In terahertz reflection imaging, a deconvolution process is often employed to extract the impulse function of the sample of interest. A band-pass filter such as a double Gaussian filter is typically incorporated into the inverse filtering to suppress the noise, but this can result in over-smoothing due to the loss of useful information. In this paper, with a view to improving the calculation of terahertz impulse response functions for systems with a low signal to noise ratio, we propose a hybrid Frequency-Wavelet Domain Deconvolution (FWDD) for terahertz reflection imaging. Our approach works well; it retrieves more accurate impulse response functions than existing approaches and these impulse functions can then also be used to better extract the terahertz spectroscopic properties of the sample.

© 2010 OSA

1. P. C. Ashworth, E. Pickwell-MacPherson, E. Provenzano, S. E. Pinder, A. D. Purushotham, M. Pepper, and V. P. Wallace, “Terahertz pulsed spectroscopy of freshly excised human breast cancer,” Opt. Express 17(15), 12444–12454 (2009). [CrossRef] [PubMed]
2. M. C. Kemp, P. F. Taday, B. E. Cole, J. A. Cluff, A. J. Fitzgerald, and W. R. Tribe, “Security applications of terahertz technology,” Terahertz for Military and Security Applications 5070, 44–52 (2003).
3. E. Pickwell, B. E. Cole, A. J. Fitzgerald, M. Pepper, and V. P. Wallace, “In vivo study of human skin using pulsed terahertz radiation,” Phys. Med. Biol. 49(9), 1595–1607 (2004). [CrossRef] [PubMed]
4. B. E. Cole, R. Woodward, D. Crawley, V. P. Wallace, D. D. Arnone, and M. Pepper, “Terahertz imaging and spectroscopy of human skin, in-vivo,” Proc. Soc. Photo Opt. Instrum. Eng. 4276, 1–10 (2001).
5. D. M. Mittleman, R. H. Jacobsen, and M. C. Nuss, “T-ray imaging,” IEEE Sel. Top. Quantum Electron. 2(3), 679–692 (1996). [CrossRef]
6. B. Ferguson and D. Abbott, “De-noising techniques for terahertz responses of biological samples,” Microelectron. J. 32(12), 943–953 (2001). [CrossRef]
7. D. L. Donoho, “De-noising by soft-thresholding,” IEE Trans. Inf. Theory 41(3), 613–627 (1995). [CrossRef]
8. K. R. Castleman, “Digital Image Processing,” Prentice-Hall, Englewood Cliffs, NJ (1996).
9. S. P. Ghael, A. M. Sayeed, and R. G. Baraniuk, “Improved wavelet denoising via empirical Wiener filtering,” Wavelet Applications in Signal and Image Processing V 3169, 389–399 (1997).
10. R. Neelamani, H. Choi, and R. Baraniuk, “Forward: Fourier-Wavelet regularized deconvolution for Ill-conditioned systems,” IEEE Trans. Signal Process. 52(2), 418–433 (2004). [CrossRef]
11. J. Pearce, H. H. Choi, D. M. Mittleman, J. White, and D. Zimdars, “Terahertz wide aperture reflection tomography,” Opt. Lett. 30(13), 1653–1655 (2005). [CrossRef] [PubMed]
12. J. C. Pesquet, H. Krim, and H. Carfantan, “Time-invariant orthonormal wavelet representations,” IEEE Trans. Acoust., Speech, Signal Process. 44, 1964–1970 (1996).
13. S. Huang, P. C. Ashworth, K. W. C. Kan, Y. Chen, V. P. Wallace, Y. T. Zhang, and E. Pickwell-MacPherson, “Improved sample characterization in terahertz reflection imaging and spectroscopy,” Opt. Express 17(5), 3848–3854 (2009). [CrossRef] [PubMed]
14. S. Y. Huang, Y. X. J. Wang, D. K. Yeung, A. T. Ahuja, Y. T. Zhang, and E. Pickwell-Macpherson, “Tissue characterization using terahertz pulsed imaging in reflection geometry,” Phys. Med. Biol. 54(1), 149–160 (2009). [CrossRef]
15. G. Nason and B. Silverman, “The Stationary Wavelet Transform and some Statistical Applications,” Wavelets and Statistics, Springer Lecture Notes in Statistics 13, 281–300 (1995).
16. P. C. Ashworth, P. O'Kelly, A. D. Purushotham, S. E. Pinder, M. Kontos, M. Pepper, and V. P. Wallace, “An intra-operative THz probe for use during the surgical removal of breast tumors,” 2008 33rd International Conference on Infrared, Millimeter and Terahertz Waves, Vols 1 and 2, 767–769 (2008).

IEE Trans. Inf. Theory

• D. L. Donoho, “De-noising by soft-thresholding,” IEE Trans. Inf. Theory 41(3), 613–627 (1995). [CrossRef]

IEEE Sel. Top. Quantum Electron.

• D. M. Mittleman, R. H. Jacobsen, and M. C. Nuss, “T-ray imaging,” IEEE Sel. Top. Quantum Electron. 2(3), 679–692 (1996). [CrossRef]

IEEE Trans. Acoust., Speech, Signal Process.

• J. C. Pesquet, H. Krim, and H. Carfantan, “Time-invariant orthonormal wavelet representations,” IEEE Trans. Acoust., Speech, Signal Process. 44, 1964–1970 (1996).

IEEE Trans. Signal Process.

• R. Neelamani, H. Choi, and R. Baraniuk, “Forward: Fourier-Wavelet regularized deconvolution for Ill-conditioned systems,” IEEE Trans. Signal Process. 52(2), 418–433 (2004). [CrossRef]

Microelectron. J.

• B. Ferguson and D. Abbott, “De-noising techniques for terahertz responses of biological samples,” Microelectron. J. 32(12), 943–953 (2001). [CrossRef]

Opt. Express

• P. C. Ashworth, E. Pickwell-MacPherson, E. Provenzano, S. E. Pinder, A. D. Purushotham, M. Pepper, and V. P. Wallace, “Terahertz pulsed spectroscopy of freshly excised human breast cancer,” Opt. Express 17(15), 12444–12454 (2009). [CrossRef] [PubMed]
• S. Huang, P. C. Ashworth, K. W. C. Kan, Y. Chen, V. P. Wallace, Y. T. Zhang, and E. Pickwell-MacPherson, “Improved sample characterization in terahertz reflection imaging and spectroscopy,” Opt. Express 17(5), 3848–3854 (2009). [CrossRef] [PubMed]

Opt. Lett.

• J. Pearce, H. H. Choi, D. M. Mittleman, J. White, and D. Zimdars, “Terahertz wide aperture reflection tomography,” Opt. Lett. 30(13), 1653–1655 (2005). [CrossRef] [PubMed]

Phys. Med. Biol.

• S. Y. Huang, Y. X. J. Wang, D. K. Yeung, A. T. Ahuja, Y. T. Zhang, and E. Pickwell-Macpherson, “Tissue characterization using terahertz pulsed imaging in reflection geometry,” Phys. Med. Biol. 54(1), 149–160 (2009). [CrossRef]
• E. Pickwell, B. E. Cole, A. J. Fitzgerald, M. Pepper, and V. P. Wallace, “In vivo study of human skin using pulsed terahertz radiation,” Phys. Med. Biol. 49(9), 1595–1607 (2004). [CrossRef] [PubMed]

Proc. Soc. Photo Opt. Instrum. Eng.

• B. E. Cole, R. Woodward, D. Crawley, V. P. Wallace, D. D. Arnone, and M. Pepper, “Terahertz imaging and spectroscopy of human skin, in-vivo,” Proc. Soc. Photo Opt. Instrum. Eng. 4276, 1–10 (2001).

Terahertz for Military and Security Applications

• M. C. Kemp, P. F. Taday, B. E. Cole, J. A. Cluff, A. J. Fitzgerald, and W. R. Tribe, “Security applications of terahertz technology,” Terahertz for Military and Security Applications 5070, 44–52 (2003).

Wavelet Applications in Signal and Image Processing V

• S. P. Ghael, A. M. Sayeed, and R. G. Baraniuk, “Improved wavelet denoising via empirical Wiener filtering,” Wavelet Applications in Signal and Image Processing V 3169, 389–399 (1997).

Wavelets and Statistics, Springer Lecture Notes in Statistics

• G. Nason and B. Silverman, “The Stationary Wavelet Transform and some Statistical Applications,” Wavelets and Statistics, Springer Lecture Notes in Statistics 13, 281–300 (1995).

Other

• P. C. Ashworth, P. O'Kelly, A. D. Purushotham, S. E. Pinder, M. Kontos, M. Pepper, and V. P. Wallace, “An intra-operative THz probe for use during the surgical removal of breast tumors,” 2008 33rd International Conference on Infrared, Millimeter and Terahertz Waves, Vols 1 and 2, 767–769 (2008).
• K. R. Castleman, “Digital Image Processing,” Prentice-Hall, Englewood Cliffs, NJ (1996).

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