Abstract

A modified algorithm of background removal based on wavelet transform was developed for spectrum correction in laser-induced breakdown spectroscopy (LIBS). The optimal type of wavelet function, decomposition level and scaling factor γ were determined by the root-mean-square error of calibration (RMSEC) of the univariate regression model of the analysis element, which is considered as the optimization criteria. After background removal by this modified algorithm with RMSEC, the root-mean-square error of cross-validation (RMSECV) and the average relative error (ARE) criteria, the accuracy of quantitative analysis on chromium (Cr), vanadium (V), cuprum (Cu), and manganese (Mn) in the low alloy steel was all improved significantly. The results demonstrated that the algorithm developed is an effective pretreatment method in LIBS to significantly improve the accuracy in the quantitative analysis.

© 2014 Optical Society of America

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  1. W. B. Lee, J. Y. Wu, Y. I. Lee, and J. Sneddon, “Recent applications of laser-induced breakdown spectrometry: a review of material approaches,” Appl. Spectrosc. Rev. 39(1), 27–97 (2004).
    [Crossref]
  2. Z. Wang, T. B. Yuan, Z. Y. Hou, W. D. Zhou, J. D. Lu, H. B. Ding, and X. Y. Zeng, “Laser-induced breakdown spectroscopy in China,” Front. Phys. (2014).
  3. L. B. Guo, Z. Q. Hao, M. Shen, W. Xiong, X. N. He, Z. Q. Xie, M. Gao, X. Y. Li, X. Y. Zeng, and Y. F. Lu, “Accuracy improvement of quantitative analysis by spatial confinement in laser-induced breakdown spectroscopy,” Opt. Express 21(15), 18188–18195 (2013).
    [Crossref] [PubMed]
  4. P. Fichet, P. Mauchien, J. F. Wagner, and C. Moulin, “Quantitative elemental determination in water and oil by laser induced breakdown spectroscopy,” Anal. Chim. Acta 429(2), 269–278 (2001).
    [Crossref]
  5. L. Dudragne, P. Adam, and J. Amouroux, “Time-resolved laser-induced breakdown spectroscopy: application for qualitative and quantitative detection of fluorine, chlorine, sulfur, and carbon in air,” Appl. Spectrosc. 52(10), 1321–1327 (1998).
    [Crossref]
  6. J. P. Singh and S. N. Thakur, Laser-Induced Breakdown Spectroscopy (Elsevier Science, 2007).
  7. Z. Wang, Z. Y. Hou, S. L. Lui, D. Jiang, J. M. Liu, and Z. Li, “Utilization of moderate cylindrical confinement for precision improvement of laser-induced breakdown spectroscopy signal,” Opt. Express 20(S6), A1011–A1018 (2012).
    [Crossref]
  8. T. Fujimoto, Plasma Spectroscopy (Clarendon, 2004).
  9. X. G. Shao, A. K. M. Leung, and F. T. Chau, “Wavelet: a new trend in chemistry,” Acc. Chem. Res. 36(4), 276–283 (2003).
    [Crossref] [PubMed]
  10. C. M. Galloway, E. C. Le Ru, and P. G. Etchegoin, “An iterative algorithm for background removal in spectroscopy by wavelet transforms,” Appl. Spectrosc. 63(12), 1370–1376 (2009).
    [Crossref] [PubMed]
  11. X. G. Ma and Z. X. Zhang, “Application of wavelet transform to background correction in inductively coupled plasma atomic emission spectrometry,” Anal. Chim. Acta 485(2), 233–239 (2003).
    [Crossref]
  12. C. X. Ma and X. G. Shao, “Continuous wavelet transform applied to removing the fluctuating background in near-infrared spectra,” J. Chem. Inf. Comput. Sci. 44(3), 907–911 (2004).
    [Crossref] [PubMed]
  13. J. Schlenke, L. Hildebrand, J. Moros, and J. J. Laserna, “Adaptive approach for variable noise suppression on laser-induced breakdown spectroscopy responses using stationary wavelet transform,” Anal. Chim. Acta 754, 8–19 (2012).
    [Crossref] [PubMed]
  14. B. Zhang, L. X. Sun, H. B. Yu, Y. Xin, and Z. B. Cong, “Wavelet denoising method for laser-induced breakdown spectroscopy,” J. Anal. At. Spectrom. 28(12), 1884–1893 (2013).
    [Crossref]
  15. T. B. Yuan, Z. Wang, Z. Li, W. D. Ni, and J. M. Liu, “A partial least squares and wavelet-transform hybrid model to analyze carbon content in coal using Laser-induced breakdown spectroscopy,” Anal. Chim. Acta 807, 29–35 (2014).
    [Crossref] [PubMed]
  16. X. G. Shao, W. S. Cai, and Z. X. Pan, “Wavelet transform and its applications in high performance liquid chromatography (HPLC) analysis,” Chemom. Intell. Lab. Syst. 45(1–2), 249–256 (1999).
    [Crossref]
  17. S. G. Mallat, “A theory of multiresolution signal decomposition: the wavelet representation,” IEEE Trans. Pattern Anal. 11(7), 674–693 (1989).
    [Crossref]
  18. S. G. Mallat, A Wavelet Tour of Signal Processing: The Sparse Way (Academic, 2008).
  19. X. G. Shao, L. M. Shao, and G. W. Zhao, “Extraction of extended X-ray absorption fine structure information from the experimental data using the wavelet transform,” Anal. Commun. 35(4), 135–137 (1998).
    [Crossref]
  20. D. Chen, X. G. Shao, B. Hu, and Q. D. Su, “A background and noise elimination method for quantitative calibration of near infrared spectra,” Anal. Chim. Acta 511(1), 37–45 (2004).
    [Crossref]
  21. I. Daubechies, Ten Lectures on Wavelets (Society for Industrial and Applied Mathematics, 1992).
  22. A. E. Kramida Y. Ralchenko, J. Reader, and NIST ASD Team, “NIST Atomic Spectra Database (version 5.1)” (National Institute of Standards and Technology, 2013), http://physics.nist.gov/asd .
  23. L. X. Sun and H. B. Yu, “Automatic estimation of varying continuum background emission in laser-induced breakdown spectroscopy,” Spectrochim. Acta, B At. Spectrosc. 64(3), 278–287 (2009).
    [Crossref]

2014 (1)

T. B. Yuan, Z. Wang, Z. Li, W. D. Ni, and J. M. Liu, “A partial least squares and wavelet-transform hybrid model to analyze carbon content in coal using Laser-induced breakdown spectroscopy,” Anal. Chim. Acta 807, 29–35 (2014).
[Crossref] [PubMed]

2013 (2)

2012 (2)

Z. Wang, Z. Y. Hou, S. L. Lui, D. Jiang, J. M. Liu, and Z. Li, “Utilization of moderate cylindrical confinement for precision improvement of laser-induced breakdown spectroscopy signal,” Opt. Express 20(S6), A1011–A1018 (2012).
[Crossref]

J. Schlenke, L. Hildebrand, J. Moros, and J. J. Laserna, “Adaptive approach for variable noise suppression on laser-induced breakdown spectroscopy responses using stationary wavelet transform,” Anal. Chim. Acta 754, 8–19 (2012).
[Crossref] [PubMed]

2009 (2)

C. M. Galloway, E. C. Le Ru, and P. G. Etchegoin, “An iterative algorithm for background removal in spectroscopy by wavelet transforms,” Appl. Spectrosc. 63(12), 1370–1376 (2009).
[Crossref] [PubMed]

L. X. Sun and H. B. Yu, “Automatic estimation of varying continuum background emission in laser-induced breakdown spectroscopy,” Spectrochim. Acta, B At. Spectrosc. 64(3), 278–287 (2009).
[Crossref]

2004 (3)

W. B. Lee, J. Y. Wu, Y. I. Lee, and J. Sneddon, “Recent applications of laser-induced breakdown spectrometry: a review of material approaches,” Appl. Spectrosc. Rev. 39(1), 27–97 (2004).
[Crossref]

C. X. Ma and X. G. Shao, “Continuous wavelet transform applied to removing the fluctuating background in near-infrared spectra,” J. Chem. Inf. Comput. Sci. 44(3), 907–911 (2004).
[Crossref] [PubMed]

D. Chen, X. G. Shao, B. Hu, and Q. D. Su, “A background and noise elimination method for quantitative calibration of near infrared spectra,” Anal. Chim. Acta 511(1), 37–45 (2004).
[Crossref]

2003 (2)

X. G. Ma and Z. X. Zhang, “Application of wavelet transform to background correction in inductively coupled plasma atomic emission spectrometry,” Anal. Chim. Acta 485(2), 233–239 (2003).
[Crossref]

X. G. Shao, A. K. M. Leung, and F. T. Chau, “Wavelet: a new trend in chemistry,” Acc. Chem. Res. 36(4), 276–283 (2003).
[Crossref] [PubMed]

2001 (1)

P. Fichet, P. Mauchien, J. F. Wagner, and C. Moulin, “Quantitative elemental determination in water and oil by laser induced breakdown spectroscopy,” Anal. Chim. Acta 429(2), 269–278 (2001).
[Crossref]

1999 (1)

X. G. Shao, W. S. Cai, and Z. X. Pan, “Wavelet transform and its applications in high performance liquid chromatography (HPLC) analysis,” Chemom. Intell. Lab. Syst. 45(1–2), 249–256 (1999).
[Crossref]

1998 (2)

X. G. Shao, L. M. Shao, and G. W. Zhao, “Extraction of extended X-ray absorption fine structure information from the experimental data using the wavelet transform,” Anal. Commun. 35(4), 135–137 (1998).
[Crossref]

L. Dudragne, P. Adam, and J. Amouroux, “Time-resolved laser-induced breakdown spectroscopy: application for qualitative and quantitative detection of fluorine, chlorine, sulfur, and carbon in air,” Appl. Spectrosc. 52(10), 1321–1327 (1998).
[Crossref]

1989 (1)

S. G. Mallat, “A theory of multiresolution signal decomposition: the wavelet representation,” IEEE Trans. Pattern Anal. 11(7), 674–693 (1989).
[Crossref]

Adam, P.

Amouroux, J.

Cai, W. S.

X. G. Shao, W. S. Cai, and Z. X. Pan, “Wavelet transform and its applications in high performance liquid chromatography (HPLC) analysis,” Chemom. Intell. Lab. Syst. 45(1–2), 249–256 (1999).
[Crossref]

Chau, F. T.

X. G. Shao, A. K. M. Leung, and F. T. Chau, “Wavelet: a new trend in chemistry,” Acc. Chem. Res. 36(4), 276–283 (2003).
[Crossref] [PubMed]

Chen, D.

D. Chen, X. G. Shao, B. Hu, and Q. D. Su, “A background and noise elimination method for quantitative calibration of near infrared spectra,” Anal. Chim. Acta 511(1), 37–45 (2004).
[Crossref]

Cong, Z. B.

B. Zhang, L. X. Sun, H. B. Yu, Y. Xin, and Z. B. Cong, “Wavelet denoising method for laser-induced breakdown spectroscopy,” J. Anal. At. Spectrom. 28(12), 1884–1893 (2013).
[Crossref]

Dudragne, L.

Etchegoin, P. G.

Fichet, P.

P. Fichet, P. Mauchien, J. F. Wagner, and C. Moulin, “Quantitative elemental determination in water and oil by laser induced breakdown spectroscopy,” Anal. Chim. Acta 429(2), 269–278 (2001).
[Crossref]

Galloway, C. M.

Gao, M.

Guo, L. B.

Hao, Z. Q.

He, X. N.

Hildebrand, L.

J. Schlenke, L. Hildebrand, J. Moros, and J. J. Laserna, “Adaptive approach for variable noise suppression on laser-induced breakdown spectroscopy responses using stationary wavelet transform,” Anal. Chim. Acta 754, 8–19 (2012).
[Crossref] [PubMed]

Hou, Z. Y.

Hu, B.

D. Chen, X. G. Shao, B. Hu, and Q. D. Su, “A background and noise elimination method for quantitative calibration of near infrared spectra,” Anal. Chim. Acta 511(1), 37–45 (2004).
[Crossref]

Jiang, D.

Laserna, J. J.

J. Schlenke, L. Hildebrand, J. Moros, and J. J. Laserna, “Adaptive approach for variable noise suppression on laser-induced breakdown spectroscopy responses using stationary wavelet transform,” Anal. Chim. Acta 754, 8–19 (2012).
[Crossref] [PubMed]

Le Ru, E. C.

Lee, W. B.

W. B. Lee, J. Y. Wu, Y. I. Lee, and J. Sneddon, “Recent applications of laser-induced breakdown spectrometry: a review of material approaches,” Appl. Spectrosc. Rev. 39(1), 27–97 (2004).
[Crossref]

Lee, Y. I.

W. B. Lee, J. Y. Wu, Y. I. Lee, and J. Sneddon, “Recent applications of laser-induced breakdown spectrometry: a review of material approaches,” Appl. Spectrosc. Rev. 39(1), 27–97 (2004).
[Crossref]

Leung, A. K. M.

X. G. Shao, A. K. M. Leung, and F. T. Chau, “Wavelet: a new trend in chemistry,” Acc. Chem. Res. 36(4), 276–283 (2003).
[Crossref] [PubMed]

Li, X. Y.

Li, Z.

T. B. Yuan, Z. Wang, Z. Li, W. D. Ni, and J. M. Liu, “A partial least squares and wavelet-transform hybrid model to analyze carbon content in coal using Laser-induced breakdown spectroscopy,” Anal. Chim. Acta 807, 29–35 (2014).
[Crossref] [PubMed]

Z. Wang, Z. Y. Hou, S. L. Lui, D. Jiang, J. M. Liu, and Z. Li, “Utilization of moderate cylindrical confinement for precision improvement of laser-induced breakdown spectroscopy signal,” Opt. Express 20(S6), A1011–A1018 (2012).
[Crossref]

Liu, J. M.

T. B. Yuan, Z. Wang, Z. Li, W. D. Ni, and J. M. Liu, “A partial least squares and wavelet-transform hybrid model to analyze carbon content in coal using Laser-induced breakdown spectroscopy,” Anal. Chim. Acta 807, 29–35 (2014).
[Crossref] [PubMed]

Z. Wang, Z. Y. Hou, S. L. Lui, D. Jiang, J. M. Liu, and Z. Li, “Utilization of moderate cylindrical confinement for precision improvement of laser-induced breakdown spectroscopy signal,” Opt. Express 20(S6), A1011–A1018 (2012).
[Crossref]

Lu, Y. F.

Lui, S. L.

Ma, C. X.

C. X. Ma and X. G. Shao, “Continuous wavelet transform applied to removing the fluctuating background in near-infrared spectra,” J. Chem. Inf. Comput. Sci. 44(3), 907–911 (2004).
[Crossref] [PubMed]

Ma, X. G.

X. G. Ma and Z. X. Zhang, “Application of wavelet transform to background correction in inductively coupled plasma atomic emission spectrometry,” Anal. Chim. Acta 485(2), 233–239 (2003).
[Crossref]

Mallat, S. G.

S. G. Mallat, “A theory of multiresolution signal decomposition: the wavelet representation,” IEEE Trans. Pattern Anal. 11(7), 674–693 (1989).
[Crossref]

Mauchien, P.

P. Fichet, P. Mauchien, J. F. Wagner, and C. Moulin, “Quantitative elemental determination in water and oil by laser induced breakdown spectroscopy,” Anal. Chim. Acta 429(2), 269–278 (2001).
[Crossref]

Moros, J.

J. Schlenke, L. Hildebrand, J. Moros, and J. J. Laserna, “Adaptive approach for variable noise suppression on laser-induced breakdown spectroscopy responses using stationary wavelet transform,” Anal. Chim. Acta 754, 8–19 (2012).
[Crossref] [PubMed]

Moulin, C.

P. Fichet, P. Mauchien, J. F. Wagner, and C. Moulin, “Quantitative elemental determination in water and oil by laser induced breakdown spectroscopy,” Anal. Chim. Acta 429(2), 269–278 (2001).
[Crossref]

Ni, W. D.

T. B. Yuan, Z. Wang, Z. Li, W. D. Ni, and J. M. Liu, “A partial least squares and wavelet-transform hybrid model to analyze carbon content in coal using Laser-induced breakdown spectroscopy,” Anal. Chim. Acta 807, 29–35 (2014).
[Crossref] [PubMed]

Pan, Z. X.

X. G. Shao, W. S. Cai, and Z. X. Pan, “Wavelet transform and its applications in high performance liquid chromatography (HPLC) analysis,” Chemom. Intell. Lab. Syst. 45(1–2), 249–256 (1999).
[Crossref]

Schlenke, J.

J. Schlenke, L. Hildebrand, J. Moros, and J. J. Laserna, “Adaptive approach for variable noise suppression on laser-induced breakdown spectroscopy responses using stationary wavelet transform,” Anal. Chim. Acta 754, 8–19 (2012).
[Crossref] [PubMed]

Shao, L. M.

X. G. Shao, L. M. Shao, and G. W. Zhao, “Extraction of extended X-ray absorption fine structure information from the experimental data using the wavelet transform,” Anal. Commun. 35(4), 135–137 (1998).
[Crossref]

Shao, X. G.

C. X. Ma and X. G. Shao, “Continuous wavelet transform applied to removing the fluctuating background in near-infrared spectra,” J. Chem. Inf. Comput. Sci. 44(3), 907–911 (2004).
[Crossref] [PubMed]

D. Chen, X. G. Shao, B. Hu, and Q. D. Su, “A background and noise elimination method for quantitative calibration of near infrared spectra,” Anal. Chim. Acta 511(1), 37–45 (2004).
[Crossref]

X. G. Shao, A. K. M. Leung, and F. T. Chau, “Wavelet: a new trend in chemistry,” Acc. Chem. Res. 36(4), 276–283 (2003).
[Crossref] [PubMed]

X. G. Shao, W. S. Cai, and Z. X. Pan, “Wavelet transform and its applications in high performance liquid chromatography (HPLC) analysis,” Chemom. Intell. Lab. Syst. 45(1–2), 249–256 (1999).
[Crossref]

X. G. Shao, L. M. Shao, and G. W. Zhao, “Extraction of extended X-ray absorption fine structure information from the experimental data using the wavelet transform,” Anal. Commun. 35(4), 135–137 (1998).
[Crossref]

Shen, M.

Sneddon, J.

W. B. Lee, J. Y. Wu, Y. I. Lee, and J. Sneddon, “Recent applications of laser-induced breakdown spectrometry: a review of material approaches,” Appl. Spectrosc. Rev. 39(1), 27–97 (2004).
[Crossref]

Su, Q. D.

D. Chen, X. G. Shao, B. Hu, and Q. D. Su, “A background and noise elimination method for quantitative calibration of near infrared spectra,” Anal. Chim. Acta 511(1), 37–45 (2004).
[Crossref]

Sun, L. X.

B. Zhang, L. X. Sun, H. B. Yu, Y. Xin, and Z. B. Cong, “Wavelet denoising method for laser-induced breakdown spectroscopy,” J. Anal. At. Spectrom. 28(12), 1884–1893 (2013).
[Crossref]

L. X. Sun and H. B. Yu, “Automatic estimation of varying continuum background emission in laser-induced breakdown spectroscopy,” Spectrochim. Acta, B At. Spectrosc. 64(3), 278–287 (2009).
[Crossref]

Wagner, J. F.

P. Fichet, P. Mauchien, J. F. Wagner, and C. Moulin, “Quantitative elemental determination in water and oil by laser induced breakdown spectroscopy,” Anal. Chim. Acta 429(2), 269–278 (2001).
[Crossref]

Wang, Z.

T. B. Yuan, Z. Wang, Z. Li, W. D. Ni, and J. M. Liu, “A partial least squares and wavelet-transform hybrid model to analyze carbon content in coal using Laser-induced breakdown spectroscopy,” Anal. Chim. Acta 807, 29–35 (2014).
[Crossref] [PubMed]

Z. Wang, Z. Y. Hou, S. L. Lui, D. Jiang, J. M. Liu, and Z. Li, “Utilization of moderate cylindrical confinement for precision improvement of laser-induced breakdown spectroscopy signal,” Opt. Express 20(S6), A1011–A1018 (2012).
[Crossref]

Wu, J. Y.

W. B. Lee, J. Y. Wu, Y. I. Lee, and J. Sneddon, “Recent applications of laser-induced breakdown spectrometry: a review of material approaches,” Appl. Spectrosc. Rev. 39(1), 27–97 (2004).
[Crossref]

Xie, Z. Q.

Xin, Y.

B. Zhang, L. X. Sun, H. B. Yu, Y. Xin, and Z. B. Cong, “Wavelet denoising method for laser-induced breakdown spectroscopy,” J. Anal. At. Spectrom. 28(12), 1884–1893 (2013).
[Crossref]

Xiong, W.

Yu, H. B.

B. Zhang, L. X. Sun, H. B. Yu, Y. Xin, and Z. B. Cong, “Wavelet denoising method for laser-induced breakdown spectroscopy,” J. Anal. At. Spectrom. 28(12), 1884–1893 (2013).
[Crossref]

L. X. Sun and H. B. Yu, “Automatic estimation of varying continuum background emission in laser-induced breakdown spectroscopy,” Spectrochim. Acta, B At. Spectrosc. 64(3), 278–287 (2009).
[Crossref]

Yuan, T. B.

T. B. Yuan, Z. Wang, Z. Li, W. D. Ni, and J. M. Liu, “A partial least squares and wavelet-transform hybrid model to analyze carbon content in coal using Laser-induced breakdown spectroscopy,” Anal. Chim. Acta 807, 29–35 (2014).
[Crossref] [PubMed]

Zeng, X. Y.

Zhang, B.

B. Zhang, L. X. Sun, H. B. Yu, Y. Xin, and Z. B. Cong, “Wavelet denoising method for laser-induced breakdown spectroscopy,” J. Anal. At. Spectrom. 28(12), 1884–1893 (2013).
[Crossref]

Zhang, Z. X.

X. G. Ma and Z. X. Zhang, “Application of wavelet transform to background correction in inductively coupled plasma atomic emission spectrometry,” Anal. Chim. Acta 485(2), 233–239 (2003).
[Crossref]

Zhao, G. W.

X. G. Shao, L. M. Shao, and G. W. Zhao, “Extraction of extended X-ray absorption fine structure information from the experimental data using the wavelet transform,” Anal. Commun. 35(4), 135–137 (1998).
[Crossref]

Acc. Chem. Res. (1)

X. G. Shao, A. K. M. Leung, and F. T. Chau, “Wavelet: a new trend in chemistry,” Acc. Chem. Res. 36(4), 276–283 (2003).
[Crossref] [PubMed]

Anal. Chim. Acta (5)

P. Fichet, P. Mauchien, J. F. Wagner, and C. Moulin, “Quantitative elemental determination in water and oil by laser induced breakdown spectroscopy,” Anal. Chim. Acta 429(2), 269–278 (2001).
[Crossref]

X. G. Ma and Z. X. Zhang, “Application of wavelet transform to background correction in inductively coupled plasma atomic emission spectrometry,” Anal. Chim. Acta 485(2), 233–239 (2003).
[Crossref]

J. Schlenke, L. Hildebrand, J. Moros, and J. J. Laserna, “Adaptive approach for variable noise suppression on laser-induced breakdown spectroscopy responses using stationary wavelet transform,” Anal. Chim. Acta 754, 8–19 (2012).
[Crossref] [PubMed]

T. B. Yuan, Z. Wang, Z. Li, W. D. Ni, and J. M. Liu, “A partial least squares and wavelet-transform hybrid model to analyze carbon content in coal using Laser-induced breakdown spectroscopy,” Anal. Chim. Acta 807, 29–35 (2014).
[Crossref] [PubMed]

D. Chen, X. G. Shao, B. Hu, and Q. D. Su, “A background and noise elimination method for quantitative calibration of near infrared spectra,” Anal. Chim. Acta 511(1), 37–45 (2004).
[Crossref]

Anal. Commun. (1)

X. G. Shao, L. M. Shao, and G. W. Zhao, “Extraction of extended X-ray absorption fine structure information from the experimental data using the wavelet transform,” Anal. Commun. 35(4), 135–137 (1998).
[Crossref]

Appl. Spectrosc. (2)

Appl. Spectrosc. Rev. (1)

W. B. Lee, J. Y. Wu, Y. I. Lee, and J. Sneddon, “Recent applications of laser-induced breakdown spectrometry: a review of material approaches,” Appl. Spectrosc. Rev. 39(1), 27–97 (2004).
[Crossref]

Chemom. Intell. Lab. Syst. (1)

X. G. Shao, W. S. Cai, and Z. X. Pan, “Wavelet transform and its applications in high performance liquid chromatography (HPLC) analysis,” Chemom. Intell. Lab. Syst. 45(1–2), 249–256 (1999).
[Crossref]

IEEE Trans. Pattern Anal. (1)

S. G. Mallat, “A theory of multiresolution signal decomposition: the wavelet representation,” IEEE Trans. Pattern Anal. 11(7), 674–693 (1989).
[Crossref]

J. Anal. At. Spectrom. (1)

B. Zhang, L. X. Sun, H. B. Yu, Y. Xin, and Z. B. Cong, “Wavelet denoising method for laser-induced breakdown spectroscopy,” J. Anal. At. Spectrom. 28(12), 1884–1893 (2013).
[Crossref]

J. Chem. Inf. Comput. Sci. (1)

C. X. Ma and X. G. Shao, “Continuous wavelet transform applied to removing the fluctuating background in near-infrared spectra,” J. Chem. Inf. Comput. Sci. 44(3), 907–911 (2004).
[Crossref] [PubMed]

Opt. Express (2)

Spectrochim. Acta, B At. Spectrosc. (1)

L. X. Sun and H. B. Yu, “Automatic estimation of varying continuum background emission in laser-induced breakdown spectroscopy,” Spectrochim. Acta, B At. Spectrosc. 64(3), 278–287 (2009).
[Crossref]

Other (6)

I. Daubechies, Ten Lectures on Wavelets (Society for Industrial and Applied Mathematics, 1992).

A. E. Kramida Y. Ralchenko, J. Reader, and NIST ASD Team, “NIST Atomic Spectra Database (version 5.1)” (National Institute of Standards and Technology, 2013), http://physics.nist.gov/asd .

T. Fujimoto, Plasma Spectroscopy (Clarendon, 2004).

Z. Wang, T. B. Yuan, Z. Y. Hou, W. D. Zhou, J. D. Lu, H. B. Ding, and X. Y. Zeng, “Laser-induced breakdown spectroscopy in China,” Front. Phys. (2014).

J. P. Singh and S. N. Thakur, Laser-Induced Breakdown Spectroscopy (Elsevier Science, 2007).

S. G. Mallat, A Wavelet Tour of Signal Processing: The Sparse Way (Academic, 2008).

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Figures (3)

Fig. 1
Fig. 1 Schematic diagram of the experimental setup.

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Fig. 2
Fig. 2 RMSEC values at different wavelet functions and decomposition levels.

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Fig. 3
Fig. 3 Influence of the scaling factor γ. (a) The effect of γ on the RMSEC with optimal decomposition level for each wavelet function. (b) Comparison of one original and its corrected spectrum without and with γ at wavelet function was db8 and decomposition level was 10.

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Tables (2)

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Table 1 Composition of Cr, V, Cu, Mn and Fe elements from the low alloy steel samples

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Table 2 Influence of different background subtraction methods on the univariate regression model

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Equations (2)

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f( t )= ∑ j≤J ∑ k∈Z d j,k ψ j,k ( t ) +( 1-γ ) ∑ k∈Z c J,k ϕ J,k ( t )
RMSEC( W,L, γ opt )= RMSEC min ( W,L,γ )

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