Abstract

We present atmospheric degradation correction of terahertz (THz) beams based on multiscale signal decomposition and a combination of a Wiener deconvolution filter and artificial neural networks. THz beams suffer from strong attenuation by water molecules in the air. The proposed signal restoration approach finds the filter coefficients from a pair of reference signals previously measured from low- humidity conditions and current background air signals. Experimental results with two material samples of different chemical compositions demonstrate that the multiscale signal restoration technique is effective in correcting atmospheric degradation compared to individual and non-multiscale approaches.

© 2010 Optical Society of America

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  1. M. v. Exter, C. Fattinger, and D. Grischkowsky, “Terahertz time-domain spectroscopy of water vapor,” Opt. Lett. 14, 1128-1130 (1989).
    [CrossRef] [PubMed]
  2. D. M. Mittleman, R. H. Jacobsen, R. Neelamani, R. G. Baraniuk, and M. C. Nuss, “Gas sensing using terahertz time-domain spectroscopy,” Appl. Phys. B 67, 379-390 (1998).
    [CrossRef]
  3. B. Ferguson and X.-C. Zhang, “Materials for terahertz science and technology,” Nat. Mater. 1, 26-33 (2002).
    [CrossRef]
  4. A. J. L. Adam, P. C. M. Planken, S. Meloni, and J. Dik, “Terahertz imaging of hidden paint layers on canvas,” Opt. Express 17, 3407-3416 (2009).
    [CrossRef] [PubMed]
  5. Y. C. Shen, T. Lo, P. F. Taday, B. E. Cole, W. R. Tribe, and M. C. Kemp, “Detection and identification of explosives using terahertz pulsed spectroscopic imaging,” Appl. Phys. Lett. 86, 241116 (2005).
    [CrossRef]
  6. R. Piesiewicz, T. Kleine-Ostmann, N. Krumbholz, D. Mittleman, M. Koch, J. Schoebel, and T. Kurner, “Short-range ultra-broadband terahertz communications: concepts and perspectives,” IEEE Antennas Propagat. Mag. 49, 24-39 (2007).
    [CrossRef]
  7. L. Möller, J. Federici, A. Sinyukov, C. Xie, H. C. Lim, and R. C. Giles, “Data encoding on terahertz signals for communication and sensing,” Opt. Lett. 33, 393-395 (2008).
    [CrossRef] [PubMed]
  8. H. M. Pickett, E. A. Cohen, B. J. Drouin, and J. C. Pearson, “Submillimeter, millimeter, and microwave spectral line catalog,” Technical report (JPL, 2003).
  9. R. W. Schafer, R. M. Mersereau, and M. A. Richards, “Constrained iterative restoration algorithm,” Proc. IEEE 69, 432-450 (1981).
    [CrossRef]
  10. W. Withayachumnankul, B. M. Fischer, and D. Abbott, “Numerical removal of water vapour effects from terahertz time-domain spectroscopy measurements,” Proc. R. Soc. London Ser. A 464, 2435-2456 (2008).
    [CrossRef]
  11. Y. Wang, Z. Zhao, Z. Chen, Y. Zhang, L. Zhang, and K. Kang, “Suppression of spectral interferences due to water-vapor rotational transitions in terahertz time-domain spectroscopy,” Opt. Lett. 33, 1354-1356 (2008).
    [CrossRef] [PubMed]
  12. Y. Wang, Z. Chen, Z. Zhao, L. Zhang, K. Kang, and Y. Zhang, “Restoration of terahertz signals distorted by atmospheric water vapor absorption,” J. Appl. Phys. 105, 103105(2009).
    [CrossRef]
  13. Y. Wang, Z. Zhao, Z. Chen, K. Kang, B. Feng, and Y. Zhang, “Terahertz absorbance spectrum fitting method for quantitative detection of concealed contraband,” J. Appl. Phys. 102, 113108 (2007).
    [CrossRef]
  14. S. G. Kong and D. H. Wu, “Signal restoration from atmospheric degradation in terahertz spectroscopy,” J. Appl. Phys. 103, 113105 (2008).
    [CrossRef]
  15. M. Unser and T. Blu, “Wavelet theory demystified,” IEEE Trans. Signal Process. 51, 470-483 (2003).
    [CrossRef]
  16. A. M. Rao and D. L. Jones, “A denoising approach to multisensor signal estimation,” IEEE Trans. Signal Process. 48, 1225-1234 (2000).
    [CrossRef]
  17. Y. Liang and E. W. Page, “Multiresolution learning paradigm and signal prediction,” IEEE Trans. Signal Process. 45, 2858-2864 (1997).
    [CrossRef]
  18. Y. Liang and Xu Liang, “Improving signal prediction performance of neural networks through multiresolution learning approach,” IEEE Trans. Syst. Man Cybern. B 36, 341-352(2006).
    [CrossRef]
  19. B. Ferguson and D. Abbott, “De-noising techniques for terahertz responses of biological samples,” Microelectron. J. 32, 943-953 (2001).
    [CrossRef]
  20. E. Berry, R. D. Boyle, A. J. Fitzgerald, and J. W. Handley, “Time-frequency analysis in terahertz-pulsed imaging,” in Computer Vision beyond the Visible Spectrum, B.Bhanu and I.Pavlidis, eds. (Springer, 2005), pp. 276-311.
  21. X. X. Yin, B. W.-H. Ng, B. Ferguson, S. P. Mickan, and D. Abbott, “Terahertz computed tomographic reconstruction and its wavelet-based segmentation by fusion,” in Proceedings of IEEE International Symposium on Industrial Electronics (IEEE2007), pp. 3409-3414.
  22. X. X. Yin, B. W.-H. Ng, B. Ferguson, S. P. Mickan, and D. Abbott, “Statistical model for the classification of the wavelet transforms of T-ray pulses,” in Proceedings of International Conference on Pattern Recognition (IEEE2006), pp. 236-239.
  23. Q. Wu, M. Litz, and X.-C. Zhang, “Broadband detection capability of ZnTe electro-optic field detectors,” Appl. Phys. Lett. 68, 2924-2926 (1996).
    [CrossRef]
  24. A. Garzarella, S. B. Qadri, T. J. Wieting, and D. H. Wu, “Spatial and temporal sensitivity variations in photorefractive electro-optic field sensors,” Appl. Phys. Lett. 88, 141106 (2006).
    [CrossRef]
  25. M. Vetterli and C. Herley, “Wavelets and filter banks: theory and design,” IEEE Trans. Signal Process. 40, 2207-2232 (1992).
    [CrossRef]
  26. S. W. Moon and S. G. Kong, “Block-based neural networks,” IEEE Trans. Neural Netw. 12, 307-317 (2001).
    [CrossRef]
  27. S. Haykin, Neural Networks: A Comprehensive Foundation, 2nd ed. (Prentice Hall, 1999).

2009 (2)

A. J. L. Adam, P. C. M. Planken, S. Meloni, and J. Dik, “Terahertz imaging of hidden paint layers on canvas,” Opt. Express 17, 3407-3416 (2009).
[CrossRef] [PubMed]

Y. Wang, Z. Chen, Z. Zhao, L. Zhang, K. Kang, and Y. Zhang, “Restoration of terahertz signals distorted by atmospheric water vapor absorption,” J. Appl. Phys. 105, 103105(2009).
[CrossRef]

2008 (4)

W. Withayachumnankul, B. M. Fischer, and D. Abbott, “Numerical removal of water vapour effects from terahertz time-domain spectroscopy measurements,” Proc. R. Soc. London Ser. A 464, 2435-2456 (2008).
[CrossRef]

Y. Wang, Z. Zhao, Z. Chen, Y. Zhang, L. Zhang, and K. Kang, “Suppression of spectral interferences due to water-vapor rotational transitions in terahertz time-domain spectroscopy,” Opt. Lett. 33, 1354-1356 (2008).
[CrossRef] [PubMed]

S. G. Kong and D. H. Wu, “Signal restoration from atmospheric degradation in terahertz spectroscopy,” J. Appl. Phys. 103, 113105 (2008).
[CrossRef]

L. Möller, J. Federici, A. Sinyukov, C. Xie, H. C. Lim, and R. C. Giles, “Data encoding on terahertz signals for communication and sensing,” Opt. Lett. 33, 393-395 (2008).
[CrossRef] [PubMed]

2007 (2)

R. Piesiewicz, T. Kleine-Ostmann, N. Krumbholz, D. Mittleman, M. Koch, J. Schoebel, and T. Kurner, “Short-range ultra-broadband terahertz communications: concepts and perspectives,” IEEE Antennas Propagat. Mag. 49, 24-39 (2007).
[CrossRef]

Y. Wang, Z. Zhao, Z. Chen, K. Kang, B. Feng, and Y. Zhang, “Terahertz absorbance spectrum fitting method for quantitative detection of concealed contraband,” J. Appl. Phys. 102, 113108 (2007).
[CrossRef]

2006 (2)

Y. Liang and Xu Liang, “Improving signal prediction performance of neural networks through multiresolution learning approach,” IEEE Trans. Syst. Man Cybern. B 36, 341-352(2006).
[CrossRef]

A. Garzarella, S. B. Qadri, T. J. Wieting, and D. H. Wu, “Spatial and temporal sensitivity variations in photorefractive electro-optic field sensors,” Appl. Phys. Lett. 88, 141106 (2006).
[CrossRef]

2005 (1)

Y. C. Shen, T. Lo, P. F. Taday, B. E. Cole, W. R. Tribe, and M. C. Kemp, “Detection and identification of explosives using terahertz pulsed spectroscopic imaging,” Appl. Phys. Lett. 86, 241116 (2005).
[CrossRef]

2003 (1)

M. Unser and T. Blu, “Wavelet theory demystified,” IEEE Trans. Signal Process. 51, 470-483 (2003).
[CrossRef]

2002 (1)

B. Ferguson and X.-C. Zhang, “Materials for terahertz science and technology,” Nat. Mater. 1, 26-33 (2002).
[CrossRef]

2001 (2)

B. Ferguson and D. Abbott, “De-noising techniques for terahertz responses of biological samples,” Microelectron. J. 32, 943-953 (2001).
[CrossRef]

S. W. Moon and S. G. Kong, “Block-based neural networks,” IEEE Trans. Neural Netw. 12, 307-317 (2001).
[CrossRef]

2000 (1)

A. M. Rao and D. L. Jones, “A denoising approach to multisensor signal estimation,” IEEE Trans. Signal Process. 48, 1225-1234 (2000).
[CrossRef]

1998 (1)

D. M. Mittleman, R. H. Jacobsen, R. Neelamani, R. G. Baraniuk, and M. C. Nuss, “Gas sensing using terahertz time-domain spectroscopy,” Appl. Phys. B 67, 379-390 (1998).
[CrossRef]

1997 (1)

Y. Liang and E. W. Page, “Multiresolution learning paradigm and signal prediction,” IEEE Trans. Signal Process. 45, 2858-2864 (1997).
[CrossRef]

1996 (1)

Q. Wu, M. Litz, and X.-C. Zhang, “Broadband detection capability of ZnTe electro-optic field detectors,” Appl. Phys. Lett. 68, 2924-2926 (1996).
[CrossRef]

1992 (1)

M. Vetterli and C. Herley, “Wavelets and filter banks: theory and design,” IEEE Trans. Signal Process. 40, 2207-2232 (1992).
[CrossRef]

1989 (1)

1981 (1)

R. W. Schafer, R. M. Mersereau, and M. A. Richards, “Constrained iterative restoration algorithm,” Proc. IEEE 69, 432-450 (1981).
[CrossRef]

Abbott, D.

W. Withayachumnankul, B. M. Fischer, and D. Abbott, “Numerical removal of water vapour effects from terahertz time-domain spectroscopy measurements,” Proc. R. Soc. London Ser. A 464, 2435-2456 (2008).
[CrossRef]

B. Ferguson and D. Abbott, “De-noising techniques for terahertz responses of biological samples,” Microelectron. J. 32, 943-953 (2001).
[CrossRef]

X. X. Yin, B. W.-H. Ng, B. Ferguson, S. P. Mickan, and D. Abbott, “Terahertz computed tomographic reconstruction and its wavelet-based segmentation by fusion,” in Proceedings of IEEE International Symposium on Industrial Electronics (IEEE2007), pp. 3409-3414.

X. X. Yin, B. W.-H. Ng, B. Ferguson, S. P. Mickan, and D. Abbott, “Statistical model for the classification of the wavelet transforms of T-ray pulses,” in Proceedings of International Conference on Pattern Recognition (IEEE2006), pp. 236-239.

Adam, A. J. L.

Baraniuk, R. G.

D. M. Mittleman, R. H. Jacobsen, R. Neelamani, R. G. Baraniuk, and M. C. Nuss, “Gas sensing using terahertz time-domain spectroscopy,” Appl. Phys. B 67, 379-390 (1998).
[CrossRef]

Berry, E.

E. Berry, R. D. Boyle, A. J. Fitzgerald, and J. W. Handley, “Time-frequency analysis in terahertz-pulsed imaging,” in Computer Vision beyond the Visible Spectrum, B.Bhanu and I.Pavlidis, eds. (Springer, 2005), pp. 276-311.

Blu, T.

M. Unser and T. Blu, “Wavelet theory demystified,” IEEE Trans. Signal Process. 51, 470-483 (2003).
[CrossRef]

Boyle, R. D.

E. Berry, R. D. Boyle, A. J. Fitzgerald, and J. W. Handley, “Time-frequency analysis in terahertz-pulsed imaging,” in Computer Vision beyond the Visible Spectrum, B.Bhanu and I.Pavlidis, eds. (Springer, 2005), pp. 276-311.

Chen, Z.

Y. Wang, Z. Chen, Z. Zhao, L. Zhang, K. Kang, and Y. Zhang, “Restoration of terahertz signals distorted by atmospheric water vapor absorption,” J. Appl. Phys. 105, 103105(2009).
[CrossRef]

Y. Wang, Z. Zhao, Z. Chen, Y. Zhang, L. Zhang, and K. Kang, “Suppression of spectral interferences due to water-vapor rotational transitions in terahertz time-domain spectroscopy,” Opt. Lett. 33, 1354-1356 (2008).
[CrossRef] [PubMed]

Y. Wang, Z. Zhao, Z. Chen, K. Kang, B. Feng, and Y. Zhang, “Terahertz absorbance spectrum fitting method for quantitative detection of concealed contraband,” J. Appl. Phys. 102, 113108 (2007).
[CrossRef]

Cohen, E. A.

H. M. Pickett, E. A. Cohen, B. J. Drouin, and J. C. Pearson, “Submillimeter, millimeter, and microwave spectral line catalog,” Technical report (JPL, 2003).

Cole, B. E.

Y. C. Shen, T. Lo, P. F. Taday, B. E. Cole, W. R. Tribe, and M. C. Kemp, “Detection and identification of explosives using terahertz pulsed spectroscopic imaging,” Appl. Phys. Lett. 86, 241116 (2005).
[CrossRef]

Dik, J.

Drouin, B. J.

H. M. Pickett, E. A. Cohen, B. J. Drouin, and J. C. Pearson, “Submillimeter, millimeter, and microwave spectral line catalog,” Technical report (JPL, 2003).

Exter, M. v.

Fattinger, C.

Federici, J.

Feng, B.

Y. Wang, Z. Zhao, Z. Chen, K. Kang, B. Feng, and Y. Zhang, “Terahertz absorbance spectrum fitting method for quantitative detection of concealed contraband,” J. Appl. Phys. 102, 113108 (2007).
[CrossRef]

Ferguson, B.

B. Ferguson and X.-C. Zhang, “Materials for terahertz science and technology,” Nat. Mater. 1, 26-33 (2002).
[CrossRef]

B. Ferguson and D. Abbott, “De-noising techniques for terahertz responses of biological samples,” Microelectron. J. 32, 943-953 (2001).
[CrossRef]

X. X. Yin, B. W.-H. Ng, B. Ferguson, S. P. Mickan, and D. Abbott, “Statistical model for the classification of the wavelet transforms of T-ray pulses,” in Proceedings of International Conference on Pattern Recognition (IEEE2006), pp. 236-239.

X. X. Yin, B. W.-H. Ng, B. Ferguson, S. P. Mickan, and D. Abbott, “Terahertz computed tomographic reconstruction and its wavelet-based segmentation by fusion,” in Proceedings of IEEE International Symposium on Industrial Electronics (IEEE2007), pp. 3409-3414.

Fischer, B. M.

W. Withayachumnankul, B. M. Fischer, and D. Abbott, “Numerical removal of water vapour effects from terahertz time-domain spectroscopy measurements,” Proc. R. Soc. London Ser. A 464, 2435-2456 (2008).
[CrossRef]

Fitzgerald, A. J.

E. Berry, R. D. Boyle, A. J. Fitzgerald, and J. W. Handley, “Time-frequency analysis in terahertz-pulsed imaging,” in Computer Vision beyond the Visible Spectrum, B.Bhanu and I.Pavlidis, eds. (Springer, 2005), pp. 276-311.

Garzarella, A.

A. Garzarella, S. B. Qadri, T. J. Wieting, and D. H. Wu, “Spatial and temporal sensitivity variations in photorefractive electro-optic field sensors,” Appl. Phys. Lett. 88, 141106 (2006).
[CrossRef]

Giles, R. C.

Grischkowsky, D.

Handley, J. W.

E. Berry, R. D. Boyle, A. J. Fitzgerald, and J. W. Handley, “Time-frequency analysis in terahertz-pulsed imaging,” in Computer Vision beyond the Visible Spectrum, B.Bhanu and I.Pavlidis, eds. (Springer, 2005), pp. 276-311.

Haykin, S.

S. Haykin, Neural Networks: A Comprehensive Foundation, 2nd ed. (Prentice Hall, 1999).

Herley, C.

M. Vetterli and C. Herley, “Wavelets and filter banks: theory and design,” IEEE Trans. Signal Process. 40, 2207-2232 (1992).
[CrossRef]

Jacobsen, R. H.

D. M. Mittleman, R. H. Jacobsen, R. Neelamani, R. G. Baraniuk, and M. C. Nuss, “Gas sensing using terahertz time-domain spectroscopy,” Appl. Phys. B 67, 379-390 (1998).
[CrossRef]

Jones, D. L.

A. M. Rao and D. L. Jones, “A denoising approach to multisensor signal estimation,” IEEE Trans. Signal Process. 48, 1225-1234 (2000).
[CrossRef]

Kang, K.

Y. Wang, Z. Chen, Z. Zhao, L. Zhang, K. Kang, and Y. Zhang, “Restoration of terahertz signals distorted by atmospheric water vapor absorption,” J. Appl. Phys. 105, 103105(2009).
[CrossRef]

Y. Wang, Z. Zhao, Z. Chen, Y. Zhang, L. Zhang, and K. Kang, “Suppression of spectral interferences due to water-vapor rotational transitions in terahertz time-domain spectroscopy,” Opt. Lett. 33, 1354-1356 (2008).
[CrossRef] [PubMed]

Y. Wang, Z. Zhao, Z. Chen, K. Kang, B. Feng, and Y. Zhang, “Terahertz absorbance spectrum fitting method for quantitative detection of concealed contraband,” J. Appl. Phys. 102, 113108 (2007).
[CrossRef]

Kemp, M. C.

Y. C. Shen, T. Lo, P. F. Taday, B. E. Cole, W. R. Tribe, and M. C. Kemp, “Detection and identification of explosives using terahertz pulsed spectroscopic imaging,” Appl. Phys. Lett. 86, 241116 (2005).
[CrossRef]

Kleine-Ostmann, T.

R. Piesiewicz, T. Kleine-Ostmann, N. Krumbholz, D. Mittleman, M. Koch, J. Schoebel, and T. Kurner, “Short-range ultra-broadband terahertz communications: concepts and perspectives,” IEEE Antennas Propagat. Mag. 49, 24-39 (2007).
[CrossRef]

Koch, M.

R. Piesiewicz, T. Kleine-Ostmann, N. Krumbholz, D. Mittleman, M. Koch, J. Schoebel, and T. Kurner, “Short-range ultra-broadband terahertz communications: concepts and perspectives,” IEEE Antennas Propagat. Mag. 49, 24-39 (2007).
[CrossRef]

Kong, S. G.

S. G. Kong and D. H. Wu, “Signal restoration from atmospheric degradation in terahertz spectroscopy,” J. Appl. Phys. 103, 113105 (2008).
[CrossRef]

S. W. Moon and S. G. Kong, “Block-based neural networks,” IEEE Trans. Neural Netw. 12, 307-317 (2001).
[CrossRef]

Krumbholz, N.

R. Piesiewicz, T. Kleine-Ostmann, N. Krumbholz, D. Mittleman, M. Koch, J. Schoebel, and T. Kurner, “Short-range ultra-broadband terahertz communications: concepts and perspectives,” IEEE Antennas Propagat. Mag. 49, 24-39 (2007).
[CrossRef]

Kurner, T.

R. Piesiewicz, T. Kleine-Ostmann, N. Krumbholz, D. Mittleman, M. Koch, J. Schoebel, and T. Kurner, “Short-range ultra-broadband terahertz communications: concepts and perspectives,” IEEE Antennas Propagat. Mag. 49, 24-39 (2007).
[CrossRef]

Liang, Xu

Y. Liang and Xu Liang, “Improving signal prediction performance of neural networks through multiresolution learning approach,” IEEE Trans. Syst. Man Cybern. B 36, 341-352(2006).
[CrossRef]

Liang, Y.

Y. Liang and Xu Liang, “Improving signal prediction performance of neural networks through multiresolution learning approach,” IEEE Trans. Syst. Man Cybern. B 36, 341-352(2006).
[CrossRef]

Y. Liang and E. W. Page, “Multiresolution learning paradigm and signal prediction,” IEEE Trans. Signal Process. 45, 2858-2864 (1997).
[CrossRef]

Lim, H. C.

Litz, M.

Q. Wu, M. Litz, and X.-C. Zhang, “Broadband detection capability of ZnTe electro-optic field detectors,” Appl. Phys. Lett. 68, 2924-2926 (1996).
[CrossRef]

Lo, T.

Y. C. Shen, T. Lo, P. F. Taday, B. E. Cole, W. R. Tribe, and M. C. Kemp, “Detection and identification of explosives using terahertz pulsed spectroscopic imaging,” Appl. Phys. Lett. 86, 241116 (2005).
[CrossRef]

Meloni, S.

Mersereau, R. M.

R. W. Schafer, R. M. Mersereau, and M. A. Richards, “Constrained iterative restoration algorithm,” Proc. IEEE 69, 432-450 (1981).
[CrossRef]

Mickan, S. P.

X. X. Yin, B. W.-H. Ng, B. Ferguson, S. P. Mickan, and D. Abbott, “Terahertz computed tomographic reconstruction and its wavelet-based segmentation by fusion,” in Proceedings of IEEE International Symposium on Industrial Electronics (IEEE2007), pp. 3409-3414.

X. X. Yin, B. W.-H. Ng, B. Ferguson, S. P. Mickan, and D. Abbott, “Statistical model for the classification of the wavelet transforms of T-ray pulses,” in Proceedings of International Conference on Pattern Recognition (IEEE2006), pp. 236-239.

Mittleman, D.

R. Piesiewicz, T. Kleine-Ostmann, N. Krumbholz, D. Mittleman, M. Koch, J. Schoebel, and T. Kurner, “Short-range ultra-broadband terahertz communications: concepts and perspectives,” IEEE Antennas Propagat. Mag. 49, 24-39 (2007).
[CrossRef]

Mittleman, D. M.

D. M. Mittleman, R. H. Jacobsen, R. Neelamani, R. G. Baraniuk, and M. C. Nuss, “Gas sensing using terahertz time-domain spectroscopy,” Appl. Phys. B 67, 379-390 (1998).
[CrossRef]

Möller, L.

Moon, S. W.

S. W. Moon and S. G. Kong, “Block-based neural networks,” IEEE Trans. Neural Netw. 12, 307-317 (2001).
[CrossRef]

Neelamani, R.

D. M. Mittleman, R. H. Jacobsen, R. Neelamani, R. G. Baraniuk, and M. C. Nuss, “Gas sensing using terahertz time-domain spectroscopy,” Appl. Phys. B 67, 379-390 (1998).
[CrossRef]

Ng, B. W.-H.

X. X. Yin, B. W.-H. Ng, B. Ferguson, S. P. Mickan, and D. Abbott, “Statistical model for the classification of the wavelet transforms of T-ray pulses,” in Proceedings of International Conference on Pattern Recognition (IEEE2006), pp. 236-239.

X. X. Yin, B. W.-H. Ng, B. Ferguson, S. P. Mickan, and D. Abbott, “Terahertz computed tomographic reconstruction and its wavelet-based segmentation by fusion,” in Proceedings of IEEE International Symposium on Industrial Electronics (IEEE2007), pp. 3409-3414.

Nuss, M. C.

D. M. Mittleman, R. H. Jacobsen, R. Neelamani, R. G. Baraniuk, and M. C. Nuss, “Gas sensing using terahertz time-domain spectroscopy,” Appl. Phys. B 67, 379-390 (1998).
[CrossRef]

Page, E. W.

Y. Liang and E. W. Page, “Multiresolution learning paradigm and signal prediction,” IEEE Trans. Signal Process. 45, 2858-2864 (1997).
[CrossRef]

Pearson, J. C.

H. M. Pickett, E. A. Cohen, B. J. Drouin, and J. C. Pearson, “Submillimeter, millimeter, and microwave spectral line catalog,” Technical report (JPL, 2003).

Pickett, H. M.

H. M. Pickett, E. A. Cohen, B. J. Drouin, and J. C. Pearson, “Submillimeter, millimeter, and microwave spectral line catalog,” Technical report (JPL, 2003).

Piesiewicz, R.

R. Piesiewicz, T. Kleine-Ostmann, N. Krumbholz, D. Mittleman, M. Koch, J. Schoebel, and T. Kurner, “Short-range ultra-broadband terahertz communications: concepts and perspectives,” IEEE Antennas Propagat. Mag. 49, 24-39 (2007).
[CrossRef]

Planken, P. C. M.

Qadri, S. B.

A. Garzarella, S. B. Qadri, T. J. Wieting, and D. H. Wu, “Spatial and temporal sensitivity variations in photorefractive electro-optic field sensors,” Appl. Phys. Lett. 88, 141106 (2006).
[CrossRef]

Rao, A. M.

A. M. Rao and D. L. Jones, “A denoising approach to multisensor signal estimation,” IEEE Trans. Signal Process. 48, 1225-1234 (2000).
[CrossRef]

Richards, M. A.

R. W. Schafer, R. M. Mersereau, and M. A. Richards, “Constrained iterative restoration algorithm,” Proc. IEEE 69, 432-450 (1981).
[CrossRef]

Schafer, R. W.

R. W. Schafer, R. M. Mersereau, and M. A. Richards, “Constrained iterative restoration algorithm,” Proc. IEEE 69, 432-450 (1981).
[CrossRef]

Schoebel, J.

R. Piesiewicz, T. Kleine-Ostmann, N. Krumbholz, D. Mittleman, M. Koch, J. Schoebel, and T. Kurner, “Short-range ultra-broadband terahertz communications: concepts and perspectives,” IEEE Antennas Propagat. Mag. 49, 24-39 (2007).
[CrossRef]

Shen, Y. C.

Y. C. Shen, T. Lo, P. F. Taday, B. E. Cole, W. R. Tribe, and M. C. Kemp, “Detection and identification of explosives using terahertz pulsed spectroscopic imaging,” Appl. Phys. Lett. 86, 241116 (2005).
[CrossRef]

Sinyukov, A.

Taday, P. F.

Y. C. Shen, T. Lo, P. F. Taday, B. E. Cole, W. R. Tribe, and M. C. Kemp, “Detection and identification of explosives using terahertz pulsed spectroscopic imaging,” Appl. Phys. Lett. 86, 241116 (2005).
[CrossRef]

Tribe, W. R.

Y. C. Shen, T. Lo, P. F. Taday, B. E. Cole, W. R. Tribe, and M. C. Kemp, “Detection and identification of explosives using terahertz pulsed spectroscopic imaging,” Appl. Phys. Lett. 86, 241116 (2005).
[CrossRef]

Unser, M.

M. Unser and T. Blu, “Wavelet theory demystified,” IEEE Trans. Signal Process. 51, 470-483 (2003).
[CrossRef]

Vetterli, M.

M. Vetterli and C. Herley, “Wavelets and filter banks: theory and design,” IEEE Trans. Signal Process. 40, 2207-2232 (1992).
[CrossRef]

Wang, Y.

Y. Wang, Z. Chen, Z. Zhao, L. Zhang, K. Kang, and Y. Zhang, “Restoration of terahertz signals distorted by atmospheric water vapor absorption,” J. Appl. Phys. 105, 103105(2009).
[CrossRef]

Y. Wang, Z. Zhao, Z. Chen, Y. Zhang, L. Zhang, and K. Kang, “Suppression of spectral interferences due to water-vapor rotational transitions in terahertz time-domain spectroscopy,” Opt. Lett. 33, 1354-1356 (2008).
[CrossRef] [PubMed]

Y. Wang, Z. Zhao, Z. Chen, K. Kang, B. Feng, and Y. Zhang, “Terahertz absorbance spectrum fitting method for quantitative detection of concealed contraband,” J. Appl. Phys. 102, 113108 (2007).
[CrossRef]

Wieting, T. J.

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X. X. Yin, B. W.-H. Ng, B. Ferguson, S. P. Mickan, and D. Abbott, “Statistical model for the classification of the wavelet transforms of T-ray pulses,” in Proceedings of International Conference on Pattern Recognition (IEEE2006), pp. 236-239.

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Figures (11)

Fig. 1
Fig. 1

Schematic diagram of the time-domain terahertz spectrometer.

Fig. 2
Fig. 2

Atmospheric degradation of THz signals: (a) time waveforms, (b) Fourier spectra.

Fig. 3
Fig. 3

Modeling of atmospheric degradation and restoration process of THz signals.

Fig. 4
Fig. 4

Level-2 discrete wavelet decomposition of a signal.

Fig. 5
Fig. 5

Fourier magnitude spectra of approximation and detail components in level-2 DWT decomposition.

Fig. 6
Fig. 6

Multiscale restoration filtering with Wiener filter and ANNs.

Fig. 7
Fig. 7

Frequency response of the Wiener deconvolution filters for approximation and detail components.

Fig. 8
Fig. 8

Fourier magnitude spectra of the testing samples: (a) DNT, (b) DNB.

Fig. 9
Fig. 9

Time waveforms of the approximation and detail components restored using the multiscale restoration filter for DNT: (a) approximation ( A 2 ), (b) detail ( D 2 ).

Fig. 10
Fig. 10

Fourier magnitude and absorption spectra of the multiscale restoration filter for DNT: (a) Fourier spectra, (b) absorbance.

Fig. 11
Fig. 11

Fourier magnitude and absorption spectra of the multiscale restoration filter for DNB: (a) Fourier spectra, (b) absorbance.

Tables (1)

Tables Icon

Table 1 Comparison of Various Terahertz Signal Restoration Schemes in Relative Improvement

Equations (12)

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

u ( t ) = H [ r ( t ) ] + v ( t ) ,
x ( t ) = G [ u ( t ) ] .
x ( t ) = H 1 [ u ( t ) ] .
Absorbance = log 10 ( A sample 2 A ref 2 ) ,
A ( t ) = k = x ( t ) φ ( t k ) ,
D ( t ) = k = x ( t ) ψ ( t k ) ,
g k ( t ) = h k ( t ) * r k ( t ) + v k ( t ) , k = A , D ,
W ( ω ) = 1 H ( ω ) | H ( ω ) | 2 | H ( ω ) | 2 + | V ( ω ) | 2 / | R ( ω ) | 2 ,
G ( ω ) = W ( ω ) G ( ω ) ,
c ( t ) = f ( g ( t ) , s ) .
g ( t ) = [ g ( t m I ) , , g ( t ) , , g ( t + m I ) ] T ,
RI ( dB ) = 10 log 10 ( MSE u MSE x ) = 10 log 10 ( 1 n ε x 2 ( t ) 1 n ε u 2 ( t ) ) ,

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