Abstract

A method to independently quantify the absorption and the scattering properties of samples based on the analysis of the Haar transform (HT) of photon time-of-flight (TOF) distributions is described. A series of reflectance photon TOF measurements were acquired from absorbing/scattering milk samples of known composition (0 < μa < 0.025 mm-1; 100 < μs < 250 mm-1). The HT of the profiles was calculated, and the regression based on the most parsimonious subset of wavelets was determined by the genetic algorithm (GA). In addition, the utility of computing the logarithm of the profiles or of the absolute value of the wavelet coefficients before the GA was studied. Results show that the absorption coefficient could be estimated with a coefficient of variation (C.V.) of 6.7% and an r 2 of 0.99 by use of the log of selected wavelets of frequency less than 800 MHz. Scattering coefficients were estimated with a C.V. of 2.3% and an r 2 of 0.99 with the log of wavelets of frequency less than 400 MHz. The above results suggest that a simplified instrument based on low-frequency switches could be developed to quantify the optical properties of highly scattering media.

© 2003 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  26. G. Strang, “Wavelets. The transformation of signals into a sum of small, overlapping waves offers a new method for analyzing, storing and transmitting information,” Am. Sci. 82, 250–255 (1994).
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    [CrossRef]
  28. M. D. Waterworth, B. J. Tarte, A. J. Joblin, T. van Doorn, H. E. Niesler, “Optical transmission properties of homogenized milk used as a phantom material in visible wavelength imaging,” Australas. Phys. Eng. Sci. Med. 18, 39–44 (1995).
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    [CrossRef]
  33. B. K. Lavine, A. J. Moores, “Genetic algorithms in analytical chemistry,” Anal. Lett. 32, 433–445 (1999).
    [CrossRef]
  34. C. B. Lucasius, G. Kateman, “Understanding and using genetic algorithms Part 1. Concepts, properties and context,” Chemom. Intell. Lab. Syst. 19, 1–33 (1993).
    [CrossRef]
  35. C. B. Lucasius, G. Kateman, “Understanding and using genetic algorithms Part 2. Representation, configuration and hybridization.,” Chemom. Intell. Lab Syst. 25, 99–145 (1994).
    [CrossRef]
  36. J.-S. R. Jang, “Derivative-free optimization,” in Neuro-Fuzzy and Soft Computing. A Computational Approach to Learning and Machine Intelligence, J.-S. R. Jang, C.-T. Sun, E. Mizutani, eds. (Prentice Hall, N.Y., 1997), pp. 175–180.
  37. Q. Ding, G. W. Small, “Genetic algorithm-based wavelength selection for the near-infrared determination of glucose in biological matrixes: initialization strategies and effects of spectral resolution,” Anal. Chem. 70, 4472–4479 (1998).
    [CrossRef] [PubMed]
  38. D. B. Hibbert, “Genetic algorithms in chemistry,” Chemom. Intell. Lab. Syst. 19, 277–293 (1993).
    [CrossRef]
  39. R. Judson, “Genetic algorithms and their use in chemistry,” Rev. Comput. Chem. 10, 1–73, (1997).
  40. D. M. Haaland, E. V. Thomas, “Partial least-squares methods for spectral analyses. 1. Relation to other quantitative calibration methods and the extraction of qualitative information,” Anal. Chem. 60, 1193–1202 (1988).
    [CrossRef]

2002

Y. Wang, L. Ma, S. Shi, “An optical method for production of Haar wavelet,” Opt. Commun. 204, 107–110 (2002).
[CrossRef]

H.-W. Tan, S. D. Brown, “Wavelet analysis applied to removing non-constant, varying spectroscopic background in multivariate calibration,” J. Chemom. 16, 228–240 (2002).
[CrossRef]

2000

B. K. Alsberg, “Parsimonious multiscale classification models,” J. Chemom. 14, 529–539, (2000).
[CrossRef]

1999

B. K. Lavine, A. J. Moores, “Genetic algorithms in analytical chemistry,” Anal. Lett. 32, 433–445 (1999).
[CrossRef]

J. A. Räty, K.-E. Peiponen, “Reflectance study of milk in the UV-visible range,” Appl. Spectrosc. 53, 1123–1127 (1999).
[CrossRef]

L. Leonardi, D. H. Burns, “Quantitative measurements in scattering media: photon time-of-flight analysis with analytical descriptors,” Appl. Spectrosc. 53, 628–636 (1999).
[CrossRef]

U. Depczynski, K. Jetter, K. Molt, A. Niemoller, “Quantitative analysis of near infrared spectra by wavelet coefficient regression using a genetic algorithm,” Chemom. Intell. Lab. Syst. 47, 179–187 (1999).
[CrossRef]

S. K. Nath, R. M. Vasu, M. Pandit, “Wavelet based compression and denoising of optical tomography data,” Opt. Commun. 167, 37–46 (1999).
[CrossRef]

1998

A. K.-M. Leung, F.-T. Chau, J.-B. Gao, T.-M. Shih, “Application of wavelet transform in infrared spectrometry: spectral compression and library search,” Chemom. Intell. Lab. Syst. 43, 69–88 (1998).
[CrossRef]

B. K. Alsberg, A. M. Woodward, M. K. Winson, J. J. Rowland, D. B. Kell, “Variable selection in wavelet regression models,” Anal. Chim. Acta 368, 29–44 (1998).
[CrossRef]

D. A. Sadler, P. R. Boulo, J. S. Soraghan, D. Littlejohn, “Tutorial guide to the use of wavelet transforms to determine peak shape parameters for interference detection in graphite-furnace atomic absorption spectrometry,” Spectrochim. Acta Part B 53, 821–835 (1998).
[CrossRef]

Q. Ding, G. W. Small, “Genetic algorithm-based wavelength selection for the near-infrared determination of glucose in biological matrixes: initialization strategies and effects of spectral resolution,” Anal. Chem. 70, 4472–4479 (1998).
[CrossRef] [PubMed]

1997

F. T. Chau, J. B. Gao, T. M. Shih, J. Wang, “Compression of infrared spectral data using the fast wavelet transform method,” Appl. Spectrosc. 51, 649–659 (1997).
[CrossRef]

R. Judson, “Genetic algorithms and their use in chemistry,” Rev. Comput. Chem. 10, 1–73, (1997).

L. Leonardi, D. H. Burns, “Quantitative constituent measurements in scattering media from statistical analysis of photon time-of-flight distributions,” Anal. Chim. Acta 348, 543–551 (1997).
[CrossRef]

B. K. Alsberg, A. M. Woodward, D. B. Kell, “An introduction to wavelet transforms for chemometricians: a time-frequency approach,” Chemom. Intell. Lab. Syst. 37, 215–239 (1997).
[CrossRef]

B. Walczak, D. L. Massart, “Noise suppression and signal compression using the wavelet packet transform,” Chemom. Intell. Lab. Syst. 36, 81–94 (1997).
[CrossRef]

S. J. Matcher, M. Cope, D. T. Delpy, “In vivo measurements of the wavelength dependence of tissue-scattering coefficients between 760 and 900 nm measured with time-resolved spectroscopy,” Appl. Opt. 36, 386–396 (1997).
[CrossRef] [PubMed]

1995

H. Liu, D. A. Boas, Y. Zhang, A. G. Yodh, B. Chance, “Determination of optical properties and blood oxygenation in tissue using continuous NIR light,” Phys. Med. Biol. 40, 1983–1993 (1995).
[CrossRef] [PubMed]

S. R. Arridge, M. Schweiger, “Direct calculation of the moments of the distribution of photon time-of-flight in tissue with a finite-element method,” Appl. Opt. 34, 2683–2687 (1995).
[CrossRef] [PubMed]

A. Graps, “An introduction to wavelets,” IEEE Comput. Sci. Eng. 2, 50–61 (1995).
[CrossRef]

M. D. Waterworth, B. J. Tarte, A. J. Joblin, T. van Doorn, H. E. Niesler, “Optical transmission properties of homogenized milk used as a phantom material in visible wavelength imaging,” Australas. Phys. Eng. Sci. Med. 18, 39–44 (1995).
[PubMed]

1994

G. Strang, “Wavelets. The transformation of signals into a sum of small, overlapping waves offers a new method for analyzing, storing and transmitting information,” Am. Sci. 82, 250–255 (1994).

C. B. Lucasius, G. Kateman, “Understanding and using genetic algorithms Part 2. Representation, configuration and hybridization.,” Chemom. Intell. Lab Syst. 25, 99–145 (1994).
[CrossRef]

R. Cubeddu, M. Musolino, A. Pifferi, P. Taroni, G. Valentini, “Time-resolved reflectance: a systematic study for application to the optical characterization of tissues,” IEEE J. Quantum Electron. 30, 2421–2430 (1994).
[CrossRef]

1993

D. B. Hibbert, “Genetic algorithms in chemistry,” Chemom. Intell. Lab. Syst. 19, 277–293 (1993).
[CrossRef]

C. B. Lucasius, G. Kateman, “Understanding and using genetic algorithms Part 1. Concepts, properties and context,” Chemom. Intell. Lab. Syst. 19, 1–33 (1993).
[CrossRef]

1992

1991

E. M. Sevick, B. Chance, J. Leigh, S. Nioka, M. Maris, “Quantitation of time- and frequency-resolved optical spectra for the determination of tissue oxygenation,” Anal. Biochem. 195, 330–351 (1991).
[CrossRef] [PubMed]

1990

W.-F. Cheong, S. A. Prahl, A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

B. C. Wilson, S. L. Jacques, “Optical reflectance and transmittance of tissues: principles and applications,” IEEE J. Quantum Electron. 26, 2186–2199 (1990).
[CrossRef]

1989

1988

D. M. Haaland, E. V. Thomas, “Partial least-squares methods for spectral analyses. 1. Relation to other quantitative calibration methods and the extraction of qualitative information,” Anal. Chem. 60, 1193–1202 (1988).
[CrossRef]

1981

R. R. Anderson, J. A. Parrish, “The optics of human skin,” J. Invest. Dermatol. 77, 13–19 (1981).
[CrossRef] [PubMed]

Aboufadel, E.

E. Aboufadel, S. Schlicker, Discovering Wavelets (Wiley, N.Y., 1999).
[CrossRef]

Alsberg, B. K.

B. K. Alsberg, “Parsimonious multiscale classification models,” J. Chemom. 14, 529–539, (2000).
[CrossRef]

B. K. Alsberg, A. M. Woodward, M. K. Winson, J. J. Rowland, D. B. Kell, “Variable selection in wavelet regression models,” Anal. Chim. Acta 368, 29–44 (1998).
[CrossRef]

B. K. Alsberg, A. M. Woodward, D. B. Kell, “An introduction to wavelet transforms for chemometricians: a time-frequency approach,” Chemom. Intell. Lab. Syst. 37, 215–239 (1997).
[CrossRef]

Anderson, R. R.

R. R. Anderson, J. A. Parrish, “The optics of human skin,” J. Invest. Dermatol. 77, 13–19 (1981).
[CrossRef] [PubMed]

Arridge, S. R.

Boas, D. A.

H. Liu, D. A. Boas, Y. Zhang, A. G. Yodh, B. Chance, “Determination of optical properties and blood oxygenation in tissue using continuous NIR light,” Phys. Med. Biol. 40, 1983–1993 (1995).
[CrossRef] [PubMed]

Boulo, P. R.

D. A. Sadler, P. R. Boulo, J. S. Soraghan, D. Littlejohn, “Tutorial guide to the use of wavelet transforms to determine peak shape parameters for interference detection in graphite-furnace atomic absorption spectrometry,” Spectrochim. Acta Part B 53, 821–835 (1998).
[CrossRef]

Brown, S. D.

H.-W. Tan, S. D. Brown, “Wavelet analysis applied to removing non-constant, varying spectroscopic background in multivariate calibration,” J. Chemom. 16, 228–240 (2002).
[CrossRef]

Burger, T.

J. M. Olinger, P. R. Griffiths, T. Burger, “Theory of diffuse reflection in the NIR region,” in Handbook of Near-Infrared Analysis, 2nd ed., D. A. Burns, E. W. Ciurczak, eds. (Marcel Dekker, New York, N.Y., 2001), pp. 19–51.

Burns, D. H.

L. Leonardi, D. H. Burns, “Quantitative measurements in scattering media: photon time-of-flight analysis with analytical descriptors,” Appl. Spectrosc. 53, 628–636 (1999).
[CrossRef]

L. Leonardi, D. H. Burns, “Quantitative constituent measurements in scattering media from statistical analysis of photon time-of-flight distributions,” Anal. Chim. Acta 348, 543–551 (1997).
[CrossRef]

Chance, B.

H. Liu, D. A. Boas, Y. Zhang, A. G. Yodh, B. Chance, “Determination of optical properties and blood oxygenation in tissue using continuous NIR light,” Phys. Med. Biol. 40, 1983–1993 (1995).
[CrossRef] [PubMed]

E. M. Sevick, B. Chance, J. Leigh, S. Nioka, M. Maris, “Quantitation of time- and frequency-resolved optical spectra for the determination of tissue oxygenation,” Anal. Biochem. 195, 330–351 (1991).
[CrossRef] [PubMed]

Chau, F. T.

Chau, F.-T.

A. K.-M. Leung, F.-T. Chau, J.-B. Gao, T.-M. Shih, “Application of wavelet transform in infrared spectrometry: spectral compression and library search,” Chemom. Intell. Lab. Syst. 43, 69–88 (1998).
[CrossRef]

Cheong, W.-F.

W.-F. Cheong, S. A. Prahl, A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

Cope, M.

Cubeddu, R.

R. Cubeddu, M. Musolino, A. Pifferi, P. Taroni, G. Valentini, “Time-resolved reflectance: a systematic study for application to the optical characterization of tissues,” IEEE J. Quantum Electron. 30, 2421–2430 (1994).
[CrossRef]

Delpy, D. T.

Depczynski, U.

U. Depczynski, K. Jetter, K. Molt, A. Niemoller, “Quantitative analysis of near infrared spectra by wavelet coefficient regression using a genetic algorithm,” Chemom. Intell. Lab. Syst. 47, 179–187 (1999).
[CrossRef]

Ding, Q.

Q. Ding, G. W. Small, “Genetic algorithm-based wavelength selection for the near-infrared determination of glucose in biological matrixes: initialization strategies and effects of spectral resolution,” Anal. Chem. 70, 4472–4479 (1998).
[CrossRef] [PubMed]

Farrell, T. J.

T. J. Farrell, B. C. Wilson, M. S. Patterson, “The use of neural network to determine tissue optical properties for spatially resolved diffuse reflectance measurements,” Phys. Med. Biol. 37, 2281–2286 (1992).
[CrossRef] [PubMed]

Gao, J. B.

Gao, J.-B.

A. K.-M. Leung, F.-T. Chau, J.-B. Gao, T.-M. Shih, “Application of wavelet transform in infrared spectrometry: spectral compression and library search,” Chemom. Intell. Lab. Syst. 43, 69–88 (1998).
[CrossRef]

Graps, A.

A. Graps, “An introduction to wavelets,” IEEE Comput. Sci. Eng. 2, 50–61 (1995).
[CrossRef]

Griffiths, P. R.

J. M. Olinger, P. R. Griffiths, T. Burger, “Theory of diffuse reflection in the NIR region,” in Handbook of Near-Infrared Analysis, 2nd ed., D. A. Burns, E. W. Ciurczak, eds. (Marcel Dekker, New York, N.Y., 2001), pp. 19–51.

Haaland, D. M.

D. M. Haaland, E. V. Thomas, “Partial least-squares methods for spectral analyses. 1. Relation to other quantitative calibration methods and the extraction of qualitative information,” Anal. Chem. 60, 1193–1202 (1988).
[CrossRef]

Hefetz, Y.

Hibbert, D. B.

D. B. Hibbert, “Genetic algorithms in chemistry,” Chemom. Intell. Lab. Syst. 19, 277–293 (1993).
[CrossRef]

Jacques, S.

Jacques, S. L.

Jang, J.-S. R.

J.-S. R. Jang, “Derivative-free optimization,” in Neuro-Fuzzy and Soft Computing. A Computational Approach to Learning and Machine Intelligence, J.-S. R. Jang, C.-T. Sun, E. Mizutani, eds. (Prentice Hall, N.Y., 1997), pp. 175–180.

Jetter, K.

U. Depczynski, K. Jetter, K. Molt, A. Niemoller, “Quantitative analysis of near infrared spectra by wavelet coefficient regression using a genetic algorithm,” Chemom. Intell. Lab. Syst. 47, 179–187 (1999).
[CrossRef]

Joblin, A. J.

M. D. Waterworth, B. J. Tarte, A. J. Joblin, T. van Doorn, H. E. Niesler, “Optical transmission properties of homogenized milk used as a phantom material in visible wavelength imaging,” Australas. Phys. Eng. Sci. Med. 18, 39–44 (1995).
[PubMed]

Judson, R.

R. Judson, “Genetic algorithms and their use in chemistry,” Rev. Comput. Chem. 10, 1–73, (1997).

Kateman, G.

C. B. Lucasius, G. Kateman, “Understanding and using genetic algorithms Part 2. Representation, configuration and hybridization.,” Chemom. Intell. Lab Syst. 25, 99–145 (1994).
[CrossRef]

C. B. Lucasius, G. Kateman, “Understanding and using genetic algorithms Part 1. Concepts, properties and context,” Chemom. Intell. Lab. Syst. 19, 1–33 (1993).
[CrossRef]

Kell, D. B.

B. K. Alsberg, A. M. Woodward, M. K. Winson, J. J. Rowland, D. B. Kell, “Variable selection in wavelet regression models,” Anal. Chim. Acta 368, 29–44 (1998).
[CrossRef]

B. K. Alsberg, A. M. Woodward, D. B. Kell, “An introduction to wavelet transforms for chemometricians: a time-frequency approach,” Chemom. Intell. Lab. Syst. 37, 215–239 (1997).
[CrossRef]

Lavine, B. K.

B. K. Lavine, A. J. Moores, “Genetic algorithms in analytical chemistry,” Anal. Lett. 32, 433–445 (1999).
[CrossRef]

Leigh, J.

E. M. Sevick, B. Chance, J. Leigh, S. Nioka, M. Maris, “Quantitation of time- and frequency-resolved optical spectra for the determination of tissue oxygenation,” Anal. Biochem. 195, 330–351 (1991).
[CrossRef] [PubMed]

Leonardi, L.

L. Leonardi, D. H. Burns, “Quantitative measurements in scattering media: photon time-of-flight analysis with analytical descriptors,” Appl. Spectrosc. 53, 628–636 (1999).
[CrossRef]

L. Leonardi, D. H. Burns, “Quantitative constituent measurements in scattering media from statistical analysis of photon time-of-flight distributions,” Anal. Chim. Acta 348, 543–551 (1997).
[CrossRef]

Leung, A. K.-M.

A. K.-M. Leung, F.-T. Chau, J.-B. Gao, T.-M. Shih, “Application of wavelet transform in infrared spectrometry: spectral compression and library search,” Chemom. Intell. Lab. Syst. 43, 69–88 (1998).
[CrossRef]

Littlejohn, D.

D. A. Sadler, P. R. Boulo, J. S. Soraghan, D. Littlejohn, “Tutorial guide to the use of wavelet transforms to determine peak shape parameters for interference detection in graphite-furnace atomic absorption spectrometry,” Spectrochim. Acta Part B 53, 821–835 (1998).
[CrossRef]

Liu, H.

H. Liu, D. A. Boas, Y. Zhang, A. G. Yodh, B. Chance, “Determination of optical properties and blood oxygenation in tissue using continuous NIR light,” Phys. Med. Biol. 40, 1983–1993 (1995).
[CrossRef] [PubMed]

Lucasius, C. B.

C. B. Lucasius, G. Kateman, “Understanding and using genetic algorithms Part 2. Representation, configuration and hybridization.,” Chemom. Intell. Lab Syst. 25, 99–145 (1994).
[CrossRef]

C. B. Lucasius, G. Kateman, “Understanding and using genetic algorithms Part 1. Concepts, properties and context,” Chemom. Intell. Lab. Syst. 19, 1–33 (1993).
[CrossRef]

Ma, L.

Y. Wang, L. Ma, S. Shi, “An optical method for production of Haar wavelet,” Opt. Commun. 204, 107–110 (2002).
[CrossRef]

Madsen, S. J.

Maris, M.

E. M. Sevick, B. Chance, J. Leigh, S. Nioka, M. Maris, “Quantitation of time- and frequency-resolved optical spectra for the determination of tissue oxygenation,” Anal. Biochem. 195, 330–351 (1991).
[CrossRef] [PubMed]

Massart, D. L.

B. Walczak, D. L. Massart, “Noise suppression and signal compression using the wavelet packet transform,” Chemom. Intell. Lab. Syst. 36, 81–94 (1997).
[CrossRef]

Matcher, S. J.

Mauze, G. R.

C. S. McNulty, G. R. Mauze, “Application of wavelet analysis for determining glucose concentration of aqueous solutions using NIR spectroscopy,” in infrared spectroscopy: New Tool in Medicine, H. H. Mantsch, M. Jackson, eds. Proc. SPIE3257, 167–176 (1998).
[CrossRef]

McNulty, C. S.

C. S. McNulty, G. R. Mauze, “Application of wavelet analysis for determining glucose concentration of aqueous solutions using NIR spectroscopy,” in infrared spectroscopy: New Tool in Medicine, H. H. Mantsch, M. Jackson, eds. Proc. SPIE3257, 167–176 (1998).
[CrossRef]

Molt, K.

U. Depczynski, K. Jetter, K. Molt, A. Niemoller, “Quantitative analysis of near infrared spectra by wavelet coefficient regression using a genetic algorithm,” Chemom. Intell. Lab. Syst. 47, 179–187 (1999).
[CrossRef]

Moores, A. J.

B. K. Lavine, A. J. Moores, “Genetic algorithms in analytical chemistry,” Anal. Lett. 32, 433–445 (1999).
[CrossRef]

Musolino, M.

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S. K. Nath, R. M. Vasu, M. Pandit, “Wavelet based compression and denoising of optical tomography data,” Opt. Commun. 167, 37–46 (1999).
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U. Depczynski, K. Jetter, K. Molt, A. Niemoller, “Quantitative analysis of near infrared spectra by wavelet coefficient regression using a genetic algorithm,” Chemom. Intell. Lab. Syst. 47, 179–187 (1999).
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M. D. Waterworth, B. J. Tarte, A. J. Joblin, T. van Doorn, H. E. Niesler, “Optical transmission properties of homogenized milk used as a phantom material in visible wavelength imaging,” Australas. Phys. Eng. Sci. Med. 18, 39–44 (1995).
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E. M. Sevick, B. Chance, J. Leigh, S. Nioka, M. Maris, “Quantitation of time- and frequency-resolved optical spectra for the determination of tissue oxygenation,” Anal. Biochem. 195, 330–351 (1991).
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J. M. Olinger, P. R. Griffiths, T. Burger, “Theory of diffuse reflection in the NIR region,” in Handbook of Near-Infrared Analysis, 2nd ed., D. A. Burns, E. W. Ciurczak, eds. (Marcel Dekker, New York, N.Y., 2001), pp. 19–51.

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S. K. Nath, R. M. Vasu, M. Pandit, “Wavelet based compression and denoising of optical tomography data,” Opt. Commun. 167, 37–46 (1999).
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R. Cubeddu, M. Musolino, A. Pifferi, P. Taroni, G. Valentini, “Time-resolved reflectance: a systematic study for application to the optical characterization of tissues,” IEEE J. Quantum Electron. 30, 2421–2430 (1994).
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W.-F. Cheong, S. A. Prahl, A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
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B. K. Alsberg, A. M. Woodward, M. K. Winson, J. J. Rowland, D. B. Kell, “Variable selection in wavelet regression models,” Anal. Chim. Acta 368, 29–44 (1998).
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D. A. Sadler, P. R. Boulo, J. S. Soraghan, D. Littlejohn, “Tutorial guide to the use of wavelet transforms to determine peak shape parameters for interference detection in graphite-furnace atomic absorption spectrometry,” Spectrochim. Acta Part B 53, 821–835 (1998).
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E. Aboufadel, S. Schlicker, Discovering Wavelets (Wiley, N.Y., 1999).
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Y. Wang, L. Ma, S. Shi, “An optical method for production of Haar wavelet,” Opt. Commun. 204, 107–110 (2002).
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Shih, T.-M.

A. K.-M. Leung, F.-T. Chau, J.-B. Gao, T.-M. Shih, “Application of wavelet transform in infrared spectrometry: spectral compression and library search,” Chemom. Intell. Lab. Syst. 43, 69–88 (1998).
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Q. Ding, G. W. Small, “Genetic algorithm-based wavelength selection for the near-infrared determination of glucose in biological matrixes: initialization strategies and effects of spectral resolution,” Anal. Chem. 70, 4472–4479 (1998).
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D. A. Sadler, P. R. Boulo, J. S. Soraghan, D. Littlejohn, “Tutorial guide to the use of wavelet transforms to determine peak shape parameters for interference detection in graphite-furnace atomic absorption spectrometry,” Spectrochim. Acta Part B 53, 821–835 (1998).
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G. Strang, “Wavelets. The transformation of signals into a sum of small, overlapping waves offers a new method for analyzing, storing and transmitting information,” Am. Sci. 82, 250–255 (1994).

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H.-W. Tan, S. D. Brown, “Wavelet analysis applied to removing non-constant, varying spectroscopic background in multivariate calibration,” J. Chemom. 16, 228–240 (2002).
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R. Cubeddu, M. Musolino, A. Pifferi, P. Taroni, G. Valentini, “Time-resolved reflectance: a systematic study for application to the optical characterization of tissues,” IEEE J. Quantum Electron. 30, 2421–2430 (1994).
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M. D. Waterworth, B. J. Tarte, A. J. Joblin, T. van Doorn, H. E. Niesler, “Optical transmission properties of homogenized milk used as a phantom material in visible wavelength imaging,” Australas. Phys. Eng. Sci. Med. 18, 39–44 (1995).
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D. M. Haaland, E. V. Thomas, “Partial least-squares methods for spectral analyses. 1. Relation to other quantitative calibration methods and the extraction of qualitative information,” Anal. Chem. 60, 1193–1202 (1988).
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R. Cubeddu, M. Musolino, A. Pifferi, P. Taroni, G. Valentini, “Time-resolved reflectance: a systematic study for application to the optical characterization of tissues,” IEEE J. Quantum Electron. 30, 2421–2430 (1994).
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M. D. Waterworth, B. J. Tarte, A. J. Joblin, T. van Doorn, H. E. Niesler, “Optical transmission properties of homogenized milk used as a phantom material in visible wavelength imaging,” Australas. Phys. Eng. Sci. Med. 18, 39–44 (1995).
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S. K. Nath, R. M. Vasu, M. Pandit, “Wavelet based compression and denoising of optical tomography data,” Opt. Commun. 167, 37–46 (1999).
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B. Walczak, D. L. Massart, “Noise suppression and signal compression using the wavelet packet transform,” Chemom. Intell. Lab. Syst. 36, 81–94 (1997).
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J. S. Walker, A Primer on Wavelets and their Scientific Applications (Chapman Hall, Boca Raton, 1999).
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Wang, Y.

Y. Wang, L. Ma, S. Shi, “An optical method for production of Haar wavelet,” Opt. Commun. 204, 107–110 (2002).
[CrossRef]

Waterworth, M. D.

M. D. Waterworth, B. J. Tarte, A. J. Joblin, T. van Doorn, H. E. Niesler, “Optical transmission properties of homogenized milk used as a phantom material in visible wavelength imaging,” Australas. Phys. Eng. Sci. Med. 18, 39–44 (1995).
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W.-F. Cheong, S. A. Prahl, A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

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T. J. Farrell, B. C. Wilson, M. S. Patterson, “The use of neural network to determine tissue optical properties for spatially resolved diffuse reflectance measurements,” Phys. Med. Biol. 37, 2281–2286 (1992).
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B. C. Wilson, S. L. Jacques, “Optical reflectance and transmittance of tissues: principles and applications,” IEEE J. Quantum Electron. 26, 2186–2199 (1990).
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B. K. Alsberg, A. M. Woodward, M. K. Winson, J. J. Rowland, D. B. Kell, “Variable selection in wavelet regression models,” Anal. Chim. Acta 368, 29–44 (1998).
[CrossRef]

Woodward, A. M.

B. K. Alsberg, A. M. Woodward, M. K. Winson, J. J. Rowland, D. B. Kell, “Variable selection in wavelet regression models,” Anal. Chim. Acta 368, 29–44 (1998).
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B. K. Alsberg, A. M. Woodward, D. B. Kell, “An introduction to wavelet transforms for chemometricians: a time-frequency approach,” Chemom. Intell. Lab. Syst. 37, 215–239 (1997).
[CrossRef]

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H. Liu, D. A. Boas, Y. Zhang, A. G. Yodh, B. Chance, “Determination of optical properties and blood oxygenation in tissue using continuous NIR light,” Phys. Med. Biol. 40, 1983–1993 (1995).
[CrossRef] [PubMed]

Zhang, Y.

H. Liu, D. A. Boas, Y. Zhang, A. G. Yodh, B. Chance, “Determination of optical properties and blood oxygenation in tissue using continuous NIR light,” Phys. Med. Biol. 40, 1983–1993 (1995).
[CrossRef] [PubMed]

Am. Sci.

G. Strang, “Wavelets. The transformation of signals into a sum of small, overlapping waves offers a new method for analyzing, storing and transmitting information,” Am. Sci. 82, 250–255 (1994).

Anal. Biochem.

E. M. Sevick, B. Chance, J. Leigh, S. Nioka, M. Maris, “Quantitation of time- and frequency-resolved optical spectra for the determination of tissue oxygenation,” Anal. Biochem. 195, 330–351 (1991).
[CrossRef] [PubMed]

Anal. Chem.

D. M. Haaland, E. V. Thomas, “Partial least-squares methods for spectral analyses. 1. Relation to other quantitative calibration methods and the extraction of qualitative information,” Anal. Chem. 60, 1193–1202 (1988).
[CrossRef]

Q. Ding, G. W. Small, “Genetic algorithm-based wavelength selection for the near-infrared determination of glucose in biological matrixes: initialization strategies and effects of spectral resolution,” Anal. Chem. 70, 4472–4479 (1998).
[CrossRef] [PubMed]

Anal. Chim. Acta

L. Leonardi, D. H. Burns, “Quantitative constituent measurements in scattering media from statistical analysis of photon time-of-flight distributions,” Anal. Chim. Acta 348, 543–551 (1997).
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B. K. Alsberg, A. M. Woodward, M. K. Winson, J. J. Rowland, D. B. Kell, “Variable selection in wavelet regression models,” Anal. Chim. Acta 368, 29–44 (1998).
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Australas. Phys. Eng. Sci. Med.

M. D. Waterworth, B. J. Tarte, A. J. Joblin, T. van Doorn, H. E. Niesler, “Optical transmission properties of homogenized milk used as a phantom material in visible wavelength imaging,” Australas. Phys. Eng. Sci. Med. 18, 39–44 (1995).
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C. B. Lucasius, G. Kateman, “Understanding and using genetic algorithms Part 2. Representation, configuration and hybridization.,” Chemom. Intell. Lab Syst. 25, 99–145 (1994).
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C. B. Lucasius, G. Kateman, “Understanding and using genetic algorithms Part 1. Concepts, properties and context,” Chemom. Intell. Lab. Syst. 19, 1–33 (1993).
[CrossRef]

B. Walczak, D. L. Massart, “Noise suppression and signal compression using the wavelet packet transform,” Chemom. Intell. Lab. Syst. 36, 81–94 (1997).
[CrossRef]

A. K.-M. Leung, F.-T. Chau, J.-B. Gao, T.-M. Shih, “Application of wavelet transform in infrared spectrometry: spectral compression and library search,” Chemom. Intell. Lab. Syst. 43, 69–88 (1998).
[CrossRef]

U. Depczynski, K. Jetter, K. Molt, A. Niemoller, “Quantitative analysis of near infrared spectra by wavelet coefficient regression using a genetic algorithm,” Chemom. Intell. Lab. Syst. 47, 179–187 (1999).
[CrossRef]

B. K. Alsberg, A. M. Woodward, D. B. Kell, “An introduction to wavelet transforms for chemometricians: a time-frequency approach,” Chemom. Intell. Lab. Syst. 37, 215–239 (1997).
[CrossRef]

D. B. Hibbert, “Genetic algorithms in chemistry,” Chemom. Intell. Lab. Syst. 19, 277–293 (1993).
[CrossRef]

IEEE Comput. Sci. Eng.

A. Graps, “An introduction to wavelets,” IEEE Comput. Sci. Eng. 2, 50–61 (1995).
[CrossRef]

IEEE J. Quantum Electron.

R. Cubeddu, M. Musolino, A. Pifferi, P. Taroni, G. Valentini, “Time-resolved reflectance: a systematic study for application to the optical characterization of tissues,” IEEE J. Quantum Electron. 30, 2421–2430 (1994).
[CrossRef]

W.-F. Cheong, S. A. Prahl, A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

B. C. Wilson, S. L. Jacques, “Optical reflectance and transmittance of tissues: principles and applications,” IEEE J. Quantum Electron. 26, 2186–2199 (1990).
[CrossRef]

J. Chemom.

B. K. Alsberg, “Parsimonious multiscale classification models,” J. Chemom. 14, 529–539, (2000).
[CrossRef]

H.-W. Tan, S. D. Brown, “Wavelet analysis applied to removing non-constant, varying spectroscopic background in multivariate calibration,” J. Chemom. 16, 228–240 (2002).
[CrossRef]

J. Invest. Dermatol.

R. R. Anderson, J. A. Parrish, “The optics of human skin,” J. Invest. Dermatol. 77, 13–19 (1981).
[CrossRef] [PubMed]

Opt. Commun.

S. K. Nath, R. M. Vasu, M. Pandit, “Wavelet based compression and denoising of optical tomography data,” Opt. Commun. 167, 37–46 (1999).
[CrossRef]

Y. Wang, L. Ma, S. Shi, “An optical method for production of Haar wavelet,” Opt. Commun. 204, 107–110 (2002).
[CrossRef]

Phys. Med. Biol.

T. J. Farrell, B. C. Wilson, M. S. Patterson, “The use of neural network to determine tissue optical properties for spatially resolved diffuse reflectance measurements,” Phys. Med. Biol. 37, 2281–2286 (1992).
[CrossRef] [PubMed]

H. Liu, D. A. Boas, Y. Zhang, A. G. Yodh, B. Chance, “Determination of optical properties and blood oxygenation in tissue using continuous NIR light,” Phys. Med. Biol. 40, 1983–1993 (1995).
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R. Judson, “Genetic algorithms and their use in chemistry,” Rev. Comput. Chem. 10, 1–73, (1997).

Spectrochim. Acta Part B

D. A. Sadler, P. R. Boulo, J. S. Soraghan, D. Littlejohn, “Tutorial guide to the use of wavelet transforms to determine peak shape parameters for interference detection in graphite-furnace atomic absorption spectrometry,” Spectrochim. Acta Part B 53, 821–835 (1998).
[CrossRef]

Other

C. S. McNulty, G. R. Mauze, “Application of wavelet analysis for determining glucose concentration of aqueous solutions using NIR spectroscopy,” in infrared spectroscopy: New Tool in Medicine, H. H. Mantsch, M. Jackson, eds. Proc. SPIE3257, 167–176 (1998).
[CrossRef]

J. M. Olinger, P. R. Griffiths, T. Burger, “Theory of diffuse reflection in the NIR region,” in Handbook of Near-Infrared Analysis, 2nd ed., D. A. Burns, E. W. Ciurczak, eds. (Marcel Dekker, New York, N.Y., 2001), pp. 19–51.

E. Aboufadel, S. Schlicker, Discovering Wavelets (Wiley, N.Y., 1999).
[CrossRef]

J. S. Walker, A Primer on Wavelets and their Scientific Applications (Chapman Hall, Boca Raton, 1999).
[CrossRef]

J.-S. R. Jang, “Derivative-free optimization,” in Neuro-Fuzzy and Soft Computing. A Computational Approach to Learning and Machine Intelligence, J.-S. R. Jang, C.-T. Sun, E. Mizutani, eds. (Prentice Hall, N.Y., 1997), pp. 175–180.

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Figures (4)

Fig. 1
Fig. 1

Photon TOF instrument. BS, beam splitter; PD, photodiode; CFD, constant fraction discriminator; DL, delay line; ND, neutral density filter; S, sample; MCP-PMT, microchannel-plate photomultiplier tube; TAC, time-to-amplitude converter; PC, personal computer.

Fig. 2
Fig. 2

Photon TOF distributions with (a) varying absorption from 0 to 0.025 mm-1 at constant low scattering and (b) varying scattering from 150 to 250 mm-1 at constant low absorption.

Fig. 3
Fig. 3

Inverse least-squares estimates with raw Haar coefficients: (a) absorption estimate with wavelets ϕ, ψ2,0, and ψ2,2 (C.V. of 7.3% and r 2 of 0.99); (b) sample TOF profile compared with calibration coefficients for absorption; (c) scattering estimate with wavelets ϕ, ψ2,1, and ψ2,2 (C.V. of 2.5% and r 2 of 0.99); (d) sample TOF profile compared with calibration coefficients for scattering.

Fig. 4
Fig. 4

Inverse least squares with the logarithm of Haar coefficients to estimate (a) absorption from wavelets ψ, ψ1,1, and ψ2,2 (C.V. of 6.9% and r 2 of 0.99) and (b) scattering from wavelets ψ and ψ1,1 (C.V. of 2.3% and r 2 of 0.99).

Tables (2)

Tables Icon

Table 1 Absorption and Scattering Estimation from Haar Transform Coefficients of Raw and Log Time-of-Flight Profiles

Tables Icon

Table 2 Absorption and Scattering Estimation from Haar Transform Coefficients of the Logarithm of Unsigned Haar Transform Coefficients of the Raw Time-of-Flight Profiles

Equations (5)

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

ϕτ=1if 0  τ  10otherwise,
ψτ=1if 0  τ  ½-1if 1/2  τ  10otherwise,
ψn,kτ=ψ2nτ-k, 0  k  2n-1.
ϕτψτ ψ1,0τ ψ1,1τ A2=111011-101-1011-10-1
Y=α0+α1X1+α2X2++αnXn

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