Abstract

The three dimensional (3-D) extension of the two well-known diffraction tomography algorithms, namely, direct Fourier interpolation (DFI) and filtered backpropagation (FBP), are presented and the problem of the data needed for a full 3-D reconstruction is investigated. These algorithms can be used efficiently to solve the inverse scattering problem for weak scatterers in the frequency domain under the first-order Born and Rytov approximations. Previous attempts of 3-D reconstruction with plane-wave illumination have used data obtained with the incident direction restricted at the xy plane. However, we show that this restriction results in the omission of the contribution of certain spatial frequencies near the ωz axis for the final reconstruction. The effect of this omission is studied by comparing the results of reconstruction with and without data obtained from other incident directions that fill the spatial frequency domain. We conclude that the use of data obtained for incident direction in only the xy plane is sufficient to achieve a satisfactory quality of reconstruction for a class of objects presenting smooth variation along the z axis, while abrupt variations along the z axis cannot be imaged. This result should be taken into account in the process of designing the acquisition geometry of a tomography scanner.

© 2005 Optical Society of America

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  1. M. P. Andre, P. J. Martin, G. P. Otto, L. K. Olson, T. K. Barrett, B. A. Spivey, D. A. Palmer, “A new consideration of diffraction computed tomography for breast imaging,” Acoust. Imaging 21, 379–390 (1995).
    [CrossRef]
  2. H. Liu, C. L. Matson, K. Lau, R. R. Mapakshi, “Experimental validation of a backpropagation algorithm for three-dimensional breast tumor localization,” IEEE J. Sel. Top. Quantum Electron. 5, 1049–1057 (1999).
    [CrossRef]
  3. P. M. Meany, K. D. Paulsen, S. D. Geimer, S. A Haider, M. W. Fanning, “Quantification of 3-D field effects during 2-D microwave imaging,” IEEE Trans. Biomed. Eng. 49, 708–720 (2002).
    [CrossRef]
  4. S. Y. Semenov, A. E. Bulyshev, A. E. Souvorov, A. G. Nazarov, Y. E. Sizov, R. H. Svenson, V. G. Posukh, A. Pavlovsky, P. N. Repin, G. P. Tatsis, “Three-dimensional microwave tomography: experimental imaging of phantoms and biological objects,” IEEE Trans. Microwave Theory Tech. 48, 1071–1074 (2000).
    [CrossRef]
  5. H. Z. Takashi, T. Takenaka, T. Tanaka, “Three-dimensional reconstruction of a shallowly buried mine using time-domain data,” Microwave Opt. Technol. Lett. 39, 276–280 (2003).
    [CrossRef]
  6. C. N. Kechribaris, K. S. Nikita, N. K. Uzunoglu, “Reconstruction of two-dimensional permittivity distribution using an improved Rytov approximation and nonlinear optimization,”J. Electromagn. Waves Appl. 17, 183–207 (2003).
    [CrossRef]
  7. T. A. Maniatis, K. S. Nikita, N. K. Uzunoglu, “Two-dimensional dielectric profile reconstruction based on spectral-domain moment method and nonlinear optimization,” IEEE Trans. Microwave Theory Tech. 48, 1831–1840 (2000).
    [CrossRef]
  8. M. Gustafsson, S. He, “An optimization approach to multi-dimensional time-domain acoustic inverse problems,” J. Acoust. Soc. Am. 108, 1548–1556 (2000).
    [CrossRef] [PubMed]
  9. A. Abubakar, P. M Van den Berg, S. Y. Semenov, “Two and three dimensional algorithms for microwave imaging and inverse scattering,” J. Electromagn. Waves Appl. 17, 209–231 (2003).
    [CrossRef]
  10. S. Caorsi, A. Massa, M. Pastorino, M. Donelli, “Improved microwave imaging procedure for nondestructive evaluations of two dimensional structures,” IEEE Trans. Antennas Propag. 52, 1386–1397 (2004).
    [CrossRef]
  11. R. K. Mueller, M. Kaveh, G. Wade, “Reconstructive tomography and applications to ultrasonics,” Proc. IEEE 67, 567–587 (1979).
    [CrossRef]
  12. R. K. Mueller, M. Kaveh, R. D. Inverson, “A new approach to acoustic tomography using diffraction techniques,” Acoust. Imaging 8, 615–628 (1980).
    [CrossRef]
  13. M. Kaveh, M. Sumekh, J. Greenleaf, “Signal processing for diffraction tomography,” IEEE Trans. Sonics Ultrason. SU-31, 230–239 (1984).
    [CrossRef]
  14. E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun. 1, 153–156 (1969).
    [CrossRef]
  15. Z. Q. Lu, “Multidimensional structure diffraction tomography for varying object orientation through generalised scattered waves,” Inverse Probl. 1, 339–356 (1985).
    [CrossRef]
  16. A. J. Devaney, “A filtered backpropagation algorithm for diffraction tomography,” Ultrason. Imaging 4, 336–350 (1982).
    [CrossRef] [PubMed]
  17. A. J. Devaney, “Inversion formula for inverse scattering within the Born approximation,” Opt. Lett. 7, 111–112 (1982).
    [CrossRef] [PubMed]
  18. A. J. Devaney, “Diffraction tomography,” in Inverse Methods in Electromagnetic Imaging: Part II, W. M. Boerner, ed. (Reidel, Dordrecht, The Netherlands, 1985), pp. 1107–1135.
  19. A. C. Kak, M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, New York, 1988).
  20. N. Sponheim, I. Johansen, “Experimental results in ultrasonic tomography using a filtered backpropagation algorithm,” Ultrason. Imaging 13, 56–70 (1991).
    [CrossRef] [PubMed]
  21. N. Sponheim, L. J. Gelius, I. Johansen, J. J. Stamnes, “Quantitative results in ultrasonic tomography of large objects using line sources and curved detector arrays,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 38, 370–379 (1991).
    [CrossRef] [PubMed]
  22. A. J. Devaney, G. Beylkin, “Diffraction tomography using arbitrary transmitter and receiver surfaces,” Ultrason. Imaging 6, 181–193 (1984).
    [CrossRef] [PubMed]
  23. M. A. Anastasio, X. Pan, “An improved reconstruction algorithm for 3-D diffraction tomography using spherical wave sources,” IEEE Trans. Biomed. Eng. 50, 517–521 (2003).
    [CrossRef] [PubMed]
  24. X. Pan, M. A. Anastasio, “Minimal-scan filtered backpropagation algorithms for diffraction tomography,” J. Opt. Soc. Am. A 16, 2896–2903 (1999).
    [CrossRef]
  25. M. A. Anastasio, X. Pan, “A new reconstruction approach for reflection mode diffraction tomography,” IEEE Trans. Image Process. 9, 1262–1271 (2000).
    [CrossRef]
  26. T. J. Cui, W. C. Chew, “Diffraction tomographic algorithm for the detection of three-dimensional objects buried in lossy half-space,” IEEE Trans. Antennas Propag. 50, 42–49 (2002).
    [CrossRef]
  27. R. D. March, T. K. K. Chan, “Improving microwave imaging by enhancing diffraction tomography,” IEEE Trans. Microwave Theory Tech. 44, 379–388 (1996).
    [CrossRef]
  28. S. Pourjavid, O. Tretiak, “Ultrasound imaging through time-domain diffraction tomography,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 38, 74–85 (1991).
    [CrossRef] [PubMed]
  29. T. Melamed, Y. Ehrlich, E. Heyman, “Short-pulse inversion of inhomogeneous media: a time-domain diffraction tomography,” Inverse Probl. 12, 977–993 (1996).
    [CrossRef]
  30. M. A. Anastasio, X. Pan, “Computationally efficient and statistically robust image reconstruction in three-dimensional diffraction tomography,” J. Opt. Soc. Am. A 17, 391–400 (2000).
    [CrossRef]
  31. O. R. Halse, J. J. Stamnes, A. J. Devaney, “Three-dimensional diffraction tomography by two-dimensional sectioning,” Opt. Commun. 224, 185–195 (2003).
    [CrossRef]
  32. D. T. Borup, O. P. Gandhi, “Fast-Fourier-transform method for calculation of SAR distributions in finely discretized inhomogeneous models of biological bodies,” IEEE Trans. Microwave Theory Tech. 32, 355–360 (1984).
    [CrossRef]
  33. A. Dutt, V. Rokhlin, “Fast Fourier transforms for nonequispaced data,” SIAM J. Sci. Comput. (USA) 14, 1368–1393 (1993).
    [CrossRef]
  34. S. Y. Semenov, R. H. Svenson, A. E. Boulyshev, A. E. Souvorov, V. Y. Borisov, Y. Sizor, A. N. Starostin, K. R. Dezern, G. P. Tatsis, V. Y. Baranov, “Microwave tomography: two-dimensional system for biological imaging,” IEEE Trans. Biomed. Eng. 43, 869–877 (1996).
    [CrossRef] [PubMed]
  35. A. Franchois, A. Joisel, C. Pichot, J. C. Bolomey, “Quantitative microwave imaging with a 2.45-GHz planar microwave camera,” IEEE Trans. Med. Imaging 17, 550–561 (1998).
    [CrossRef] [PubMed]

2004 (1)

S. Caorsi, A. Massa, M. Pastorino, M. Donelli, “Improved microwave imaging procedure for nondestructive evaluations of two dimensional structures,” IEEE Trans. Antennas Propag. 52, 1386–1397 (2004).
[CrossRef]

2003 (5)

A. Abubakar, P. M Van den Berg, S. Y. Semenov, “Two and three dimensional algorithms for microwave imaging and inverse scattering,” J. Electromagn. Waves Appl. 17, 209–231 (2003).
[CrossRef]

H. Z. Takashi, T. Takenaka, T. Tanaka, “Three-dimensional reconstruction of a shallowly buried mine using time-domain data,” Microwave Opt. Technol. Lett. 39, 276–280 (2003).
[CrossRef]

C. N. Kechribaris, K. S. Nikita, N. K. Uzunoglu, “Reconstruction of two-dimensional permittivity distribution using an improved Rytov approximation and nonlinear optimization,”J. Electromagn. Waves Appl. 17, 183–207 (2003).
[CrossRef]

M. A. Anastasio, X. Pan, “An improved reconstruction algorithm for 3-D diffraction tomography using spherical wave sources,” IEEE Trans. Biomed. Eng. 50, 517–521 (2003).
[CrossRef] [PubMed]

O. R. Halse, J. J. Stamnes, A. J. Devaney, “Three-dimensional diffraction tomography by two-dimensional sectioning,” Opt. Commun. 224, 185–195 (2003).
[CrossRef]

2002 (2)

T. J. Cui, W. C. Chew, “Diffraction tomographic algorithm for the detection of three-dimensional objects buried in lossy half-space,” IEEE Trans. Antennas Propag. 50, 42–49 (2002).
[CrossRef]

P. M. Meany, K. D. Paulsen, S. D. Geimer, S. A Haider, M. W. Fanning, “Quantification of 3-D field effects during 2-D microwave imaging,” IEEE Trans. Biomed. Eng. 49, 708–720 (2002).
[CrossRef]

2000 (5)

S. Y. Semenov, A. E. Bulyshev, A. E. Souvorov, A. G. Nazarov, Y. E. Sizov, R. H. Svenson, V. G. Posukh, A. Pavlovsky, P. N. Repin, G. P. Tatsis, “Three-dimensional microwave tomography: experimental imaging of phantoms and biological objects,” IEEE Trans. Microwave Theory Tech. 48, 1071–1074 (2000).
[CrossRef]

T. A. Maniatis, K. S. Nikita, N. K. Uzunoglu, “Two-dimensional dielectric profile reconstruction based on spectral-domain moment method and nonlinear optimization,” IEEE Trans. Microwave Theory Tech. 48, 1831–1840 (2000).
[CrossRef]

M. Gustafsson, S. He, “An optimization approach to multi-dimensional time-domain acoustic inverse problems,” J. Acoust. Soc. Am. 108, 1548–1556 (2000).
[CrossRef] [PubMed]

M. A. Anastasio, X. Pan, “A new reconstruction approach for reflection mode diffraction tomography,” IEEE Trans. Image Process. 9, 1262–1271 (2000).
[CrossRef]

M. A. Anastasio, X. Pan, “Computationally efficient and statistically robust image reconstruction in three-dimensional diffraction tomography,” J. Opt. Soc. Am. A 17, 391–400 (2000).
[CrossRef]

1999 (2)

X. Pan, M. A. Anastasio, “Minimal-scan filtered backpropagation algorithms for diffraction tomography,” J. Opt. Soc. Am. A 16, 2896–2903 (1999).
[CrossRef]

H. Liu, C. L. Matson, K. Lau, R. R. Mapakshi, “Experimental validation of a backpropagation algorithm for three-dimensional breast tumor localization,” IEEE J. Sel. Top. Quantum Electron. 5, 1049–1057 (1999).
[CrossRef]

1998 (1)

A. Franchois, A. Joisel, C. Pichot, J. C. Bolomey, “Quantitative microwave imaging with a 2.45-GHz planar microwave camera,” IEEE Trans. Med. Imaging 17, 550–561 (1998).
[CrossRef] [PubMed]

1996 (3)

S. Y. Semenov, R. H. Svenson, A. E. Boulyshev, A. E. Souvorov, V. Y. Borisov, Y. Sizor, A. N. Starostin, K. R. Dezern, G. P. Tatsis, V. Y. Baranov, “Microwave tomography: two-dimensional system for biological imaging,” IEEE Trans. Biomed. Eng. 43, 869–877 (1996).
[CrossRef] [PubMed]

T. Melamed, Y. Ehrlich, E. Heyman, “Short-pulse inversion of inhomogeneous media: a time-domain diffraction tomography,” Inverse Probl. 12, 977–993 (1996).
[CrossRef]

R. D. March, T. K. K. Chan, “Improving microwave imaging by enhancing diffraction tomography,” IEEE Trans. Microwave Theory Tech. 44, 379–388 (1996).
[CrossRef]

1995 (1)

M. P. Andre, P. J. Martin, G. P. Otto, L. K. Olson, T. K. Barrett, B. A. Spivey, D. A. Palmer, “A new consideration of diffraction computed tomography for breast imaging,” Acoust. Imaging 21, 379–390 (1995).
[CrossRef]

1993 (1)

A. Dutt, V. Rokhlin, “Fast Fourier transforms for nonequispaced data,” SIAM J. Sci. Comput. (USA) 14, 1368–1393 (1993).
[CrossRef]

1991 (3)

S. Pourjavid, O. Tretiak, “Ultrasound imaging through time-domain diffraction tomography,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 38, 74–85 (1991).
[CrossRef] [PubMed]

N. Sponheim, I. Johansen, “Experimental results in ultrasonic tomography using a filtered backpropagation algorithm,” Ultrason. Imaging 13, 56–70 (1991).
[CrossRef] [PubMed]

N. Sponheim, L. J. Gelius, I. Johansen, J. J. Stamnes, “Quantitative results in ultrasonic tomography of large objects using line sources and curved detector arrays,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 38, 370–379 (1991).
[CrossRef] [PubMed]

1985 (1)

Z. Q. Lu, “Multidimensional structure diffraction tomography for varying object orientation through generalised scattered waves,” Inverse Probl. 1, 339–356 (1985).
[CrossRef]

1984 (3)

M. Kaveh, M. Sumekh, J. Greenleaf, “Signal processing for diffraction tomography,” IEEE Trans. Sonics Ultrason. SU-31, 230–239 (1984).
[CrossRef]

A. J. Devaney, G. Beylkin, “Diffraction tomography using arbitrary transmitter and receiver surfaces,” Ultrason. Imaging 6, 181–193 (1984).
[CrossRef] [PubMed]

D. T. Borup, O. P. Gandhi, “Fast-Fourier-transform method for calculation of SAR distributions in finely discretized inhomogeneous models of biological bodies,” IEEE Trans. Microwave Theory Tech. 32, 355–360 (1984).
[CrossRef]

1982 (2)

A. J. Devaney, “Inversion formula for inverse scattering within the Born approximation,” Opt. Lett. 7, 111–112 (1982).
[CrossRef] [PubMed]

A. J. Devaney, “A filtered backpropagation algorithm for diffraction tomography,” Ultrason. Imaging 4, 336–350 (1982).
[CrossRef] [PubMed]

1980 (1)

R. K. Mueller, M. Kaveh, R. D. Inverson, “A new approach to acoustic tomography using diffraction techniques,” Acoust. Imaging 8, 615–628 (1980).
[CrossRef]

1979 (1)

R. K. Mueller, M. Kaveh, G. Wade, “Reconstructive tomography and applications to ultrasonics,” Proc. IEEE 67, 567–587 (1979).
[CrossRef]

1969 (1)

E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun. 1, 153–156 (1969).
[CrossRef]

Abubakar, A.

A. Abubakar, P. M Van den Berg, S. Y. Semenov, “Two and three dimensional algorithms for microwave imaging and inverse scattering,” J. Electromagn. Waves Appl. 17, 209–231 (2003).
[CrossRef]

Anastasio, M. A.

M. A. Anastasio, X. Pan, “An improved reconstruction algorithm for 3-D diffraction tomography using spherical wave sources,” IEEE Trans. Biomed. Eng. 50, 517–521 (2003).
[CrossRef] [PubMed]

M. A. Anastasio, X. Pan, “Computationally efficient and statistically robust image reconstruction in three-dimensional diffraction tomography,” J. Opt. Soc. Am. A 17, 391–400 (2000).
[CrossRef]

M. A. Anastasio, X. Pan, “A new reconstruction approach for reflection mode diffraction tomography,” IEEE Trans. Image Process. 9, 1262–1271 (2000).
[CrossRef]

X. Pan, M. A. Anastasio, “Minimal-scan filtered backpropagation algorithms for diffraction tomography,” J. Opt. Soc. Am. A 16, 2896–2903 (1999).
[CrossRef]

Andre, M. P.

M. P. Andre, P. J. Martin, G. P. Otto, L. K. Olson, T. K. Barrett, B. A. Spivey, D. A. Palmer, “A new consideration of diffraction computed tomography for breast imaging,” Acoust. Imaging 21, 379–390 (1995).
[CrossRef]

Baranov, V. Y.

S. Y. Semenov, R. H. Svenson, A. E. Boulyshev, A. E. Souvorov, V. Y. Borisov, Y. Sizor, A. N. Starostin, K. R. Dezern, G. P. Tatsis, V. Y. Baranov, “Microwave tomography: two-dimensional system for biological imaging,” IEEE Trans. Biomed. Eng. 43, 869–877 (1996).
[CrossRef] [PubMed]

Barrett, T. K.

M. P. Andre, P. J. Martin, G. P. Otto, L. K. Olson, T. K. Barrett, B. A. Spivey, D. A. Palmer, “A new consideration of diffraction computed tomography for breast imaging,” Acoust. Imaging 21, 379–390 (1995).
[CrossRef]

Beylkin, G.

A. J. Devaney, G. Beylkin, “Diffraction tomography using arbitrary transmitter and receiver surfaces,” Ultrason. Imaging 6, 181–193 (1984).
[CrossRef] [PubMed]

Bolomey, J. C.

A. Franchois, A. Joisel, C. Pichot, J. C. Bolomey, “Quantitative microwave imaging with a 2.45-GHz planar microwave camera,” IEEE Trans. Med. Imaging 17, 550–561 (1998).
[CrossRef] [PubMed]

Borisov, V. Y.

S. Y. Semenov, R. H. Svenson, A. E. Boulyshev, A. E. Souvorov, V. Y. Borisov, Y. Sizor, A. N. Starostin, K. R. Dezern, G. P. Tatsis, V. Y. Baranov, “Microwave tomography: two-dimensional system for biological imaging,” IEEE Trans. Biomed. Eng. 43, 869–877 (1996).
[CrossRef] [PubMed]

Borup, D. T.

D. T. Borup, O. P. Gandhi, “Fast-Fourier-transform method for calculation of SAR distributions in finely discretized inhomogeneous models of biological bodies,” IEEE Trans. Microwave Theory Tech. 32, 355–360 (1984).
[CrossRef]

Boulyshev, A. E.

S. Y. Semenov, R. H. Svenson, A. E. Boulyshev, A. E. Souvorov, V. Y. Borisov, Y. Sizor, A. N. Starostin, K. R. Dezern, G. P. Tatsis, V. Y. Baranov, “Microwave tomography: two-dimensional system for biological imaging,” IEEE Trans. Biomed. Eng. 43, 869–877 (1996).
[CrossRef] [PubMed]

Bulyshev, A. E.

S. Y. Semenov, A. E. Bulyshev, A. E. Souvorov, A. G. Nazarov, Y. E. Sizov, R. H. Svenson, V. G. Posukh, A. Pavlovsky, P. N. Repin, G. P. Tatsis, “Three-dimensional microwave tomography: experimental imaging of phantoms and biological objects,” IEEE Trans. Microwave Theory Tech. 48, 1071–1074 (2000).
[CrossRef]

Caorsi, S.

S. Caorsi, A. Massa, M. Pastorino, M. Donelli, “Improved microwave imaging procedure for nondestructive evaluations of two dimensional structures,” IEEE Trans. Antennas Propag. 52, 1386–1397 (2004).
[CrossRef]

Chan, T. K. K.

R. D. March, T. K. K. Chan, “Improving microwave imaging by enhancing diffraction tomography,” IEEE Trans. Microwave Theory Tech. 44, 379–388 (1996).
[CrossRef]

Chew, W. C.

T. J. Cui, W. C. Chew, “Diffraction tomographic algorithm for the detection of three-dimensional objects buried in lossy half-space,” IEEE Trans. Antennas Propag. 50, 42–49 (2002).
[CrossRef]

Cui, T. J.

T. J. Cui, W. C. Chew, “Diffraction tomographic algorithm for the detection of three-dimensional objects buried in lossy half-space,” IEEE Trans. Antennas Propag. 50, 42–49 (2002).
[CrossRef]

Devaney, A. J.

O. R. Halse, J. J. Stamnes, A. J. Devaney, “Three-dimensional diffraction tomography by two-dimensional sectioning,” Opt. Commun. 224, 185–195 (2003).
[CrossRef]

A. J. Devaney, G. Beylkin, “Diffraction tomography using arbitrary transmitter and receiver surfaces,” Ultrason. Imaging 6, 181–193 (1984).
[CrossRef] [PubMed]

A. J. Devaney, “Inversion formula for inverse scattering within the Born approximation,” Opt. Lett. 7, 111–112 (1982).
[CrossRef] [PubMed]

A. J. Devaney, “A filtered backpropagation algorithm for diffraction tomography,” Ultrason. Imaging 4, 336–350 (1982).
[CrossRef] [PubMed]

A. J. Devaney, “Diffraction tomography,” in Inverse Methods in Electromagnetic Imaging: Part II, W. M. Boerner, ed. (Reidel, Dordrecht, The Netherlands, 1985), pp. 1107–1135.

Dezern, K. R.

S. Y. Semenov, R. H. Svenson, A. E. Boulyshev, A. E. Souvorov, V. Y. Borisov, Y. Sizor, A. N. Starostin, K. R. Dezern, G. P. Tatsis, V. Y. Baranov, “Microwave tomography: two-dimensional system for biological imaging,” IEEE Trans. Biomed. Eng. 43, 869–877 (1996).
[CrossRef] [PubMed]

Donelli, M.

S. Caorsi, A. Massa, M. Pastorino, M. Donelli, “Improved microwave imaging procedure for nondestructive evaluations of two dimensional structures,” IEEE Trans. Antennas Propag. 52, 1386–1397 (2004).
[CrossRef]

Dutt, A.

A. Dutt, V. Rokhlin, “Fast Fourier transforms for nonequispaced data,” SIAM J. Sci. Comput. (USA) 14, 1368–1393 (1993).
[CrossRef]

Ehrlich, Y.

T. Melamed, Y. Ehrlich, E. Heyman, “Short-pulse inversion of inhomogeneous media: a time-domain diffraction tomography,” Inverse Probl. 12, 977–993 (1996).
[CrossRef]

Fanning, M. W.

P. M. Meany, K. D. Paulsen, S. D. Geimer, S. A Haider, M. W. Fanning, “Quantification of 3-D field effects during 2-D microwave imaging,” IEEE Trans. Biomed. Eng. 49, 708–720 (2002).
[CrossRef]

Franchois, A.

A. Franchois, A. Joisel, C. Pichot, J. C. Bolomey, “Quantitative microwave imaging with a 2.45-GHz planar microwave camera,” IEEE Trans. Med. Imaging 17, 550–561 (1998).
[CrossRef] [PubMed]

Gandhi, O. P.

D. T. Borup, O. P. Gandhi, “Fast-Fourier-transform method for calculation of SAR distributions in finely discretized inhomogeneous models of biological bodies,” IEEE Trans. Microwave Theory Tech. 32, 355–360 (1984).
[CrossRef]

Geimer, S. D.

P. M. Meany, K. D. Paulsen, S. D. Geimer, S. A Haider, M. W. Fanning, “Quantification of 3-D field effects during 2-D microwave imaging,” IEEE Trans. Biomed. Eng. 49, 708–720 (2002).
[CrossRef]

Gelius, L. J.

N. Sponheim, L. J. Gelius, I. Johansen, J. J. Stamnes, “Quantitative results in ultrasonic tomography of large objects using line sources and curved detector arrays,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 38, 370–379 (1991).
[CrossRef] [PubMed]

Greenleaf, J.

M. Kaveh, M. Sumekh, J. Greenleaf, “Signal processing for diffraction tomography,” IEEE Trans. Sonics Ultrason. SU-31, 230–239 (1984).
[CrossRef]

Gustafsson, M.

M. Gustafsson, S. He, “An optimization approach to multi-dimensional time-domain acoustic inverse problems,” J. Acoust. Soc. Am. 108, 1548–1556 (2000).
[CrossRef] [PubMed]

Haider, S. A

P. M. Meany, K. D. Paulsen, S. D. Geimer, S. A Haider, M. W. Fanning, “Quantification of 3-D field effects during 2-D microwave imaging,” IEEE Trans. Biomed. Eng. 49, 708–720 (2002).
[CrossRef]

Halse, O. R.

O. R. Halse, J. J. Stamnes, A. J. Devaney, “Three-dimensional diffraction tomography by two-dimensional sectioning,” Opt. Commun. 224, 185–195 (2003).
[CrossRef]

He, S.

M. Gustafsson, S. He, “An optimization approach to multi-dimensional time-domain acoustic inverse problems,” J. Acoust. Soc. Am. 108, 1548–1556 (2000).
[CrossRef] [PubMed]

Heyman, E.

T. Melamed, Y. Ehrlich, E. Heyman, “Short-pulse inversion of inhomogeneous media: a time-domain diffraction tomography,” Inverse Probl. 12, 977–993 (1996).
[CrossRef]

Inverson, R. D.

R. K. Mueller, M. Kaveh, R. D. Inverson, “A new approach to acoustic tomography using diffraction techniques,” Acoust. Imaging 8, 615–628 (1980).
[CrossRef]

Johansen, I.

N. Sponheim, L. J. Gelius, I. Johansen, J. J. Stamnes, “Quantitative results in ultrasonic tomography of large objects using line sources and curved detector arrays,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 38, 370–379 (1991).
[CrossRef] [PubMed]

N. Sponheim, I. Johansen, “Experimental results in ultrasonic tomography using a filtered backpropagation algorithm,” Ultrason. Imaging 13, 56–70 (1991).
[CrossRef] [PubMed]

Joisel, A.

A. Franchois, A. Joisel, C. Pichot, J. C. Bolomey, “Quantitative microwave imaging with a 2.45-GHz planar microwave camera,” IEEE Trans. Med. Imaging 17, 550–561 (1998).
[CrossRef] [PubMed]

Kak, A. C.

A. C. Kak, M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, New York, 1988).

Kaveh, M.

M. Kaveh, M. Sumekh, J. Greenleaf, “Signal processing for diffraction tomography,” IEEE Trans. Sonics Ultrason. SU-31, 230–239 (1984).
[CrossRef]

R. K. Mueller, M. Kaveh, R. D. Inverson, “A new approach to acoustic tomography using diffraction techniques,” Acoust. Imaging 8, 615–628 (1980).
[CrossRef]

R. K. Mueller, M. Kaveh, G. Wade, “Reconstructive tomography and applications to ultrasonics,” Proc. IEEE 67, 567–587 (1979).
[CrossRef]

Kechribaris, C. N.

C. N. Kechribaris, K. S. Nikita, N. K. Uzunoglu, “Reconstruction of two-dimensional permittivity distribution using an improved Rytov approximation and nonlinear optimization,”J. Electromagn. Waves Appl. 17, 183–207 (2003).
[CrossRef]

Lau, K.

H. Liu, C. L. Matson, K. Lau, R. R. Mapakshi, “Experimental validation of a backpropagation algorithm for three-dimensional breast tumor localization,” IEEE J. Sel. Top. Quantum Electron. 5, 1049–1057 (1999).
[CrossRef]

Liu, H.

H. Liu, C. L. Matson, K. Lau, R. R. Mapakshi, “Experimental validation of a backpropagation algorithm for three-dimensional breast tumor localization,” IEEE J. Sel. Top. Quantum Electron. 5, 1049–1057 (1999).
[CrossRef]

Lu, Z. Q.

Z. Q. Lu, “Multidimensional structure diffraction tomography for varying object orientation through generalised scattered waves,” Inverse Probl. 1, 339–356 (1985).
[CrossRef]

Maniatis, T. A.

T. A. Maniatis, K. S. Nikita, N. K. Uzunoglu, “Two-dimensional dielectric profile reconstruction based on spectral-domain moment method and nonlinear optimization,” IEEE Trans. Microwave Theory Tech. 48, 1831–1840 (2000).
[CrossRef]

Mapakshi, R. R.

H. Liu, C. L. Matson, K. Lau, R. R. Mapakshi, “Experimental validation of a backpropagation algorithm for three-dimensional breast tumor localization,” IEEE J. Sel. Top. Quantum Electron. 5, 1049–1057 (1999).
[CrossRef]

March, R. D.

R. D. March, T. K. K. Chan, “Improving microwave imaging by enhancing diffraction tomography,” IEEE Trans. Microwave Theory Tech. 44, 379–388 (1996).
[CrossRef]

Martin, P. J.

M. P. Andre, P. J. Martin, G. P. Otto, L. K. Olson, T. K. Barrett, B. A. Spivey, D. A. Palmer, “A new consideration of diffraction computed tomography for breast imaging,” Acoust. Imaging 21, 379–390 (1995).
[CrossRef]

Massa, A.

S. Caorsi, A. Massa, M. Pastorino, M. Donelli, “Improved microwave imaging procedure for nondestructive evaluations of two dimensional structures,” IEEE Trans. Antennas Propag. 52, 1386–1397 (2004).
[CrossRef]

Matson, C. L.

H. Liu, C. L. Matson, K. Lau, R. R. Mapakshi, “Experimental validation of a backpropagation algorithm for three-dimensional breast tumor localization,” IEEE J. Sel. Top. Quantum Electron. 5, 1049–1057 (1999).
[CrossRef]

Meany, P. M.

P. M. Meany, K. D. Paulsen, S. D. Geimer, S. A Haider, M. W. Fanning, “Quantification of 3-D field effects during 2-D microwave imaging,” IEEE Trans. Biomed. Eng. 49, 708–720 (2002).
[CrossRef]

Melamed, T.

T. Melamed, Y. Ehrlich, E. Heyman, “Short-pulse inversion of inhomogeneous media: a time-domain diffraction tomography,” Inverse Probl. 12, 977–993 (1996).
[CrossRef]

Mueller, R. K.

R. K. Mueller, M. Kaveh, R. D. Inverson, “A new approach to acoustic tomography using diffraction techniques,” Acoust. Imaging 8, 615–628 (1980).
[CrossRef]

R. K. Mueller, M. Kaveh, G. Wade, “Reconstructive tomography and applications to ultrasonics,” Proc. IEEE 67, 567–587 (1979).
[CrossRef]

Nazarov, A. G.

S. Y. Semenov, A. E. Bulyshev, A. E. Souvorov, A. G. Nazarov, Y. E. Sizov, R. H. Svenson, V. G. Posukh, A. Pavlovsky, P. N. Repin, G. P. Tatsis, “Three-dimensional microwave tomography: experimental imaging of phantoms and biological objects,” IEEE Trans. Microwave Theory Tech. 48, 1071–1074 (2000).
[CrossRef]

Nikita, K. S.

C. N. Kechribaris, K. S. Nikita, N. K. Uzunoglu, “Reconstruction of two-dimensional permittivity distribution using an improved Rytov approximation and nonlinear optimization,”J. Electromagn. Waves Appl. 17, 183–207 (2003).
[CrossRef]

T. A. Maniatis, K. S. Nikita, N. K. Uzunoglu, “Two-dimensional dielectric profile reconstruction based on spectral-domain moment method and nonlinear optimization,” IEEE Trans. Microwave Theory Tech. 48, 1831–1840 (2000).
[CrossRef]

Olson, L. K.

M. P. Andre, P. J. Martin, G. P. Otto, L. K. Olson, T. K. Barrett, B. A. Spivey, D. A. Palmer, “A new consideration of diffraction computed tomography for breast imaging,” Acoust. Imaging 21, 379–390 (1995).
[CrossRef]

Otto, G. P.

M. P. Andre, P. J. Martin, G. P. Otto, L. K. Olson, T. K. Barrett, B. A. Spivey, D. A. Palmer, “A new consideration of diffraction computed tomography for breast imaging,” Acoust. Imaging 21, 379–390 (1995).
[CrossRef]

Palmer, D. A.

M. P. Andre, P. J. Martin, G. P. Otto, L. K. Olson, T. K. Barrett, B. A. Spivey, D. A. Palmer, “A new consideration of diffraction computed tomography for breast imaging,” Acoust. Imaging 21, 379–390 (1995).
[CrossRef]

Pan, X.

M. A. Anastasio, X. Pan, “An improved reconstruction algorithm for 3-D diffraction tomography using spherical wave sources,” IEEE Trans. Biomed. Eng. 50, 517–521 (2003).
[CrossRef] [PubMed]

M. A. Anastasio, X. Pan, “Computationally efficient and statistically robust image reconstruction in three-dimensional diffraction tomography,” J. Opt. Soc. Am. A 17, 391–400 (2000).
[CrossRef]

M. A. Anastasio, X. Pan, “A new reconstruction approach for reflection mode diffraction tomography,” IEEE Trans. Image Process. 9, 1262–1271 (2000).
[CrossRef]

X. Pan, M. A. Anastasio, “Minimal-scan filtered backpropagation algorithms for diffraction tomography,” J. Opt. Soc. Am. A 16, 2896–2903 (1999).
[CrossRef]

Pastorino, M.

S. Caorsi, A. Massa, M. Pastorino, M. Donelli, “Improved microwave imaging procedure for nondestructive evaluations of two dimensional structures,” IEEE Trans. Antennas Propag. 52, 1386–1397 (2004).
[CrossRef]

Paulsen, K. D.

P. M. Meany, K. D. Paulsen, S. D. Geimer, S. A Haider, M. W. Fanning, “Quantification of 3-D field effects during 2-D microwave imaging,” IEEE Trans. Biomed. Eng. 49, 708–720 (2002).
[CrossRef]

Pavlovsky, A.

S. Y. Semenov, A. E. Bulyshev, A. E. Souvorov, A. G. Nazarov, Y. E. Sizov, R. H. Svenson, V. G. Posukh, A. Pavlovsky, P. N. Repin, G. P. Tatsis, “Three-dimensional microwave tomography: experimental imaging of phantoms and biological objects,” IEEE Trans. Microwave Theory Tech. 48, 1071–1074 (2000).
[CrossRef]

Pichot, C.

A. Franchois, A. Joisel, C. Pichot, J. C. Bolomey, “Quantitative microwave imaging with a 2.45-GHz planar microwave camera,” IEEE Trans. Med. Imaging 17, 550–561 (1998).
[CrossRef] [PubMed]

Posukh, V. G.

S. Y. Semenov, A. E. Bulyshev, A. E. Souvorov, A. G. Nazarov, Y. E. Sizov, R. H. Svenson, V. G. Posukh, A. Pavlovsky, P. N. Repin, G. P. Tatsis, “Three-dimensional microwave tomography: experimental imaging of phantoms and biological objects,” IEEE Trans. Microwave Theory Tech. 48, 1071–1074 (2000).
[CrossRef]

Pourjavid, S.

S. Pourjavid, O. Tretiak, “Ultrasound imaging through time-domain diffraction tomography,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 38, 74–85 (1991).
[CrossRef] [PubMed]

Repin, P. N.

S. Y. Semenov, A. E. Bulyshev, A. E. Souvorov, A. G. Nazarov, Y. E. Sizov, R. H. Svenson, V. G. Posukh, A. Pavlovsky, P. N. Repin, G. P. Tatsis, “Three-dimensional microwave tomography: experimental imaging of phantoms and biological objects,” IEEE Trans. Microwave Theory Tech. 48, 1071–1074 (2000).
[CrossRef]

Rokhlin, V.

A. Dutt, V. Rokhlin, “Fast Fourier transforms for nonequispaced data,” SIAM J. Sci. Comput. (USA) 14, 1368–1393 (1993).
[CrossRef]

Semenov, S. Y.

A. Abubakar, P. M Van den Berg, S. Y. Semenov, “Two and three dimensional algorithms for microwave imaging and inverse scattering,” J. Electromagn. Waves Appl. 17, 209–231 (2003).
[CrossRef]

S. Y. Semenov, A. E. Bulyshev, A. E. Souvorov, A. G. Nazarov, Y. E. Sizov, R. H. Svenson, V. G. Posukh, A. Pavlovsky, P. N. Repin, G. P. Tatsis, “Three-dimensional microwave tomography: experimental imaging of phantoms and biological objects,” IEEE Trans. Microwave Theory Tech. 48, 1071–1074 (2000).
[CrossRef]

S. Y. Semenov, R. H. Svenson, A. E. Boulyshev, A. E. Souvorov, V. Y. Borisov, Y. Sizor, A. N. Starostin, K. R. Dezern, G. P. Tatsis, V. Y. Baranov, “Microwave tomography: two-dimensional system for biological imaging,” IEEE Trans. Biomed. Eng. 43, 869–877 (1996).
[CrossRef] [PubMed]

Sizor, Y.

S. Y. Semenov, R. H. Svenson, A. E. Boulyshev, A. E. Souvorov, V. Y. Borisov, Y. Sizor, A. N. Starostin, K. R. Dezern, G. P. Tatsis, V. Y. Baranov, “Microwave tomography: two-dimensional system for biological imaging,” IEEE Trans. Biomed. Eng. 43, 869–877 (1996).
[CrossRef] [PubMed]

Sizov, Y. E.

S. Y. Semenov, A. E. Bulyshev, A. E. Souvorov, A. G. Nazarov, Y. E. Sizov, R. H. Svenson, V. G. Posukh, A. Pavlovsky, P. N. Repin, G. P. Tatsis, “Three-dimensional microwave tomography: experimental imaging of phantoms and biological objects,” IEEE Trans. Microwave Theory Tech. 48, 1071–1074 (2000).
[CrossRef]

Slaney, M.

A. C. Kak, M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, New York, 1988).

Souvorov, A. E.

S. Y. Semenov, A. E. Bulyshev, A. E. Souvorov, A. G. Nazarov, Y. E. Sizov, R. H. Svenson, V. G. Posukh, A. Pavlovsky, P. N. Repin, G. P. Tatsis, “Three-dimensional microwave tomography: experimental imaging of phantoms and biological objects,” IEEE Trans. Microwave Theory Tech. 48, 1071–1074 (2000).
[CrossRef]

S. Y. Semenov, R. H. Svenson, A. E. Boulyshev, A. E. Souvorov, V. Y. Borisov, Y. Sizor, A. N. Starostin, K. R. Dezern, G. P. Tatsis, V. Y. Baranov, “Microwave tomography: two-dimensional system for biological imaging,” IEEE Trans. Biomed. Eng. 43, 869–877 (1996).
[CrossRef] [PubMed]

Spivey, B. A.

M. P. Andre, P. J. Martin, G. P. Otto, L. K. Olson, T. K. Barrett, B. A. Spivey, D. A. Palmer, “A new consideration of diffraction computed tomography for breast imaging,” Acoust. Imaging 21, 379–390 (1995).
[CrossRef]

Sponheim, N.

N. Sponheim, I. Johansen, “Experimental results in ultrasonic tomography using a filtered backpropagation algorithm,” Ultrason. Imaging 13, 56–70 (1991).
[CrossRef] [PubMed]

N. Sponheim, L. J. Gelius, I. Johansen, J. J. Stamnes, “Quantitative results in ultrasonic tomography of large objects using line sources and curved detector arrays,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 38, 370–379 (1991).
[CrossRef] [PubMed]

Stamnes, J. J.

O. R. Halse, J. J. Stamnes, A. J. Devaney, “Three-dimensional diffraction tomography by two-dimensional sectioning,” Opt. Commun. 224, 185–195 (2003).
[CrossRef]

N. Sponheim, L. J. Gelius, I. Johansen, J. J. Stamnes, “Quantitative results in ultrasonic tomography of large objects using line sources and curved detector arrays,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 38, 370–379 (1991).
[CrossRef] [PubMed]

Starostin, A. N.

S. Y. Semenov, R. H. Svenson, A. E. Boulyshev, A. E. Souvorov, V. Y. Borisov, Y. Sizor, A. N. Starostin, K. R. Dezern, G. P. Tatsis, V. Y. Baranov, “Microwave tomography: two-dimensional system for biological imaging,” IEEE Trans. Biomed. Eng. 43, 869–877 (1996).
[CrossRef] [PubMed]

Sumekh, M.

M. Kaveh, M. Sumekh, J. Greenleaf, “Signal processing for diffraction tomography,” IEEE Trans. Sonics Ultrason. SU-31, 230–239 (1984).
[CrossRef]

Svenson, R. H.

S. Y. Semenov, A. E. Bulyshev, A. E. Souvorov, A. G. Nazarov, Y. E. Sizov, R. H. Svenson, V. G. Posukh, A. Pavlovsky, P. N. Repin, G. P. Tatsis, “Three-dimensional microwave tomography: experimental imaging of phantoms and biological objects,” IEEE Trans. Microwave Theory Tech. 48, 1071–1074 (2000).
[CrossRef]

S. Y. Semenov, R. H. Svenson, A. E. Boulyshev, A. E. Souvorov, V. Y. Borisov, Y. Sizor, A. N. Starostin, K. R. Dezern, G. P. Tatsis, V. Y. Baranov, “Microwave tomography: two-dimensional system for biological imaging,” IEEE Trans. Biomed. Eng. 43, 869–877 (1996).
[CrossRef] [PubMed]

Takashi, H. Z.

H. Z. Takashi, T. Takenaka, T. Tanaka, “Three-dimensional reconstruction of a shallowly buried mine using time-domain data,” Microwave Opt. Technol. Lett. 39, 276–280 (2003).
[CrossRef]

Takenaka, T.

H. Z. Takashi, T. Takenaka, T. Tanaka, “Three-dimensional reconstruction of a shallowly buried mine using time-domain data,” Microwave Opt. Technol. Lett. 39, 276–280 (2003).
[CrossRef]

Tanaka, T.

H. Z. Takashi, T. Takenaka, T. Tanaka, “Three-dimensional reconstruction of a shallowly buried mine using time-domain data,” Microwave Opt. Technol. Lett. 39, 276–280 (2003).
[CrossRef]

Tatsis, G. P.

S. Y. Semenov, A. E. Bulyshev, A. E. Souvorov, A. G. Nazarov, Y. E. Sizov, R. H. Svenson, V. G. Posukh, A. Pavlovsky, P. N. Repin, G. P. Tatsis, “Three-dimensional microwave tomography: experimental imaging of phantoms and biological objects,” IEEE Trans. Microwave Theory Tech. 48, 1071–1074 (2000).
[CrossRef]

S. Y. Semenov, R. H. Svenson, A. E. Boulyshev, A. E. Souvorov, V. Y. Borisov, Y. Sizor, A. N. Starostin, K. R. Dezern, G. P. Tatsis, V. Y. Baranov, “Microwave tomography: two-dimensional system for biological imaging,” IEEE Trans. Biomed. Eng. 43, 869–877 (1996).
[CrossRef] [PubMed]

Tretiak, O.

S. Pourjavid, O. Tretiak, “Ultrasound imaging through time-domain diffraction tomography,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 38, 74–85 (1991).
[CrossRef] [PubMed]

Uzunoglu, N. K.

C. N. Kechribaris, K. S. Nikita, N. K. Uzunoglu, “Reconstruction of two-dimensional permittivity distribution using an improved Rytov approximation and nonlinear optimization,”J. Electromagn. Waves Appl. 17, 183–207 (2003).
[CrossRef]

T. A. Maniatis, K. S. Nikita, N. K. Uzunoglu, “Two-dimensional dielectric profile reconstruction based on spectral-domain moment method and nonlinear optimization,” IEEE Trans. Microwave Theory Tech. 48, 1831–1840 (2000).
[CrossRef]

Van den Berg, P. M

A. Abubakar, P. M Van den Berg, S. Y. Semenov, “Two and three dimensional algorithms for microwave imaging and inverse scattering,” J. Electromagn. Waves Appl. 17, 209–231 (2003).
[CrossRef]

Wade, G.

R. K. Mueller, M. Kaveh, G. Wade, “Reconstructive tomography and applications to ultrasonics,” Proc. IEEE 67, 567–587 (1979).
[CrossRef]

Wolf, E.

E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun. 1, 153–156 (1969).
[CrossRef]

Acoust. Imaging (2)

M. P. Andre, P. J. Martin, G. P. Otto, L. K. Olson, T. K. Barrett, B. A. Spivey, D. A. Palmer, “A new consideration of diffraction computed tomography for breast imaging,” Acoust. Imaging 21, 379–390 (1995).
[CrossRef]

R. K. Mueller, M. Kaveh, R. D. Inverson, “A new approach to acoustic tomography using diffraction techniques,” Acoust. Imaging 8, 615–628 (1980).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

H. Liu, C. L. Matson, K. Lau, R. R. Mapakshi, “Experimental validation of a backpropagation algorithm for three-dimensional breast tumor localization,” IEEE J. Sel. Top. Quantum Electron. 5, 1049–1057 (1999).
[CrossRef]

IEEE Trans. Antennas Propag. (2)

S. Caorsi, A. Massa, M. Pastorino, M. Donelli, “Improved microwave imaging procedure for nondestructive evaluations of two dimensional structures,” IEEE Trans. Antennas Propag. 52, 1386–1397 (2004).
[CrossRef]

T. J. Cui, W. C. Chew, “Diffraction tomographic algorithm for the detection of three-dimensional objects buried in lossy half-space,” IEEE Trans. Antennas Propag. 50, 42–49 (2002).
[CrossRef]

IEEE Trans. Biomed. Eng. (3)

M. A. Anastasio, X. Pan, “An improved reconstruction algorithm for 3-D diffraction tomography using spherical wave sources,” IEEE Trans. Biomed. Eng. 50, 517–521 (2003).
[CrossRef] [PubMed]

S. Y. Semenov, R. H. Svenson, A. E. Boulyshev, A. E. Souvorov, V. Y. Borisov, Y. Sizor, A. N. Starostin, K. R. Dezern, G. P. Tatsis, V. Y. Baranov, “Microwave tomography: two-dimensional system for biological imaging,” IEEE Trans. Biomed. Eng. 43, 869–877 (1996).
[CrossRef] [PubMed]

P. M. Meany, K. D. Paulsen, S. D. Geimer, S. A Haider, M. W. Fanning, “Quantification of 3-D field effects during 2-D microwave imaging,” IEEE Trans. Biomed. Eng. 49, 708–720 (2002).
[CrossRef]

IEEE Trans. Image Process. (1)

M. A. Anastasio, X. Pan, “A new reconstruction approach for reflection mode diffraction tomography,” IEEE Trans. Image Process. 9, 1262–1271 (2000).
[CrossRef]

IEEE Trans. Med. Imaging (1)

A. Franchois, A. Joisel, C. Pichot, J. C. Bolomey, “Quantitative microwave imaging with a 2.45-GHz planar microwave camera,” IEEE Trans. Med. Imaging 17, 550–561 (1998).
[CrossRef] [PubMed]

IEEE Trans. Microwave Theory Tech. (4)

D. T. Borup, O. P. Gandhi, “Fast-Fourier-transform method for calculation of SAR distributions in finely discretized inhomogeneous models of biological bodies,” IEEE Trans. Microwave Theory Tech. 32, 355–360 (1984).
[CrossRef]

R. D. March, T. K. K. Chan, “Improving microwave imaging by enhancing diffraction tomography,” IEEE Trans. Microwave Theory Tech. 44, 379–388 (1996).
[CrossRef]

S. Y. Semenov, A. E. Bulyshev, A. E. Souvorov, A. G. Nazarov, Y. E. Sizov, R. H. Svenson, V. G. Posukh, A. Pavlovsky, P. N. Repin, G. P. Tatsis, “Three-dimensional microwave tomography: experimental imaging of phantoms and biological objects,” IEEE Trans. Microwave Theory Tech. 48, 1071–1074 (2000).
[CrossRef]

T. A. Maniatis, K. S. Nikita, N. K. Uzunoglu, “Two-dimensional dielectric profile reconstruction based on spectral-domain moment method and nonlinear optimization,” IEEE Trans. Microwave Theory Tech. 48, 1831–1840 (2000).
[CrossRef]

IEEE Trans. Sonics Ultrason. (1)

M. Kaveh, M. Sumekh, J. Greenleaf, “Signal processing for diffraction tomography,” IEEE Trans. Sonics Ultrason. SU-31, 230–239 (1984).
[CrossRef]

IEEE Trans. Ultrason. Ferroelectr. Freq. Control (2)

S. Pourjavid, O. Tretiak, “Ultrasound imaging through time-domain diffraction tomography,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 38, 74–85 (1991).
[CrossRef] [PubMed]

N. Sponheim, L. J. Gelius, I. Johansen, J. J. Stamnes, “Quantitative results in ultrasonic tomography of large objects using line sources and curved detector arrays,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 38, 370–379 (1991).
[CrossRef] [PubMed]

Inverse Probl. (2)

T. Melamed, Y. Ehrlich, E. Heyman, “Short-pulse inversion of inhomogeneous media: a time-domain diffraction tomography,” Inverse Probl. 12, 977–993 (1996).
[CrossRef]

Z. Q. Lu, “Multidimensional structure diffraction tomography for varying object orientation through generalised scattered waves,” Inverse Probl. 1, 339–356 (1985).
[CrossRef]

J. Acoust. Soc. Am. (1)

M. Gustafsson, S. He, “An optimization approach to multi-dimensional time-domain acoustic inverse problems,” J. Acoust. Soc. Am. 108, 1548–1556 (2000).
[CrossRef] [PubMed]

J. Electromagn. Waves Appl. (2)

A. Abubakar, P. M Van den Berg, S. Y. Semenov, “Two and three dimensional algorithms for microwave imaging and inverse scattering,” J. Electromagn. Waves Appl. 17, 209–231 (2003).
[CrossRef]

C. N. Kechribaris, K. S. Nikita, N. K. Uzunoglu, “Reconstruction of two-dimensional permittivity distribution using an improved Rytov approximation and nonlinear optimization,”J. Electromagn. Waves Appl. 17, 183–207 (2003).
[CrossRef]

J. Opt. Soc. Am. A (2)

Microwave Opt. Technol. Lett. (1)

H. Z. Takashi, T. Takenaka, T. Tanaka, “Three-dimensional reconstruction of a shallowly buried mine using time-domain data,” Microwave Opt. Technol. Lett. 39, 276–280 (2003).
[CrossRef]

Opt. Commun. (2)

E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun. 1, 153–156 (1969).
[CrossRef]

O. R. Halse, J. J. Stamnes, A. J. Devaney, “Three-dimensional diffraction tomography by two-dimensional sectioning,” Opt. Commun. 224, 185–195 (2003).
[CrossRef]

Opt. Lett. (1)

Proc. IEEE (1)

R. K. Mueller, M. Kaveh, G. Wade, “Reconstructive tomography and applications to ultrasonics,” Proc. IEEE 67, 567–587 (1979).
[CrossRef]

SIAM J. Sci. Comput. (USA) (1)

A. Dutt, V. Rokhlin, “Fast Fourier transforms for nonequispaced data,” SIAM J. Sci. Comput. (USA) 14, 1368–1393 (1993).
[CrossRef]

Ultrason. Imaging (3)

A. J. Devaney, G. Beylkin, “Diffraction tomography using arbitrary transmitter and receiver surfaces,” Ultrason. Imaging 6, 181–193 (1984).
[CrossRef] [PubMed]

N. Sponheim, I. Johansen, “Experimental results in ultrasonic tomography using a filtered backpropagation algorithm,” Ultrason. Imaging 13, 56–70 (1991).
[CrossRef] [PubMed]

A. J. Devaney, “A filtered backpropagation algorithm for diffraction tomography,” Ultrason. Imaging 4, 336–350 (1982).
[CrossRef] [PubMed]

Other (2)

A. J. Devaney, “Diffraction tomography,” in Inverse Methods in Electromagnetic Imaging: Part II, W. M. Boerner, ed. (Reidel, Dordrecht, The Netherlands, 1985), pp. 1107–1135.

A. C. Kak, M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, New York, 1988).

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Figures (15)

Fig. 1
Fig. 1

Geometry of the problem with the coordinate systems ( ω ξ , ω η , ω z ) and ( ϕ 1 , θ 1 ) and the Ewald sphere centered at ( 0 , k 0 , 0 ) .

Fig. 2
Fig. 2

Geometry of the problem with the rotated coordinates system ω ξ , ω η , ω z and the Ewald hemisphere coverage resulting from an incident plane-wave direction at an angle ϕ.

Fig. 3
Fig. 3

The spatial-frequency coverage obtained by using incident plane-wave directions only on the x y plane. The gray hatching specifies the region that is located outside the sphere with radius 2 k 0 . The white hatched region shows the frequencies that can be specified when the incident-wave propagation direction is restricted to the x y plane. The solid black region shows the spatial frequencies for which the Fourier transform of the object function cannot be determined.

Fig. 4
Fig. 4

Reconstructed images at the plane y = 0 for the case of the simple cylinder.

Fig. 5
Fig. 5

Simple cylinder real part profile reconstruction with various data sets ( x = y = 0 ) .

Fig. 6
Fig. 6

Mean square reconstruction error along the z axis of the simple cylinder.

Fig. 7
Fig. 7

Reconstructed images at the plane y = 0 for the case of the stepped cylinder.

Fig. 8
Fig. 8

Reconstructed real part profile of the stepped cylinder along the z axis ( x = y = 0 ) .

Fig. 9
Fig. 9

Mean square reconstruction error along the z axis of the stepped cylinder.

Fig. 10
Fig. 10

Reconstructed images at the plane y = 0 for the case of the homogeneous cone.

Fig. 11
Fig. 11

Homogeneous cone real part profile reconstruction along the z axis ( x = y = 0 ) .

Fig. 12
Fig. 12

Mean square reconstruction error along the z axis of the constant cone.

Fig. 13
Fig. 13

Reconstructed images at the plane y = 0 for the case of the two-part sphere.

Fig. 14
Fig. 14

Two-part sphere profile reconstruction along (real part) the z axis ( x = y = 0 ) .

Fig. 15
Fig. 15

Mean square reconstruction error along the z axis of the two-part sphere ( z = constant ) .

Tables (4)

Tables Icon

Table 1 Mean Square Error for the Simple Cylinder Reconstruction

Tables Icon

Table 2 Mean Square Error for the Stepped Cylinder Reconstruction

Tables Icon

Table 3 Mean Square Error for the Homogeneous Cone Reconstruction

Tables Icon

Table 4 Mean Square Error for the Two-Part Sphere Reconstruction

Equations (34)

Equations on this page are rendered with MathJax. Learn more.

ψ ( r ) = ψ inc ( r ) + V g ( r r ) o ( r ) ψ ( r ) d r ,
o ( r ) = k 0 2 ( n 2 ( r ) 1 ) ,
g ( r r ) = exp ( i k 0 R ) 4 π R ,
ψ sc ( r ) ψ sc B ( r ) = V g ( r r ) o ( r ) exp ( i k 0 y ) d r ,
ψ sc ( r ) = ψ ( r ) ψ inc ( r )
g ( r r ) = i 8 π 2 + + 1 β exp { i [ α ( x x ) + β ( y y ) + γ ( z z ) ] } d α d γ ,
ψ B , l 0 ( x , z ) = ψ sc B ( x , l 0 , z ) = i 8 π 2 + + 1 β O ( α , β k 0 , γ ) exp { i [ α x + β l 0 + γ z ] } d α d γ ,
O ( α , β k 0 , γ ) = V o ( r ) exp { i [ α x + ( β k 0 ) y + γ z ] } d r
Ψ B , l 0 ( ω ξ , ω z ) = + + ψ B , l 0 ( ξ , z ) { exp [ i ( ω ξ ξ + ω z z ) ] } d ξ d z ,
+ + exp [ i ( α ξ + γ z ) ] exp [ i ( ω ξ ξ + ω z z ) ] d ξ d z = 4 π 2 δ ( ω ξ α , ω z γ ) ,
Ψ B , l 0 ( ω ξ , ω z ) = i 2 exp ( i k 0 2 ω ξ 2 ω z 2 l 0 ) k 0 2 ω ξ 2 ω z 2 × O ( ω ξ , k 0 2 ω ξ 2 ω z 2 k 0 , ω z )
O ( ω ξ , k 0 2 ω ξ 2 ω z 2 k 0 , ω z ) = 2 i k 0 2 ω ξ 2 ω z 2 exp ( i k 0 2 ω ξ 2 ω z 2 l 0 ) Ψ B , l 0 ( ω ξ , ω z ) ,
O ( ω ξ , ω z , ϕ ) = 2 i k 0 2 ω ξ 2 ω z 2 exp ( i k 0 2 ω ξ 2 ω z 2 l 0 ) × Ψ B , l 0 , ϕ ( ω ξ , ω z ) .
p s ( r ) = 1 ψ inc ( r ) V g ( r r ) ψ inc ( r ) o ( r ) d r .
O ( ω ξ , ω z , ϕ )
= 2 i k 0 2 ω ξ 2 ω z 2 exp ( i k 0 2 ω ξ 2 ω z 2 l 0 ) P l 0 ( ω ξ , ω z ) exp ( i k 0 l 0 ) ,
ω ξ = ± 4 k 0 2 R 2 R 4 4 k 0 2 ω z 2 2 k 0 ,
φ = tan 1 ( ω y ω x ) + sin 1 ( ω x 2 + ω y 2 2 k 0 ) + π 2 .
o LP ( r ) = 1 ( 2 π ) 3 + + + O LP ( k ) exp ( i k r ) d k ,
k = k 0 ( s ̂ 1 s ̂ 0 ) ,
o LP ( r ) = 1 2 k 0 3 ( 2 π ) 3 0 2 π 0 2 π 0 π sin θ 1 sin 2 θ 1 ( s 1 s 0 ) 2 O LP ( k 0 ( s 1 s 0 ) ) exp [ i k 0 ( s 1 s 0 ) r ] d ϕ 0 d ϕ 1 d θ 1 ,
o LP ( r ) = 1 2 k 0 ( 2 π ) 3 0 2 π k 0 k 0 k 0 k 0 ω ξ k 0 2 ω ξ 2 ω z 2 O LP ( k 0 ( s 1 s 0 ) ) exp { i [ ω ξ ξ + ( k 0 2 ω ξ 2 ω z 2 k 0 ) η + ω z z ] } d ω ξ d ω z d θ 1 .
ψ ( ξ , η = l 1 , z ) = ψ ( ξ , η = l 0 , z ) exp [ j k 0 2 ω ξ 2 ω z 2 ( l 1 l 0 ) ] .
err = { D [ n recon ( r ) n cor ( r ) ] 2 d r D n cor 2 ( r ) d r } 1 2 .
ω z = z ,
ω ξ = ( 1 , ϕ 0 π 2 , π 2 ) ,
ω η = s 0 .
cos ϕ 1 = ω ξ k 0 2 ω z 2 ,
sin ϕ 1 = k 0 2 ω ξ 2 ω z 2 k 0 2 ω z 2 ,
cos θ 1 = ω z k 0 ,
sin θ 1 = k 0 2 ω z 2 k 0 .
J = 1 k 0 2 ω ξ 2 ω z 2 k 0 2 ω z 2 .
s 1 s 0 = k 0 2 ω ξ 2 ω z 2 k 0 ,
k 0 ( s 1 s 0 ) r = ω ξ ξ + ( k 0 2 ω ξ 2 ω z 2 k 0 ) η + ω z z .

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