Abstract

We address an original statistical method for unsupervised identification and concentration estimation of spectrally interfering gas components of unknown nature and number. We show that such spectral unmixing can be efficiently achieved using information criteria derived from the Minimum Description Length (MDL) principle, outperforming standard information criteria such as AICc or BIC. In the context of spectroscopic applications, we also show that the most efficient MDL technique implemented shows good robustness to experimental artifacts.

© 2011 OSA

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  1. P. Weibring, C. Abrahamsson, M. Sjholm, J. N. Smith, H. Edner, and S. Svanberg, “Multi-component chemical analysis of gas mixtures using a continuously tuneable lidar system,” Appl. Phys. B 79, 525–530 (2004).
    [CrossRef]
  2. J. R. Quagliano, P. O. Stoutland, R. R. Petrin, R. K. Sander, R. J. Romero, M. C. Whitehead, C. R. Quick, J. J. Tiee, and L. J. Jolin, “Quantitative chemical identification of four gases in remote infrared (9–11μm) differential absorption lidar experiments,” Appl. Opt. 36, 1915–1927 (1997).
    [CrossRef] [PubMed]
  3. G. Wysocki, R. Lewicki, R. Curl, F. Tittel, L. Diehl, F. Capasso, M. Troccoli, G. Hofler, D. Bour, S. Corzine, R. Maulini, M. Giovannini, and J. Faist, “Widely tunable mode-hop free external cavity quantum cascade lasers for high resolution spectroscopy and chemical sensing,” Appl. Phys. B 92, 305–311 (2008).
    [CrossRef]
  4. U. Platt and J. Stutz, Differential Optical Absorption Spectroscopy (Springer, 2008).
  5. R. A. Hashmonay, R. M. Varma, M. Modrak, R. H. Kagann, and P. D. Sullivan, “Simultaneous measurement of vaporous and aerosolized threats by active open path FTIR,” Unclassified Technical Report ADA449529, Arcadis Geraghty and Miller Research, Triangle Park, NC (2004).
  6. J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. André, A. Mysyrowicz, R. Sauerbrey, J. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
    [CrossRef] [PubMed]
  7. D. M. Brown, K. Shi, Z. Liu, and C. R. Philbrick, “Long-path supercontinuum absorption spectroscopy for measurement of atmospheric constituents,” Opt. Express 16, 8457–8471 (2008).
    [CrossRef] [PubMed]
  8. P. S. Edwards, A. M. Wyant, D. M. Brown, Z. Liu, and C. R. Philbrick, “Supercontinuum laser sensing of atmospheric constituents,” Proc. SPIE 7323, 73230S (2009).
    [CrossRef]
  9. E. R. Warren, “Optimum detection of multiple vapor materials with frequency-agile lidar,” Appl. Opt. 35, 4180–4193 (1996).
    [CrossRef] [PubMed]
  10. S. Yin and W. Wang, “Novel algorithm for simultaneously detecting multiple vapor materials with multiple-wavelength differential absorption lidar,” Chin. Opt. Lett. 4, 360–363 (2006).
  11. J. Fade and N. Cézard, “Supercontinuum lidar absorption spectroscopy for gas detection and concentration estimation,” in Proceedings of the 25th International Laser and Remote-sensing Conference , (2010), pp. 798–801.
  12. J. Rissanen, Information and Complexity in Statistical Modeling (Springer, 2007).
  13. R. A. Stine, “Model selection using information theory and the MDL principle,” Sociolog. Methods Res. 33, 230–260 (2004).
    [CrossRef]
  14. C. D. Giurcaneanu, “Stochastic complexity for the detection of periodically expressed genes,” in Proceedings of the IEEE International Workshop on Genomic Signal Processing and Statistics , (2007), pp. 1–4.
    [CrossRef]
  15. H. Chen, T. Kirubarajan, Y. Bar-Shalom, and K. R. Pattipati, “MDL approach for multiple low-observable track initiation,” Proc. SPIE 4728, 477–488 (2002).
    [CrossRef]
  16. M. Hansen and B. Yu, “Model selection and the principle of minimum description length,” J. Am. Stat. Assoc. 96, 746–774 (2001).
    [CrossRef]
  17. C. L. Mallows, “Some comments on cp,” Technometrics 15, 661–675 (1973).
    [CrossRef]
  18. H. Akaike, “A new look at the statistical model identification,” IEEE Trans. Autom. Control 19, 716–723 (1974).
    [CrossRef]
  19. G. Schwartz, “Estimating the dimension of a model,” Ann. Stat. 9, 461–464 (1978).
    [CrossRef]
  20. D. P. Foster and E. I. G., “The risk inflation criterion for multiple regression,” Ann. Stat. 22, 1947–1975 (1994).
    [CrossRef]
  21. J. Rissanen, Stochastic Complexity in Statistical Inquiry, Series in Computer Science (World Scientific, 1989), Vol. 15.
  22. J. Rissanen, “Fisher information and stochastic complexity,” IEEE Trans. Inf. Theory 42, 48–54 (1996).
    [CrossRef]
  23. M. Duhant, W. Renard, G. Canat, F. Smektala, J. Troles, P. Bourdon, and C. Planchat, “Improving mid-infrared supercontinuum generation efficiency by pumping a fluoride fiber directly into the anomalous regime at 1995 nm,” in CLEO/Europe and EQEC 2011 Conference Digest, (2011), p. CD9_1. (to be published)
  24. A. Berrou, M. Raybaut, A. Godard, and M. Lefebvre, “High-resolution photoacoustic and direct absorption spectroscopy of main greenhouse gases by use of a pulsed entangled cavity doubly resonant OPO,” Appl. Phys. B 98, 217–230 (2010).
    [CrossRef]
  25. R. Tibshirani, “Regression shrinkage and selection via the lasso,” J. R. Stat. Soc. Ser. B 58, 267–288 (1996).
  26. E. J. Candès and Y. Plan, “Near-ideal model selection by ℓ1 minimization,” Ann. Stat. 37, 2145–2177 (2009).
    [CrossRef]

2010 (1)

A. Berrou, M. Raybaut, A. Godard, and M. Lefebvre, “High-resolution photoacoustic and direct absorption spectroscopy of main greenhouse gases by use of a pulsed entangled cavity doubly resonant OPO,” Appl. Phys. B 98, 217–230 (2010).
[CrossRef]

2009 (2)

P. S. Edwards, A. M. Wyant, D. M. Brown, Z. Liu, and C. R. Philbrick, “Supercontinuum laser sensing of atmospheric constituents,” Proc. SPIE 7323, 73230S (2009).
[CrossRef]

E. J. Candès and Y. Plan, “Near-ideal model selection by ℓ1 minimization,” Ann. Stat. 37, 2145–2177 (2009).
[CrossRef]

2008 (3)

D. M. Brown, K. Shi, Z. Liu, and C. R. Philbrick, “Long-path supercontinuum absorption spectroscopy for measurement of atmospheric constituents,” Opt. Express 16, 8457–8471 (2008).
[CrossRef] [PubMed]

G. Wysocki, R. Lewicki, R. Curl, F. Tittel, L. Diehl, F. Capasso, M. Troccoli, G. Hofler, D. Bour, S. Corzine, R. Maulini, M. Giovannini, and J. Faist, “Widely tunable mode-hop free external cavity quantum cascade lasers for high resolution spectroscopy and chemical sensing,” Appl. Phys. B 92, 305–311 (2008).
[CrossRef]

U. Platt and J. Stutz, Differential Optical Absorption Spectroscopy (Springer, 2008).

2007 (1)

J. Rissanen, Information and Complexity in Statistical Modeling (Springer, 2007).

2006 (1)

2004 (3)

R. A. Stine, “Model selection using information theory and the MDL principle,” Sociolog. Methods Res. 33, 230–260 (2004).
[CrossRef]

R. A. Hashmonay, R. M. Varma, M. Modrak, R. H. Kagann, and P. D. Sullivan, “Simultaneous measurement of vaporous and aerosolized threats by active open path FTIR,” Unclassified Technical Report ADA449529, Arcadis Geraghty and Miller Research, Triangle Park, NC (2004).

P. Weibring, C. Abrahamsson, M. Sjholm, J. N. Smith, H. Edner, and S. Svanberg, “Multi-component chemical analysis of gas mixtures using a continuously tuneable lidar system,” Appl. Phys. B 79, 525–530 (2004).
[CrossRef]

2003 (1)

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. André, A. Mysyrowicz, R. Sauerbrey, J. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[CrossRef] [PubMed]

2002 (1)

H. Chen, T. Kirubarajan, Y. Bar-Shalom, and K. R. Pattipati, “MDL approach for multiple low-observable track initiation,” Proc. SPIE 4728, 477–488 (2002).
[CrossRef]

2001 (1)

M. Hansen and B. Yu, “Model selection and the principle of minimum description length,” J. Am. Stat. Assoc. 96, 746–774 (2001).
[CrossRef]

1997 (1)

1996 (3)

E. R. Warren, “Optimum detection of multiple vapor materials with frequency-agile lidar,” Appl. Opt. 35, 4180–4193 (1996).
[CrossRef] [PubMed]

R. Tibshirani, “Regression shrinkage and selection via the lasso,” J. R. Stat. Soc. Ser. B 58, 267–288 (1996).

J. Rissanen, “Fisher information and stochastic complexity,” IEEE Trans. Inf. Theory 42, 48–54 (1996).
[CrossRef]

1994 (1)

D. P. Foster and E. I. G., “The risk inflation criterion for multiple regression,” Ann. Stat. 22, 1947–1975 (1994).
[CrossRef]

1989 (1)

J. Rissanen, Stochastic Complexity in Statistical Inquiry, Series in Computer Science (World Scientific, 1989), Vol. 15.

1978 (1)

G. Schwartz, “Estimating the dimension of a model,” Ann. Stat. 9, 461–464 (1978).
[CrossRef]

1974 (1)

H. Akaike, “A new look at the statistical model identification,” IEEE Trans. Autom. Control 19, 716–723 (1974).
[CrossRef]

1973 (1)

C. L. Mallows, “Some comments on cp,” Technometrics 15, 661–675 (1973).
[CrossRef]

Abrahamsson, C.

P. Weibring, C. Abrahamsson, M. Sjholm, J. N. Smith, H. Edner, and S. Svanberg, “Multi-component chemical analysis of gas mixtures using a continuously tuneable lidar system,” Appl. Phys. B 79, 525–530 (2004).
[CrossRef]

Akaike, H.

H. Akaike, “A new look at the statistical model identification,” IEEE Trans. Autom. Control 19, 716–723 (1974).
[CrossRef]

André, Y.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. André, A. Mysyrowicz, R. Sauerbrey, J. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[CrossRef] [PubMed]

Bar-Shalom, Y.

H. Chen, T. Kirubarajan, Y. Bar-Shalom, and K. R. Pattipati, “MDL approach for multiple low-observable track initiation,” Proc. SPIE 4728, 477–488 (2002).
[CrossRef]

Berrou, A.

A. Berrou, M. Raybaut, A. Godard, and M. Lefebvre, “High-resolution photoacoustic and direct absorption spectroscopy of main greenhouse gases by use of a pulsed entangled cavity doubly resonant OPO,” Appl. Phys. B 98, 217–230 (2010).
[CrossRef]

Bour, D.

G. Wysocki, R. Lewicki, R. Curl, F. Tittel, L. Diehl, F. Capasso, M. Troccoli, G. Hofler, D. Bour, S. Corzine, R. Maulini, M. Giovannini, and J. Faist, “Widely tunable mode-hop free external cavity quantum cascade lasers for high resolution spectroscopy and chemical sensing,” Appl. Phys. B 92, 305–311 (2008).
[CrossRef]

Bourayou, R.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. André, A. Mysyrowicz, R. Sauerbrey, J. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[CrossRef] [PubMed]

Brown, D. M.

P. S. Edwards, A. M. Wyant, D. M. Brown, Z. Liu, and C. R. Philbrick, “Supercontinuum laser sensing of atmospheric constituents,” Proc. SPIE 7323, 73230S (2009).
[CrossRef]

D. M. Brown, K. Shi, Z. Liu, and C. R. Philbrick, “Long-path supercontinuum absorption spectroscopy for measurement of atmospheric constituents,” Opt. Express 16, 8457–8471 (2008).
[CrossRef] [PubMed]

Candès, E. J.

E. J. Candès and Y. Plan, “Near-ideal model selection by ℓ1 minimization,” Ann. Stat. 37, 2145–2177 (2009).
[CrossRef]

Capasso, F.

G. Wysocki, R. Lewicki, R. Curl, F. Tittel, L. Diehl, F. Capasso, M. Troccoli, G. Hofler, D. Bour, S. Corzine, R. Maulini, M. Giovannini, and J. Faist, “Widely tunable mode-hop free external cavity quantum cascade lasers for high resolution spectroscopy and chemical sensing,” Appl. Phys. B 92, 305–311 (2008).
[CrossRef]

Chen, H.

H. Chen, T. Kirubarajan, Y. Bar-Shalom, and K. R. Pattipati, “MDL approach for multiple low-observable track initiation,” Proc. SPIE 4728, 477–488 (2002).
[CrossRef]

Corzine, S.

G. Wysocki, R. Lewicki, R. Curl, F. Tittel, L. Diehl, F. Capasso, M. Troccoli, G. Hofler, D. Bour, S. Corzine, R. Maulini, M. Giovannini, and J. Faist, “Widely tunable mode-hop free external cavity quantum cascade lasers for high resolution spectroscopy and chemical sensing,” Appl. Phys. B 92, 305–311 (2008).
[CrossRef]

Curl, R.

G. Wysocki, R. Lewicki, R. Curl, F. Tittel, L. Diehl, F. Capasso, M. Troccoli, G. Hofler, D. Bour, S. Corzine, R. Maulini, M. Giovannini, and J. Faist, “Widely tunable mode-hop free external cavity quantum cascade lasers for high resolution spectroscopy and chemical sensing,” Appl. Phys. B 92, 305–311 (2008).
[CrossRef]

Diehl, L.

G. Wysocki, R. Lewicki, R. Curl, F. Tittel, L. Diehl, F. Capasso, M. Troccoli, G. Hofler, D. Bour, S. Corzine, R. Maulini, M. Giovannini, and J. Faist, “Widely tunable mode-hop free external cavity quantum cascade lasers for high resolution spectroscopy and chemical sensing,” Appl. Phys. B 92, 305–311 (2008).
[CrossRef]

E. I. G.,

D. P. Foster and E. I. G., “The risk inflation criterion for multiple regression,” Ann. Stat. 22, 1947–1975 (1994).
[CrossRef]

Edner, H.

P. Weibring, C. Abrahamsson, M. Sjholm, J. N. Smith, H. Edner, and S. Svanberg, “Multi-component chemical analysis of gas mixtures using a continuously tuneable lidar system,” Appl. Phys. B 79, 525–530 (2004).
[CrossRef]

Edwards, P. S.

P. S. Edwards, A. M. Wyant, D. M. Brown, Z. Liu, and C. R. Philbrick, “Supercontinuum laser sensing of atmospheric constituents,” Proc. SPIE 7323, 73230S (2009).
[CrossRef]

Faist, J.

G. Wysocki, R. Lewicki, R. Curl, F. Tittel, L. Diehl, F. Capasso, M. Troccoli, G. Hofler, D. Bour, S. Corzine, R. Maulini, M. Giovannini, and J. Faist, “Widely tunable mode-hop free external cavity quantum cascade lasers for high resolution spectroscopy and chemical sensing,” Appl. Phys. B 92, 305–311 (2008).
[CrossRef]

Foster, D. P.

D. P. Foster and E. I. G., “The risk inflation criterion for multiple regression,” Ann. Stat. 22, 1947–1975 (1994).
[CrossRef]

Frey, S.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. André, A. Mysyrowicz, R. Sauerbrey, J. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[CrossRef] [PubMed]

Giovannini, M.

G. Wysocki, R. Lewicki, R. Curl, F. Tittel, L. Diehl, F. Capasso, M. Troccoli, G. Hofler, D. Bour, S. Corzine, R. Maulini, M. Giovannini, and J. Faist, “Widely tunable mode-hop free external cavity quantum cascade lasers for high resolution spectroscopy and chemical sensing,” Appl. Phys. B 92, 305–311 (2008).
[CrossRef]

Godard, A.

A. Berrou, M. Raybaut, A. Godard, and M. Lefebvre, “High-resolution photoacoustic and direct absorption spectroscopy of main greenhouse gases by use of a pulsed entangled cavity doubly resonant OPO,” Appl. Phys. B 98, 217–230 (2010).
[CrossRef]

Hansen, M.

M. Hansen and B. Yu, “Model selection and the principle of minimum description length,” J. Am. Stat. Assoc. 96, 746–774 (2001).
[CrossRef]

Hashmonay, R. A.

R. A. Hashmonay, R. M. Varma, M. Modrak, R. H. Kagann, and P. D. Sullivan, “Simultaneous measurement of vaporous and aerosolized threats by active open path FTIR,” Unclassified Technical Report ADA449529, Arcadis Geraghty and Miller Research, Triangle Park, NC (2004).

Hofler, G.

G. Wysocki, R. Lewicki, R. Curl, F. Tittel, L. Diehl, F. Capasso, M. Troccoli, G. Hofler, D. Bour, S. Corzine, R. Maulini, M. Giovannini, and J. Faist, “Widely tunable mode-hop free external cavity quantum cascade lasers for high resolution spectroscopy and chemical sensing,” Appl. Phys. B 92, 305–311 (2008).
[CrossRef]

Jolin, L. J.

Kagann, R. H.

R. A. Hashmonay, R. M. Varma, M. Modrak, R. H. Kagann, and P. D. Sullivan, “Simultaneous measurement of vaporous and aerosolized threats by active open path FTIR,” Unclassified Technical Report ADA449529, Arcadis Geraghty and Miller Research, Triangle Park, NC (2004).

Kasparian, J.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. André, A. Mysyrowicz, R. Sauerbrey, J. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[CrossRef] [PubMed]

Kirubarajan, T.

H. Chen, T. Kirubarajan, Y. Bar-Shalom, and K. R. Pattipati, “MDL approach for multiple low-observable track initiation,” Proc. SPIE 4728, 477–488 (2002).
[CrossRef]

Lefebvre, M.

A. Berrou, M. Raybaut, A. Godard, and M. Lefebvre, “High-resolution photoacoustic and direct absorption spectroscopy of main greenhouse gases by use of a pulsed entangled cavity doubly resonant OPO,” Appl. Phys. B 98, 217–230 (2010).
[CrossRef]

Lewicki, R.

G. Wysocki, R. Lewicki, R. Curl, F. Tittel, L. Diehl, F. Capasso, M. Troccoli, G. Hofler, D. Bour, S. Corzine, R. Maulini, M. Giovannini, and J. Faist, “Widely tunable mode-hop free external cavity quantum cascade lasers for high resolution spectroscopy and chemical sensing,” Appl. Phys. B 92, 305–311 (2008).
[CrossRef]

Liu, Z.

P. S. Edwards, A. M. Wyant, D. M. Brown, Z. Liu, and C. R. Philbrick, “Supercontinuum laser sensing of atmospheric constituents,” Proc. SPIE 7323, 73230S (2009).
[CrossRef]

D. M. Brown, K. Shi, Z. Liu, and C. R. Philbrick, “Long-path supercontinuum absorption spectroscopy for measurement of atmospheric constituents,” Opt. Express 16, 8457–8471 (2008).
[CrossRef] [PubMed]

Mallows, C. L.

C. L. Mallows, “Some comments on cp,” Technometrics 15, 661–675 (1973).
[CrossRef]

Maulini, R.

G. Wysocki, R. Lewicki, R. Curl, F. Tittel, L. Diehl, F. Capasso, M. Troccoli, G. Hofler, D. Bour, S. Corzine, R. Maulini, M. Giovannini, and J. Faist, “Widely tunable mode-hop free external cavity quantum cascade lasers for high resolution spectroscopy and chemical sensing,” Appl. Phys. B 92, 305–311 (2008).
[CrossRef]

Méjean, G.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. André, A. Mysyrowicz, R. Sauerbrey, J. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[CrossRef] [PubMed]

Modrak, M.

R. A. Hashmonay, R. M. Varma, M. Modrak, R. H. Kagann, and P. D. Sullivan, “Simultaneous measurement of vaporous and aerosolized threats by active open path FTIR,” Unclassified Technical Report ADA449529, Arcadis Geraghty and Miller Research, Triangle Park, NC (2004).

Mysyrowicz, A.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. André, A. Mysyrowicz, R. Sauerbrey, J. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[CrossRef] [PubMed]

Pattipati, K. R.

H. Chen, T. Kirubarajan, Y. Bar-Shalom, and K. R. Pattipati, “MDL approach for multiple low-observable track initiation,” Proc. SPIE 4728, 477–488 (2002).
[CrossRef]

Petrin, R. R.

Philbrick, C. R.

P. S. Edwards, A. M. Wyant, D. M. Brown, Z. Liu, and C. R. Philbrick, “Supercontinuum laser sensing of atmospheric constituents,” Proc. SPIE 7323, 73230S (2009).
[CrossRef]

D. M. Brown, K. Shi, Z. Liu, and C. R. Philbrick, “Long-path supercontinuum absorption spectroscopy for measurement of atmospheric constituents,” Opt. Express 16, 8457–8471 (2008).
[CrossRef] [PubMed]

Plan, Y.

E. J. Candès and Y. Plan, “Near-ideal model selection by ℓ1 minimization,” Ann. Stat. 37, 2145–2177 (2009).
[CrossRef]

Platt, U.

U. Platt and J. Stutz, Differential Optical Absorption Spectroscopy (Springer, 2008).

Quagliano, J. R.

Quick, C. R.

Raybaut, M.

A. Berrou, M. Raybaut, A. Godard, and M. Lefebvre, “High-resolution photoacoustic and direct absorption spectroscopy of main greenhouse gases by use of a pulsed entangled cavity doubly resonant OPO,” Appl. Phys. B 98, 217–230 (2010).
[CrossRef]

Rissanen, J.

J. Rissanen, Information and Complexity in Statistical Modeling (Springer, 2007).

J. Rissanen, “Fisher information and stochastic complexity,” IEEE Trans. Inf. Theory 42, 48–54 (1996).
[CrossRef]

J. Rissanen, Stochastic Complexity in Statistical Inquiry, Series in Computer Science (World Scientific, 1989), Vol. 15.

Rodriguez, M.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. André, A. Mysyrowicz, R. Sauerbrey, J. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[CrossRef] [PubMed]

Romero, R. J.

Salmon, E.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. André, A. Mysyrowicz, R. Sauerbrey, J. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[CrossRef] [PubMed]

Sander, R. K.

Sauerbrey, R.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. André, A. Mysyrowicz, R. Sauerbrey, J. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[CrossRef] [PubMed]

Schwartz, G.

G. Schwartz, “Estimating the dimension of a model,” Ann. Stat. 9, 461–464 (1978).
[CrossRef]

Shi, K.

Sjholm, M.

P. Weibring, C. Abrahamsson, M. Sjholm, J. N. Smith, H. Edner, and S. Svanberg, “Multi-component chemical analysis of gas mixtures using a continuously tuneable lidar system,” Appl. Phys. B 79, 525–530 (2004).
[CrossRef]

Smith, J. N.

P. Weibring, C. Abrahamsson, M. Sjholm, J. N. Smith, H. Edner, and S. Svanberg, “Multi-component chemical analysis of gas mixtures using a continuously tuneable lidar system,” Appl. Phys. B 79, 525–530 (2004).
[CrossRef]

Stine, R. A.

R. A. Stine, “Model selection using information theory and the MDL principle,” Sociolog. Methods Res. 33, 230–260 (2004).
[CrossRef]

Stoutland, P. O.

Stutz, J.

U. Platt and J. Stutz, Differential Optical Absorption Spectroscopy (Springer, 2008).

Sullivan, P. D.

R. A. Hashmonay, R. M. Varma, M. Modrak, R. H. Kagann, and P. D. Sullivan, “Simultaneous measurement of vaporous and aerosolized threats by active open path FTIR,” Unclassified Technical Report ADA449529, Arcadis Geraghty and Miller Research, Triangle Park, NC (2004).

Svanberg, S.

P. Weibring, C. Abrahamsson, M. Sjholm, J. N. Smith, H. Edner, and S. Svanberg, “Multi-component chemical analysis of gas mixtures using a continuously tuneable lidar system,” Appl. Phys. B 79, 525–530 (2004).
[CrossRef]

Tibshirani, R.

R. Tibshirani, “Regression shrinkage and selection via the lasso,” J. R. Stat. Soc. Ser. B 58, 267–288 (1996).

Tiee, J. J.

Tittel, F.

G. Wysocki, R. Lewicki, R. Curl, F. Tittel, L. Diehl, F. Capasso, M. Troccoli, G. Hofler, D. Bour, S. Corzine, R. Maulini, M. Giovannini, and J. Faist, “Widely tunable mode-hop free external cavity quantum cascade lasers for high resolution spectroscopy and chemical sensing,” Appl. Phys. B 92, 305–311 (2008).
[CrossRef]

Troccoli, M.

G. Wysocki, R. Lewicki, R. Curl, F. Tittel, L. Diehl, F. Capasso, M. Troccoli, G. Hofler, D. Bour, S. Corzine, R. Maulini, M. Giovannini, and J. Faist, “Widely tunable mode-hop free external cavity quantum cascade lasers for high resolution spectroscopy and chemical sensing,” Appl. Phys. B 92, 305–311 (2008).
[CrossRef]

Varma, R. M.

R. A. Hashmonay, R. M. Varma, M. Modrak, R. H. Kagann, and P. D. Sullivan, “Simultaneous measurement of vaporous and aerosolized threats by active open path FTIR,” Unclassified Technical Report ADA449529, Arcadis Geraghty and Miller Research, Triangle Park, NC (2004).

Wang, W.

Warren, E. R.

Weibring, P.

P. Weibring, C. Abrahamsson, M. Sjholm, J. N. Smith, H. Edner, and S. Svanberg, “Multi-component chemical analysis of gas mixtures using a continuously tuneable lidar system,” Appl. Phys. B 79, 525–530 (2004).
[CrossRef]

Whitehead, M. C.

Wille, H.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. André, A. Mysyrowicz, R. Sauerbrey, J. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[CrossRef] [PubMed]

Wolf, J.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. André, A. Mysyrowicz, R. Sauerbrey, J. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[CrossRef] [PubMed]

Wöste, L.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. André, A. Mysyrowicz, R. Sauerbrey, J. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[CrossRef] [PubMed]

Wyant, A. M.

P. S. Edwards, A. M. Wyant, D. M. Brown, Z. Liu, and C. R. Philbrick, “Supercontinuum laser sensing of atmospheric constituents,” Proc. SPIE 7323, 73230S (2009).
[CrossRef]

Wysocki, G.

G. Wysocki, R. Lewicki, R. Curl, F. Tittel, L. Diehl, F. Capasso, M. Troccoli, G. Hofler, D. Bour, S. Corzine, R. Maulini, M. Giovannini, and J. Faist, “Widely tunable mode-hop free external cavity quantum cascade lasers for high resolution spectroscopy and chemical sensing,” Appl. Phys. B 92, 305–311 (2008).
[CrossRef]

Yin, S.

Yu, B.

M. Hansen and B. Yu, “Model selection and the principle of minimum description length,” J. Am. Stat. Assoc. 96, 746–774 (2001).
[CrossRef]

Yu, J.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. André, A. Mysyrowicz, R. Sauerbrey, J. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[CrossRef] [PubMed]

Ann. Stat. (3)

G. Schwartz, “Estimating the dimension of a model,” Ann. Stat. 9, 461–464 (1978).
[CrossRef]

D. P. Foster and E. I. G., “The risk inflation criterion for multiple regression,” Ann. Stat. 22, 1947–1975 (1994).
[CrossRef]

E. J. Candès and Y. Plan, “Near-ideal model selection by ℓ1 minimization,” Ann. Stat. 37, 2145–2177 (2009).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. B (3)

G. Wysocki, R. Lewicki, R. Curl, F. Tittel, L. Diehl, F. Capasso, M. Troccoli, G. Hofler, D. Bour, S. Corzine, R. Maulini, M. Giovannini, and J. Faist, “Widely tunable mode-hop free external cavity quantum cascade lasers for high resolution spectroscopy and chemical sensing,” Appl. Phys. B 92, 305–311 (2008).
[CrossRef]

P. Weibring, C. Abrahamsson, M. Sjholm, J. N. Smith, H. Edner, and S. Svanberg, “Multi-component chemical analysis of gas mixtures using a continuously tuneable lidar system,” Appl. Phys. B 79, 525–530 (2004).
[CrossRef]

A. Berrou, M. Raybaut, A. Godard, and M. Lefebvre, “High-resolution photoacoustic and direct absorption spectroscopy of main greenhouse gases by use of a pulsed entangled cavity doubly resonant OPO,” Appl. Phys. B 98, 217–230 (2010).
[CrossRef]

Chin. Opt. Lett. (1)

IEEE Trans. Autom. Control (1)

H. Akaike, “A new look at the statistical model identification,” IEEE Trans. Autom. Control 19, 716–723 (1974).
[CrossRef]

IEEE Trans. Inf. Theory (1)

J. Rissanen, “Fisher information and stochastic complexity,” IEEE Trans. Inf. Theory 42, 48–54 (1996).
[CrossRef]

J. Am. Stat. Assoc. (1)

M. Hansen and B. Yu, “Model selection and the principle of minimum description length,” J. Am. Stat. Assoc. 96, 746–774 (2001).
[CrossRef]

J. R. Stat. Soc. Ser. B (1)

R. Tibshirani, “Regression shrinkage and selection via the lasso,” J. R. Stat. Soc. Ser. B 58, 267–288 (1996).

Opt. Express (1)

Proc. SPIE (1)

H. Chen, T. Kirubarajan, Y. Bar-Shalom, and K. R. Pattipati, “MDL approach for multiple low-observable track initiation,” Proc. SPIE 4728, 477–488 (2002).
[CrossRef]

Proc. SPIE (1)

P. S. Edwards, A. M. Wyant, D. M. Brown, Z. Liu, and C. R. Philbrick, “Supercontinuum laser sensing of atmospheric constituents,” Proc. SPIE 7323, 73230S (2009).
[CrossRef]

Science (1)

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. André, A. Mysyrowicz, R. Sauerbrey, J. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[CrossRef] [PubMed]

Sociolog. Methods Res. (1)

R. A. Stine, “Model selection using information theory and the MDL principle,” Sociolog. Methods Res. 33, 230–260 (2004).
[CrossRef]

Technometrics (1)

C. L. Mallows, “Some comments on cp,” Technometrics 15, 661–675 (1973).
[CrossRef]

Other (7)

C. D. Giurcaneanu, “Stochastic complexity for the detection of periodically expressed genes,” in Proceedings of the IEEE International Workshop on Genomic Signal Processing and Statistics , (2007), pp. 1–4.
[CrossRef]

J. Fade and N. Cézard, “Supercontinuum lidar absorption spectroscopy for gas detection and concentration estimation,” in Proceedings of the 25th International Laser and Remote-sensing Conference , (2010), pp. 798–801.

J. Rissanen, Information and Complexity in Statistical Modeling (Springer, 2007).

U. Platt and J. Stutz, Differential Optical Absorption Spectroscopy (Springer, 2008).

R. A. Hashmonay, R. M. Varma, M. Modrak, R. H. Kagann, and P. D. Sullivan, “Simultaneous measurement of vaporous and aerosolized threats by active open path FTIR,” Unclassified Technical Report ADA449529, Arcadis Geraghty and Miller Research, Triangle Park, NC (2004).

J. Rissanen, Stochastic Complexity in Statistical Inquiry, Series in Computer Science (World Scientific, 1989), Vol. 15.

M. Duhant, W. Renard, G. Canat, F. Smektala, J. Troles, P. Bourdon, and C. Planchat, “Improving mid-infrared supercontinuum generation efficiency by pumping a fluoride fiber directly into the anomalous regime at 1995 nm,” in CLEO/Europe and EQEC 2011 Conference Digest, (2011), p. CD9_1. (to be published)

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Figures (4)

Fig. 1
Fig. 1

Illustration of an absorption spectroscopy experiment using an active broadband illumination or tunable laser source.

Fig. 2
Fig. 2

(a) Example of simulated noisy data with S-SNR=6.3 dB (blue curve) superimposed with the true spectrum (black curve) and baseline (green dashed curve). (b)–(f) Comparison of the reconstructed signal after various steps of nMDL-based stepwise model selection (red dotted curve) with the true spectrum (black curve).

Fig. 3
Fig. 3

Absorption spectra of the 4 gas components present in the mixture (red curves) and of 4 other chemicals of the spectral database (black and green curves) with resolution 2.3 nm. The green curve corresponds to the absorption spectrum of HCl, which is used in section 3.4 to simulate anomalous measurements (outliers).

Fig. 4
Fig. 4

Histograms of the number of regressors selected by AICc, BIC, gMDL and nMDL criteria for S-SNR=6.3 dB, (a): with a 4-components gas mixture; (b): without gas mixture.

Tables (3)

Tables Icon

Table 1 Percentage of Correct Models Selected by Stepwise Algorithm with Four Information Criteria (AICc, BIC, gMDL, nMDL) and for Various Values of SNR

Tables Icon

Table 2 Percentage of Correct Models Selected by Stepwise Algorithm Implementing Positivity Constraint on Regression Coefficients (i.e., on Gas Components Concentrations)

Tables Icon

Table 3 Percentage of Correct Models Selected by Stepwise Algorithm with S-SNR=6.3 dB for Varying Proportion of Measurement Outliers

Equations (12)

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X = ( a 0 u e H u c ) * g ,
X = a 0 e Hc ,
= ln X ˜ = b 0 H c + n ,
( | H ) = ln P ( | H ) = M 2 ln RSS + ct ,
𝒞 ( a ) = M 2 1 + K / M 1 ( K + 2 ) / M .
𝒞 ( b ) = K 2 ln M .
min { M 2 ln RSS + 𝒞 ( g ) if  F > 1 M 2 ln ( b 0 ) T ( b 0 ) otherwise ,
𝒞 ( g ) = K 2 ln F + M 2 ln M M K .
𝒞 ( n ) = M 2 ln 2 π M + 1 2 ln M 2 + ln ln b a .
𝒞 ( n ) = K 2 ln F + 1 2 ln K ( M K ) + K 2 ln M + M 2 ln 2 π M K + 2 ln ln b a ln 2 + c ,
c = min { K max , [ ln K ! ( K max K ) ! K max ! + ln K + log 2 ln ( e K max ) ] }
S - SNR  = 1 M ( b 0 - Y ) T ( b 0 - Y ) σ = 1 M c T H T Hc σ .

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