. I. Plane layer; II. Circular cylindrical layer,” IEEE Trans. Antennas Propag. 38, 1608–1624 (1990).

J. J. Maciel, L. B. Felsen, “Systematic study of fields due to extended apertures by Gaussian beam discretization,” IEEE Trans. Antennas Propag. 37, 884–892 (1989).
[CrossRef]

L. B. Felsen, N. Marcuvitz, Radiation and Scattering of Waves (Prentice-Hall, Englewood Cliffs, N.J., 1973), Chap. 4 (republished by the Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1994).

Franchois, A.

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

Gabor, D.

D. Gabor, “Theory of communication,” J. Inst. Elect. Eng. 93, 429–457 (1946).

Gandhi, O. P.

D. T. Borup, O. P. Gandhi, “Calculation of high resolution SAR distributions in biological bodies using the FFT algorithm and conjugate gradient method,” IEEE Trans. Microwave Theory Tech. MTT-33, 417–419 (1985).
[CrossRef]

Harrington, R. F.

R. F. Harrington, Field Computation by Moment Methods (Kreiger, Malabar, Fla., 1985).

Joachimowicz, N.

W. Tabbara, B. Duchene, Ch. Pichot, D. Lesselier, L. Chomeloux, N. Joachimowicz, “Diffraction tomography: contribution to the analysis of applications in microwaves and ultrasonics,” Inverse Probl. 4, 305–331 (1988).
[CrossRef]

Kunz, K. S.

K. S. Kunz, R. J. Luebbers, The Finite Difference Time Domain Method for Electromagnetics (CRC Press, Boca Raton, Fla., 1993).

Lesselier, D.

W. Tabbara, B. Duchene, Ch. Pichot, D. Lesselier, L. Chomeloux, N. Joachimowicz, “Diffraction tomography: contribution to the analysis of applications in microwaves and ultrasonics,” Inverse Probl. 4, 305–331 (1988).
[CrossRef]

Luebbers, R. J.

K. S. Kunz, R. J. Luebbers, The Finite Difference Time Domain Method for Electromagnetics (CRC Press, Boca Raton, Fla., 1993).

Maciel, J. J.

J. J. Maciel, L. B. Felsen, “Gaussian beam analysis of propagation from an extended plane aperture distribution through dielectric layers. I. Plane layer; II. Circular cylindrical layer,” IEEE Trans. Antennas Propag. 38, 1608–1624 (1990).

J. J. Maciel, L. B. Felsen, “Systematic study of fields due to extended apertures by Gaussian beam discretization,” IEEE Trans. Antennas Propag. 37, 884–892 (1989).
[CrossRef]

Mallat, S. G.

S. G. Mallat, Z. Zhang, “Matching pursuits with a wave-based dictionary,” IEEE Trans. Signal Process. 45, 2912–2927 (1997).
[CrossRef]

Marcuvitz, N.

L. B. Felsen, N. Marcuvitz, Radiation and Scattering of Waves (Prentice-Hall, Englewood Cliffs, N.J., 1973), Chap. 4 (republished by the Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1994).

Miller, E. L.

E. L. Miller, A. S. Willsky, “A multiscale, statistically based inversion scheme for linearized inverse scattering problems,” IEEE Trans. Geoscience Remote Sens. 34, 346–357 (1995).
[CrossRef]

Moghaddam, M.

M. Moghaddam, W. Chew, “Nonlinear two-dimensional velocity profile inversion using time-domain data,” IEEE Trans. Geosci. Remote Sens. 30, 147–156 (1992).
[CrossRef]

Petropoulos, P. G.

P. G. Petropoulos, “Phase error control for FDTD methods of second and fourth order accuracy,” IEEE Trans. Antennas Propag. 42, 859–862 (1994).
[CrossRef]

Pichot, C.

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

Pichot, Ch.

W. Tabbara, B. Duchene, Ch. Pichot, D. Lesselier, L. Chomeloux, N. Joachimowicz, “Diffraction tomography: contribution to the analysis of applications in microwaves and ultrasonics,” Inverse Probl. 4, 305–331 (1988).
[CrossRef]

Popov, M. M.

V. Červený, M. M. Popov, I. Pšenčik, “Computation of wave fields in inhomogeneous media—Gaussian beam approach,” Geophys. J. R. Astron. Soc. 70, 109–128 (1982).
[CrossRef]

Porter, M. B.

M. B. Porter, H. P. Bucker, “Gaussian beam tracing for computing ocean acoustic fields,” J. Acoust. Soc. Am. 82, 1349–1359 (1987).
[CrossRef]

Pšencik, I.

V. Červený, M. M. Popov, I. Pšenčik, “Computation of wave fields in inhomogeneous media—Gaussian beam approach,” Geophys. J. R. Astron. Soc. 70, 109–128 (1982).
[CrossRef]

Rao, B.

B. Rao, L. Carin, “A hybrid (parabolic equation)-(gaussian beam) algorithm for wave propagation through large inhomogeneous regions,” IEEE Trans. Antennas Propag. 46, 700–709 (1998).
[CrossRef]

B. Rao, “Imaging algorithms for electrically large targets,” Ph.D. dissertation (Duke University, Durham, N.C., 1999).

B. Rao, L. Carin, “Inverse scattering for electrically large regions with a gaussian-beam forward model,” IEEE Trans. Antennas Propag. (to be published).

B. Rao, “Gabor based gaussian beam tracing algorithm for wave propagation through large inhomogeneous regions,” M.S. thesis (Duke University, Durham, N.C., 1997).

Reilly, M. H.

M. H. Reilly, E. L. Strobel, “Efficient ray tracing through a realistic ionosphere,” Radio Sci. 23, 247–256 (1988).
[CrossRef]

Strobel, E. L.

M. H. Reilly, E. L. Strobel, “Efficient ray tracing through a realistic ionosphere,” Radio Sci. 23, 247–256 (1988).
[CrossRef]

Tabbara, W.

W. Tabbara, B. Duchene, Ch. Pichot, D. Lesselier, L. Chomeloux, N. Joachimowicz, “Diffraction tomography: contribution to the analysis of applications in microwaves and ultrasonics,” Inverse Probl. 4, 305–331 (1988).
[CrossRef]

Tijhuis, A. J.

A. J. Tijhuis, “Iterative determination of permittivity and conductivity profiles of a dielectric slab in time domain,” IEEE Trans. Antennas Propag. 29, 239–245 (1981).
[CrossRef]

Tikhonov, A. N.

A. N. Tikhonov, V. Y. Arsenin, Solution of Ill-Posed Problems (Winston, Washington D.C., 1977).

Wang, Y. M.

W. C. Chew, Y. M. Wang, “Reconstruction of two-dimensional permittivity distribution using the distorted Born iterative method,” IEEE Trans. Med. Imaging 9, 218–225 (1990).
[CrossRef] [PubMed]

Y. M. Wang, W. C. Chew, “An iterative solution of the two-dimensional electromagnetic inverse scattering problem,” Int. J. Imaging Syst. Technol. 1, 100–108 (1989).
[CrossRef]

Willsky, A. S.

E. L. Miller, A. S. Willsky, “A multiscale, statistically based inversion scheme for linearized inverse scattering problems,” IEEE Trans. Geoscience Remote Sens. 34, 346–357 (1995).
[CrossRef]

Zhang, Z.

S. G. Mallat, Z. Zhang, “Matching pursuits with a wave-based dictionary,” IEEE Trans. Signal Process. 45, 2912–2927 (1997).
[CrossRef]

Geophys. J. R. Astron. Soc. (1)

V. Červený, M. M. Popov, I. Pšenčik, “Computation of wave fields in inhomogeneous media—Gaussian beam approach,” Geophys. J. R. Astron. Soc. 70, 109–128 (1982).
[CrossRef]

IEEE Trans. Antennas Propag. (6)

A. J. Tijhuis, “Iterative determination of permittivity and conductivity profiles of a dielectric slab in time domain,” IEEE Trans. Antennas Propag. 29, 239–245 (1981).
[CrossRef]

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

J. J. Maciel, L. B. Felsen, “Systematic study of fields due to extended apertures by Gaussian beam discretization,” IEEE Trans. Antennas Propag. 37, 884–892 (1989).
[CrossRef]

J. J. Maciel, L. B. Felsen, “Gaussian beam analysis of propagation from an extended plane aperture distribution through dielectric layers. I. Plane layer; II. Circular cylindrical layer,” IEEE Trans. Antennas Propag. 38, 1608–1624 (1990).

B. Rao, L. Carin, “A hybrid (parabolic equation)-(gaussian beam) algorithm for wave propagation through large inhomogeneous regions,” IEEE Trans. Antennas Propag. 46, 700–709 (1998).
[CrossRef]

P. G. Petropoulos, “Phase error control for FDTD methods of second and fourth order accuracy,” IEEE Trans. Antennas Propag. 42, 859–862 (1994).
[CrossRef]

IEEE Trans. Biomed. Eng. (1)

A. J. Devaney, “A computer simulation study of diffraction tomography,” IEEE Trans. Biomed. Eng. 30, 377–386 (1983).
[CrossRef] [PubMed]

IEEE Trans. Geosci. Remote Sens. (1)

M. Moghaddam, W. Chew, “Nonlinear two-dimensional velocity profile inversion using time-domain data,” IEEE Trans. Geosci. Remote Sens. 30, 147–156 (1992).
[CrossRef]

IEEE Trans. Geoscience Remote Sens. (1)

E. L. Miller, A. S. Willsky, “A multiscale, statistically based inversion scheme for linearized inverse scattering problems,” IEEE Trans. Geoscience Remote Sens. 34, 346–357 (1995).
[CrossRef]

IEEE Trans. Med. Imaging (1)

W. C. Chew, Y. M. Wang, “Reconstruction of two-dimensional permittivity distribution using the distorted Born iterative method,” IEEE Trans. Med. Imaging 9, 218–225 (1990).
[CrossRef] [PubMed]

IEEE Trans. Microwave Theory Tech. (1)

D. T. Borup, O. P. Gandhi, “Calculation of high resolution SAR distributions in biological bodies using the FFT algorithm and conjugate gradient method,” IEEE Trans. Microwave Theory Tech. MTT-33, 417–419 (1985).
[CrossRef]

IEEE Trans. Signal Process. (1)

S. G. Mallat, Z. Zhang, “Matching pursuits with a wave-based dictionary,” IEEE Trans. Signal Process. 45, 2912–2927 (1997).
[CrossRef]

Int. J. Imaging Syst. Technol. (1)

Y. M. Wang, W. C. Chew, “An iterative solution of the two-dimensional electromagnetic inverse scattering problem,” Int. J. Imaging Syst. Technol. 1, 100–108 (1989).
[CrossRef]

Inverse Probl. (1)

W. Tabbara, B. Duchene, Ch. Pichot, D. Lesselier, L. Chomeloux, N. Joachimowicz, “Diffraction tomography: contribution to the analysis of applications in microwaves and ultrasonics,” Inverse Probl. 4, 305–331 (1988).
[CrossRef]

J. Acoust. Soc. Am. (1)

M. B. Porter, H. P. Bucker, “Gaussian beam tracing for computing ocean acoustic fields,” J. Acoust. Soc. Am. 82, 1349–1359 (1987).
[CrossRef]

J. Inst. Elect. Eng. (1)

D. Gabor, “Theory of communication,” J. Inst. Elect. Eng. 93, 429–457 (1946).

Opt. Lett. (1)

Radio Sci. (1)

M. H. Reilly, E. L. Strobel, “Efficient ray tracing through a realistic ionosphere,” Radio Sci. 23, 247–256 (1988).
[CrossRef]

Ultrason. Imaging (1)

A. J. Devaney, “A filtered backpropagation algorithm for diffraction tomography,” Ultrason. Imaging 4, 336–360 (1982).
[CrossRef] [PubMed]

Other (9)

R. F. Harrington, Field Computation by Moment Methods (Kreiger, Malabar, Fla., 1985).

F. B. Jensen, W. A. Kuperman, M. B. Porter, H. Schmidt, eds., Computational Ocean Acoustics (American Institute of Physics, New York, 1994), Chap. 3.

L. B. Felsen, N. Marcuvitz, Radiation and Scattering of Waves (Prentice-Hall, Englewood Cliffs, N.J., 1973), Chap. 4 (republished by the Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1994).

B. Rao, “Gabor based gaussian beam tracing algorithm for wave propagation through large inhomogeneous regions,” M.S. thesis (Duke University, Durham, N.C., 1997).

B. Rao, L. Carin, “Inverse scattering for electrically large regions with a gaussian-beam forward model,” IEEE Trans. Antennas Propag. (to be published).

C. T. H. Baker, The Numerical Treatment of Integral Equations (Clarendon, Oxford, 1977).

A. N. Tikhonov, V. Y. Arsenin, Solution of Ill-Posed Problems (Winston, Washington D.C., 1977).

K. S. Kunz, R. J. Luebbers, The Finite Difference Time Domain Method for Electromagnetics (CRC Press, Boca Raton, Fla., 1993).

B. Rao, “Imaging algorithms for electrically large targets,” Ph.D. dissertation (Duke University, Durham, N.C., 1999).

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Figures (12)

Fig. 1
Fig. 1

General configuration used in inversion algorithm.

Fig. 2
Fig. 2

Outline of iterative-Born and distorted-Born schemes: (a) unknown profile; (b) initial guess, which is a flat profile; (c) first-order reconstruction of the profile; (d) computation of fields in the object; (e) final reconstructed profile.

Fig. 3
Fig. 3

Asymptotic fields due to the Gaussian-beam aperture, used as starter fields for the beam-tracing algorithm.

Fig. 4
Fig. 4

Schematic of wave-number-configuration phase-space lattice for the GT.

Fig. 5
Fig. 5

Representation of Gabor basis function parameters on the kxLx plane. A shows the curve for the optimal parameters [see Eq. (34)], B shows the Gabor basis parameter values for narrow beams, C shows the parameters for wide beams, and D shows those for tight beams.

Fig. 6
Fig. 6

Locations of the MP and the GT basis functions in the Lxkx space with respect to the optimality curve, for the reconstruction of the aperture function in Eq. (44).

Fig. 7
Fig. 7

Implementation of the inversion scheme using an arbitrary aperture antenna. The aperture is rotated through the dotted circle to get multiaspect measurements.

Fig. 8
Fig. 8

Imaging an object with the profile described in Eq. (46), with the aperture distribution given in Eq. (44): (a) original object project; (b) first-order Born approximation; (c)–(e) results after the second, third, and fifth iterations, respectively; (f) final profile after eight iterations; (g) plot of CF [see Eq. (11)] versus the iteration steps.

Fig. 9
Fig. 9

Imaging an object with the profile given in Eq. (47), by use of the aperture distribution given in Eq. (44): (a) original profile, (b) first-order Born approximation, (c) intermediate reconstruction, (d) final profile.

Fig. 10
Fig. 10

Imaging an object with the profile given in Eq. (48), by use of the aperture distribution given in Eq. (45): (a) original profile, (b) first-order Born approximation, (c) intermediate reconstruction, (d) final profile after six iterations.

Fig. 11
Fig. 11

Reconstruction of a square object with ξ=0.2: (a) exact profile; (b) result of the first-order Born approximation; (c)–(e) results after the second, third, and fifth iterations, respectively; (f) final profile after ten iterations.

Fig. 12
Fig. 12

Imaging with noisy data, an object with the profile given in (46), by use of the aperture distribution given in Eq. (44): (a), (b), (c), and (d) show the reconstructions at 50-, 45-, 40-, and 35-dB SNR levels, respectively; (e) shows the trend in CF for each of the four cases.

Equations (58)

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s2Ez(x, y)+k2(x, y)Ez(x, y)=-iωμoJzi,
k2=ω2μo(x, y).
Ez(x, y)=Ezinc(x, y)+Ezscat(x, y),
Ezscat(x, y)=DG(x, y; x, y)×ko2δrEz(x, y)dxdy.
G(x, y, x, y)=i4 Ho(1){ko[(x-x)2+(y-y)2]1/2},
δr=r(x, y)-rb(x, y)
Ez(x, y)=j=1Nujpj(x, y),
ko2δr(x, y)=j=1Nξjpj(x, y),
ul=uincl+GDξul,l=1Ms,
fl=GRξul,l=1Ms,
CF=l=1Msfl-GRξul2fl2.
fM=Kξ,
[K]p,q=DqG(xp, yp; x, y)Ezinc(x, y)dxdy,
p=1:M,q=1:N,
fM=Kcsξcs,
KcsHKcs+γHHHξcs=KcsHfM
Ezyˆ=-×Pxˆ.
2P(x, y)x2+2P(x, y)y2+ω2c2(x, y) P(x, y)=0,
dds 1c(x, y) dtds=-1c2(x, y) c(x, y),
dxds=cη(s),dηds=-1c2 cr,
dyds=cζ(s),dξds=-1c2 cy.
P(s, n)=W(s, n)exp[iωτ(s)],
W(s, n)=Kc(s)q(s)1/2 expiω 12 p(s)q(s) n2,
P(s, n)=Kc(s)q(s)1/2 expiωτ(s)+12 p(s)q(s) n2.
dqds=cp(s),dpds=-cnnc2 q(s),
B={2/ω Im[p(s)/q(s)]}1/2.
Bmin=2π sλ1/2.
w(x)=A exp-π(x-mx)2/Lx2exp(ikxx).
P(x, y)=C exp(iπ/4)λyR-ib1/2×expik0yR+12 xR2yR-ib,
θ=sin-1(kx/k)
b=(Lx cos θ)2/λ.
q(0)=c(0)(d-ib),
p(0)=1,
τ(0)=dc(0).
K=C exp(iπ/4)λ.
p(s)=1,q(s)=co(s+d)-icob.
B=2k01/2(s+d)2+b2b1/2.
bs.
λ4π2 Lx2(k02-kx2)=s.
f(x)=m,nAmn exp[-(x-mLx)2/Lx2]×exp(inkxx)kx=2π/Lx.
f(x)=f|w1w1(x)+R1(x),
S(f, w1)S(f, wk)wkD,
f|wk=f(x)wk*(x)dx,
f(x)=f|w1w1(x)+R1(x).
f2=|f|w1|2+R12,
Rn(x)=Rn|wnwn(x)+Rn+1(x),
S(Rn, wn)S(f, wk)wkD,
f(x)=n=1NRn-1|wnwn(x)+RN+1(x),
f2=n=1N|Rn-1|wn|2+RN+12.
f(x)=m exp(-(x-m)2/S2),
m=-5λ:5λinstepsofλ,
f(x)=exp(ik0r)/(i2πk0r)1/2,|x|10λ,
r=(x2+1002)1/2,
f(x)=0elsewhere.
ξ=K cos(ax)cos(ay).
ξ=K exp{-a[(x+xs)2+(y+ys)2]}+K exp{-a[(x-xs)2+(y-ys)2]},
ξ=K cosa(x-xshift)cosa(y-yshift).
SNR=l=1Msfl2/σ2,

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