Abstract

By use of time-resolved spectroscopy it is possible to separate light scattering effects from chemical absorption effects in samples. In the study of propagation of short light pulses in turbid samples the reduced scattering coefficient and the absorption coefficient are usually obtained by fitting diffusion or Monte Carlo models to the measured data by use of numerical optimization techniques. In this study we propose a prediction model obtained with a semiparametric modeling technique: the least-squares support vector machines. The main advantage of this technique is that it uses theoretical time dispersion curves during the calibration step. Predictions can then be performed by use of data measured on different kinds of sample, such as apples.

© 2005 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. B. Chance, J. Leigh, H. Miyake, D. Smith, S. Nioka, R. Greenfeld, M. Finander, K. Kaufmann, W. Levy, M. Young, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
    [CrossRef]
  2. S. L. Jacques, “Time-resolved propagation of ultrashort laser pulses within turbid tissues,” Appl. Opt. 28, 2223–2229 (1989).
    [CrossRef] [PubMed]
  3. S. Andersson-Engels, R. Berg, S. Svanberg, O. Jarlman, “Time-resolved transillumination for medical diagnostics,” Opt. Lett 15, 1179–1181 (1990).
    [CrossRef] [PubMed]
  4. J. Johansson, S. Folestad, M. Josefson, A. Sparen, C. Abrahamsson, S. Andersson-Engels, S. Svanberg, “Time-resolved NIR/Vis spectroscopy for analysis of solids: pharmaceutical tablets,” Appl. Spectrosc. 56, 725–731 (2002).
    [CrossRef]
  5. P. E. Zerbini, M. Grassi, R. Cubeddu, A. Pifferi, A. Torricelli, “Nondestructive detection of brown heart in pears by time-resolved reflectance spectroscopy,” Postharvest Biol. Technol. 25, 87–97 (2002).
    [CrossRef]
  6. J. Johansson, R. Berg, A. Pifferi, S. Svanberg, L. Bjorn, “Time-resolved studies of light propagation in Crassula and Phaseolus leaves,” Photochem Photobiol. 69, 242–247 (1999).
    [CrossRef]
  7. M. S. Patterson, B. Chance, B. C. Wilson, “Time-resolved reflectance and transmittance for the noninvasive measurement of tissue optical properties,” Appl. Opt. 28, 2331–2336 (1989).
    [CrossRef] [PubMed]
  8. S. Andersson-Engels, R. Berg, A. Persson, S. Svanberg, “Multispectral tissue characterization with time-resolved detection of diffusely scattered white light,” Opt. Lett. 18, 1697–1699 (1993).
    [CrossRef] [PubMed]
  9. C. Abrahamsson, T. Svensson, S. Svanberg, S. Andersson-Engels, J. Johansson, S. Folestad, “Time and wavelength resolved spectroscopy of turbid media using light continuum generated in a crystal fiber,” Opt. Express 12, 4103–4112 (2004).
    [CrossRef] [PubMed]
  10. T. J. Farrell, M. S. Patterson, B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
    [CrossRef] [PubMed]
  11. R. Cubeddu, A. Pifferi, P. Taroni, A. Torricelli, G. Valentini, “Experimental test of theoretical models for time resolved reflectance,” Med. Phys. 23, 1625–1633 (1996).
    [CrossRef] [PubMed]
  12. S. J. Madsen, B. C. Wilson, M. S. Patterson, Y. D. Park, S. L. Jacques, Y. Hefetz, “Experimental tests of a simple diffusion model for the estimation of scattering and absorption coefficients of turbid media from time resolved diffuse reflectance measurements,” Appl. Opt. 31, 3509–3517 (1992).
    [CrossRef] [PubMed]
  13. 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]
  14. J. A. K. Suykens, T. Van Gestel, J. De Brabanter, B. De Moor, J. Vandewalle, Least Squares Support Vector Machines (World Scientific, 2002).
  15. A. I. Belousov, S. A. Verzakov, J. von Frese, “Applicational aspects of support vector machines,” J. Chemom. 16, 482–489 (2002).
    [CrossRef]
  16. R. Goodacre, “Explanatory analysis of spectroscopic data using machine learning of simple, interpretable rules,” Vib. Spectrosc. 32, 33–45 (2003).
    [CrossRef]
  17. F. Chauchard, R. Cogdill, S. Roussel, J. M. Roger, V. Bellon-Maurel, “Application of LS-SVM to non-linear phenomena in NIR spectroscopy: development of a robust and portable sensor for acidity prediction in grapes,” Chemom. Intell. Lab. Syst. 71, 141–150 (2004).
    [CrossRef]
  18. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978).
  19. V. Vapnik, A. Lerner, “Pattern recognition using generalized portrait method,” Autom. Remote Control 24, 774–780 (1963).
  20. R. Cubeddu, C. D’Andrea, A. Pifferi, P. Taroni, A. Torricelli, G. Valentini, C. Dover, D. Johnson, M. Ruiz-Altisent, C. Valero, “Nondestructive quantification of chemical and physical properties of fruits by time-resolved reflectance spectroscopy in the wavelength range 650–1000 nm,” Appl. Opt. 40, 538–543 (2001).
    [CrossRef]
  21. LS SVMs toolbox, www.esat.kuleuven.ac.be/sista/lssumlab/ .

2004

C. Abrahamsson, T. Svensson, S. Svanberg, S. Andersson-Engels, J. Johansson, S. Folestad, “Time and wavelength resolved spectroscopy of turbid media using light continuum generated in a crystal fiber,” Opt. Express 12, 4103–4112 (2004).
[CrossRef] [PubMed]

F. Chauchard, R. Cogdill, S. Roussel, J. M. Roger, V. Bellon-Maurel, “Application of LS-SVM to non-linear phenomena in NIR spectroscopy: development of a robust and portable sensor for acidity prediction in grapes,” Chemom. Intell. Lab. Syst. 71, 141–150 (2004).
[CrossRef]

2003

R. Goodacre, “Explanatory analysis of spectroscopic data using machine learning of simple, interpretable rules,” Vib. Spectrosc. 32, 33–45 (2003).
[CrossRef]

2002

A. I. Belousov, S. A. Verzakov, J. von Frese, “Applicational aspects of support vector machines,” J. Chemom. 16, 482–489 (2002).
[CrossRef]

J. Johansson, S. Folestad, M. Josefson, A. Sparen, C. Abrahamsson, S. Andersson-Engels, S. Svanberg, “Time-resolved NIR/Vis spectroscopy for analysis of solids: pharmaceutical tablets,” Appl. Spectrosc. 56, 725–731 (2002).
[CrossRef]

P. E. Zerbini, M. Grassi, R. Cubeddu, A. Pifferi, A. Torricelli, “Nondestructive detection of brown heart in pears by time-resolved reflectance spectroscopy,” Postharvest Biol. Technol. 25, 87–97 (2002).
[CrossRef]

2001

1999

J. Johansson, R. Berg, A. Pifferi, S. Svanberg, L. Bjorn, “Time-resolved studies of light propagation in Crassula and Phaseolus leaves,” Photochem Photobiol. 69, 242–247 (1999).
[CrossRef]

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]

1996

R. Cubeddu, A. Pifferi, P. Taroni, A. Torricelli, G. Valentini, “Experimental test of theoretical models for time resolved reflectance,” Med. Phys. 23, 1625–1633 (1996).
[CrossRef] [PubMed]

1993

1992

S. J. Madsen, B. C. Wilson, M. S. Patterson, Y. D. Park, S. L. Jacques, Y. Hefetz, “Experimental tests of a simple diffusion model for the estimation of scattering and absorption coefficients of turbid media from time resolved diffuse reflectance measurements,” Appl. Opt. 31, 3509–3517 (1992).
[CrossRef] [PubMed]

T. J. Farrell, M. S. Patterson, B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
[CrossRef] [PubMed]

1990

S. Andersson-Engels, R. Berg, S. Svanberg, O. Jarlman, “Time-resolved transillumination for medical diagnostics,” Opt. Lett 15, 1179–1181 (1990).
[CrossRef] [PubMed]

1989

1988

B. Chance, J. Leigh, H. Miyake, D. Smith, S. Nioka, R. Greenfeld, M. Finander, K. Kaufmann, W. Levy, M. Young, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef]

1963

V. Vapnik, A. Lerner, “Pattern recognition using generalized portrait method,” Autom. Remote Control 24, 774–780 (1963).

Abrahamsson, C.

Andersson-Engels, S.

Bellon-Maurel, V.

F. Chauchard, R. Cogdill, S. Roussel, J. M. Roger, V. Bellon-Maurel, “Application of LS-SVM to non-linear phenomena in NIR spectroscopy: development of a robust and portable sensor for acidity prediction in grapes,” Chemom. Intell. Lab. Syst. 71, 141–150 (2004).
[CrossRef]

Belousov, A. I.

A. I. Belousov, S. A. Verzakov, J. von Frese, “Applicational aspects of support vector machines,” J. Chemom. 16, 482–489 (2002).
[CrossRef]

Berg, R.

J. Johansson, R. Berg, A. Pifferi, S. Svanberg, L. Bjorn, “Time-resolved studies of light propagation in Crassula and Phaseolus leaves,” Photochem Photobiol. 69, 242–247 (1999).
[CrossRef]

S. Andersson-Engels, R. Berg, A. Persson, S. Svanberg, “Multispectral tissue characterization with time-resolved detection of diffusely scattered white light,” Opt. Lett. 18, 1697–1699 (1993).
[CrossRef] [PubMed]

S. Andersson-Engels, R. Berg, S. Svanberg, O. Jarlman, “Time-resolved transillumination for medical diagnostics,” Opt. Lett 15, 1179–1181 (1990).
[CrossRef] [PubMed]

Bjorn, L.

J. Johansson, R. Berg, A. Pifferi, S. Svanberg, L. Bjorn, “Time-resolved studies of light propagation in Crassula and Phaseolus leaves,” Photochem Photobiol. 69, 242–247 (1999).
[CrossRef]

Burns, D. H.

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.

M. S. Patterson, B. Chance, B. C. Wilson, “Time-resolved reflectance and transmittance for the noninvasive measurement of tissue optical properties,” Appl. Opt. 28, 2331–2336 (1989).
[CrossRef] [PubMed]

B. Chance, J. Leigh, H. Miyake, D. Smith, S. Nioka, R. Greenfeld, M. Finander, K. Kaufmann, W. Levy, M. Young, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef]

Chauchard, F.

F. Chauchard, R. Cogdill, S. Roussel, J. M. Roger, V. Bellon-Maurel, “Application of LS-SVM to non-linear phenomena in NIR spectroscopy: development of a robust and portable sensor for acidity prediction in grapes,” Chemom. Intell. Lab. Syst. 71, 141–150 (2004).
[CrossRef]

Cogdill, R.

F. Chauchard, R. Cogdill, S. Roussel, J. M. Roger, V. Bellon-Maurel, “Application of LS-SVM to non-linear phenomena in NIR spectroscopy: development of a robust and portable sensor for acidity prediction in grapes,” Chemom. Intell. Lab. Syst. 71, 141–150 (2004).
[CrossRef]

Cubeddu, R.

P. E. Zerbini, M. Grassi, R. Cubeddu, A. Pifferi, A. Torricelli, “Nondestructive detection of brown heart in pears by time-resolved reflectance spectroscopy,” Postharvest Biol. Technol. 25, 87–97 (2002).
[CrossRef]

R. Cubeddu, C. D’Andrea, A. Pifferi, P. Taroni, A. Torricelli, G. Valentini, C. Dover, D. Johnson, M. Ruiz-Altisent, C. Valero, “Nondestructive quantification of chemical and physical properties of fruits by time-resolved reflectance spectroscopy in the wavelength range 650–1000 nm,” Appl. Opt. 40, 538–543 (2001).
[CrossRef]

R. Cubeddu, A. Pifferi, P. Taroni, A. Torricelli, G. Valentini, “Experimental test of theoretical models for time resolved reflectance,” Med. Phys. 23, 1625–1633 (1996).
[CrossRef] [PubMed]

D’Andrea, C.

De Brabanter, J.

J. A. K. Suykens, T. Van Gestel, J. De Brabanter, B. De Moor, J. Vandewalle, Least Squares Support Vector Machines (World Scientific, 2002).

De Moor, B.

J. A. K. Suykens, T. Van Gestel, J. De Brabanter, B. De Moor, J. Vandewalle, Least Squares Support Vector Machines (World Scientific, 2002).

Dover, C.

Farrell, T. J.

T. J. Farrell, M. S. Patterson, B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
[CrossRef] [PubMed]

Finander, M.

B. Chance, J. Leigh, H. Miyake, D. Smith, S. Nioka, R. Greenfeld, M. Finander, K. Kaufmann, W. Levy, M. Young, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef]

Folestad, S.

Goodacre, R.

R. Goodacre, “Explanatory analysis of spectroscopic data using machine learning of simple, interpretable rules,” Vib. Spectrosc. 32, 33–45 (2003).
[CrossRef]

Grassi, M.

P. E. Zerbini, M. Grassi, R. Cubeddu, A. Pifferi, A. Torricelli, “Nondestructive detection of brown heart in pears by time-resolved reflectance spectroscopy,” Postharvest Biol. Technol. 25, 87–97 (2002).
[CrossRef]

Greenfeld, R.

B. Chance, J. Leigh, H. Miyake, D. Smith, S. Nioka, R. Greenfeld, M. Finander, K. Kaufmann, W. Levy, M. Young, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef]

Hefetz, Y.

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978).

Jacques, S. L.

Jarlman, O.

S. Andersson-Engels, R. Berg, S. Svanberg, O. Jarlman, “Time-resolved transillumination for medical diagnostics,” Opt. Lett 15, 1179–1181 (1990).
[CrossRef] [PubMed]

Johansson, J.

Johnson, D.

Josefson, M.

Kaufmann, K.

B. Chance, J. Leigh, H. Miyake, D. Smith, S. Nioka, R. Greenfeld, M. Finander, K. Kaufmann, W. Levy, M. Young, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef]

Leigh, J.

B. Chance, J. Leigh, H. Miyake, D. Smith, S. Nioka, R. Greenfeld, M. Finander, K. Kaufmann, W. Levy, M. Young, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef]

Leonardi, L.

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]

Lerner, A.

V. Vapnik, A. Lerner, “Pattern recognition using generalized portrait method,” Autom. Remote Control 24, 774–780 (1963).

Levy, W.

B. Chance, J. Leigh, H. Miyake, D. Smith, S. Nioka, R. Greenfeld, M. Finander, K. Kaufmann, W. Levy, M. Young, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef]

Madsen, S. J.

Miyake, H.

B. Chance, J. Leigh, H. Miyake, D. Smith, S. Nioka, R. Greenfeld, M. Finander, K. Kaufmann, W. Levy, M. Young, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef]

Nioka, S.

B. Chance, J. Leigh, H. Miyake, D. Smith, S. Nioka, R. Greenfeld, M. Finander, K. Kaufmann, W. Levy, M. Young, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef]

Park, Y. D.

Patterson, M. S.

Persson, A.

Pifferi, A.

P. E. Zerbini, M. Grassi, R. Cubeddu, A. Pifferi, A. Torricelli, “Nondestructive detection of brown heart in pears by time-resolved reflectance spectroscopy,” Postharvest Biol. Technol. 25, 87–97 (2002).
[CrossRef]

R. Cubeddu, C. D’Andrea, A. Pifferi, P. Taroni, A. Torricelli, G. Valentini, C. Dover, D. Johnson, M. Ruiz-Altisent, C. Valero, “Nondestructive quantification of chemical and physical properties of fruits by time-resolved reflectance spectroscopy in the wavelength range 650–1000 nm,” Appl. Opt. 40, 538–543 (2001).
[CrossRef]

J. Johansson, R. Berg, A. Pifferi, S. Svanberg, L. Bjorn, “Time-resolved studies of light propagation in Crassula and Phaseolus leaves,” Photochem Photobiol. 69, 242–247 (1999).
[CrossRef]

R. Cubeddu, A. Pifferi, P. Taroni, A. Torricelli, G. Valentini, “Experimental test of theoretical models for time resolved reflectance,” Med. Phys. 23, 1625–1633 (1996).
[CrossRef] [PubMed]

Roger, J. M.

F. Chauchard, R. Cogdill, S. Roussel, J. M. Roger, V. Bellon-Maurel, “Application of LS-SVM to non-linear phenomena in NIR spectroscopy: development of a robust and portable sensor for acidity prediction in grapes,” Chemom. Intell. Lab. Syst. 71, 141–150 (2004).
[CrossRef]

Roussel, S.

F. Chauchard, R. Cogdill, S. Roussel, J. M. Roger, V. Bellon-Maurel, “Application of LS-SVM to non-linear phenomena in NIR spectroscopy: development of a robust and portable sensor for acidity prediction in grapes,” Chemom. Intell. Lab. Syst. 71, 141–150 (2004).
[CrossRef]

Ruiz-Altisent, M.

Smith, D.

B. Chance, J. Leigh, H. Miyake, D. Smith, S. Nioka, R. Greenfeld, M. Finander, K. Kaufmann, W. Levy, M. Young, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef]

Sparen, A.

Suykens, J. A. K.

J. A. K. Suykens, T. Van Gestel, J. De Brabanter, B. De Moor, J. Vandewalle, Least Squares Support Vector Machines (World Scientific, 2002).

Svanberg, S.

Svensson, T.

Taroni, P.

Torricelli, A.

P. E. Zerbini, M. Grassi, R. Cubeddu, A. Pifferi, A. Torricelli, “Nondestructive detection of brown heart in pears by time-resolved reflectance spectroscopy,” Postharvest Biol. Technol. 25, 87–97 (2002).
[CrossRef]

R. Cubeddu, C. D’Andrea, A. Pifferi, P. Taroni, A. Torricelli, G. Valentini, C. Dover, D. Johnson, M. Ruiz-Altisent, C. Valero, “Nondestructive quantification of chemical and physical properties of fruits by time-resolved reflectance spectroscopy in the wavelength range 650–1000 nm,” Appl. Opt. 40, 538–543 (2001).
[CrossRef]

R. Cubeddu, A. Pifferi, P. Taroni, A. Torricelli, G. Valentini, “Experimental test of theoretical models for time resolved reflectance,” Med. Phys. 23, 1625–1633 (1996).
[CrossRef] [PubMed]

Valentini, G.

Valero, C.

Van Gestel, T.

J. A. K. Suykens, T. Van Gestel, J. De Brabanter, B. De Moor, J. Vandewalle, Least Squares Support Vector Machines (World Scientific, 2002).

Vandewalle, J.

J. A. K. Suykens, T. Van Gestel, J. De Brabanter, B. De Moor, J. Vandewalle, Least Squares Support Vector Machines (World Scientific, 2002).

Vapnik, V.

V. Vapnik, A. Lerner, “Pattern recognition using generalized portrait method,” Autom. Remote Control 24, 774–780 (1963).

Verzakov, S. A.

A. I. Belousov, S. A. Verzakov, J. von Frese, “Applicational aspects of support vector machines,” J. Chemom. 16, 482–489 (2002).
[CrossRef]

von Frese, J.

A. I. Belousov, S. A. Verzakov, J. von Frese, “Applicational aspects of support vector machines,” J. Chemom. 16, 482–489 (2002).
[CrossRef]

Wilson, B.

T. J. Farrell, M. S. Patterson, B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
[CrossRef] [PubMed]

Wilson, B. C.

Young, M.

B. Chance, J. Leigh, H. Miyake, D. Smith, S. Nioka, R. Greenfeld, M. Finander, K. Kaufmann, W. Levy, M. Young, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef]

Zerbini, P. E.

P. E. Zerbini, M. Grassi, R. Cubeddu, A. Pifferi, A. Torricelli, “Nondestructive detection of brown heart in pears by time-resolved reflectance spectroscopy,” Postharvest Biol. Technol. 25, 87–97 (2002).
[CrossRef]

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).
[CrossRef]

Appl. Opt.

Appl. Spectrosc.

Autom. Remote Control

V. Vapnik, A. Lerner, “Pattern recognition using generalized portrait method,” Autom. Remote Control 24, 774–780 (1963).

Chemom. Intell. Lab. Syst.

F. Chauchard, R. Cogdill, S. Roussel, J. M. Roger, V. Bellon-Maurel, “Application of LS-SVM to non-linear phenomena in NIR spectroscopy: development of a robust and portable sensor for acidity prediction in grapes,” Chemom. Intell. Lab. Syst. 71, 141–150 (2004).
[CrossRef]

J. Chemom.

A. I. Belousov, S. A. Verzakov, J. von Frese, “Applicational aspects of support vector machines,” J. Chemom. 16, 482–489 (2002).
[CrossRef]

Med. Phys.

T. J. Farrell, M. S. Patterson, B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
[CrossRef] [PubMed]

R. Cubeddu, A. Pifferi, P. Taroni, A. Torricelli, G. Valentini, “Experimental test of theoretical models for time resolved reflectance,” Med. Phys. 23, 1625–1633 (1996).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett

S. Andersson-Engels, R. Berg, S. Svanberg, O. Jarlman, “Time-resolved transillumination for medical diagnostics,” Opt. Lett 15, 1179–1181 (1990).
[CrossRef] [PubMed]

Opt. Lett.

Photochem Photobiol.

J. Johansson, R. Berg, A. Pifferi, S. Svanberg, L. Bjorn, “Time-resolved studies of light propagation in Crassula and Phaseolus leaves,” Photochem Photobiol. 69, 242–247 (1999).
[CrossRef]

Postharvest Biol. Technol.

P. E. Zerbini, M. Grassi, R. Cubeddu, A. Pifferi, A. Torricelli, “Nondestructive detection of brown heart in pears by time-resolved reflectance spectroscopy,” Postharvest Biol. Technol. 25, 87–97 (2002).
[CrossRef]

Proc. Natl. Acad. Sci. USA

B. Chance, J. Leigh, H. Miyake, D. Smith, S. Nioka, R. Greenfeld, M. Finander, K. Kaufmann, W. Levy, M. Young, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef]

Vib. Spectrosc.

R. Goodacre, “Explanatory analysis of spectroscopic data using machine learning of simple, interpretable rules,” Vib. Spectrosc. 32, 33–45 (2003).
[CrossRef]

Other

J. A. K. Suykens, T. Van Gestel, J. De Brabanter, B. De Moor, J. Vandewalle, Least Squares Support Vector Machines (World Scientific, 2002).

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978).

LS SVMs toolbox, www.esat.kuleuven.ac.be/sista/lssumlab/ .

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1
Fig. 1

Setup for TRS spectrum acquisition

Fig. 2
Fig. 2

(a) Values of µa and µs for the training set: ★, calibration (A); ●, validation (B) for γ and σ2 parameter tuning. (b) Four theoretical dispersion profiles.

Fig. 3
Fig. 3

Recording of two-dimensional time-resolved measurements: (a) multispectral light pulse for sample irradiation and (b) recorded signal for an apple.

Fig. 4
Fig. 4

Optimization surface for γ and σ2 tuning for µa modelization.

Fig. 5
Fig. 5

Results for µa and µs prediction for an apple at all wavelengths.

Fig. 6
Fig. 6

Measured signal and fitted signals for three wavelengths.

Fig. 7
Fig. 7

Predicted performance of the µa prediction model.

Fig. 8
Fig. 8

Predicted performance of the µs prediction model.

Fig. 9
Fig. 9

Predicted performance of the µs prediction model with a convolution approach.

Fig. 10
Fig. 10

Measured signal and fitted signals with the LS SVM obtained with convolution and determination coefficients: (a) predicted signals for three wavelengths and (b) r2 between curves for each wavelength.

Equations (7)

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

1 c L ( r , s , t ) t + s · L ( r , s , t ) + ( μ s + μ a ) L ( r , s , t ) = μ s 4 π L ( r , s , t ) p ( s , s ) d ω + Q ( r , s , t ) .
R ( ρ , t ) = ( 4 π D ν ) 3 / 2 z 0 t 5 / 2 exp ( μ a ν t ) × exp ( ρ 2 + z 0 2 4 D ν t ) .
K = ( k 1 , 1 k 1 , n k n , 1 k n , n ) .
k i , j = exp ( x i T x j T 2 σ 2 ) ,
ŷ = K β + β 0 ,
min ( e ) = min [ i = 1 n ( y i ŷ i ) 2 2 + 1 γ ( β T β ) 2 ] ,
[ 0 l n T l n K + I γ ] [ b ̂ 0 b ̂ ] = [ 0 y ] ,

Metrics