Abstract

A blind deconvolution algorithm with modified Tikhonov regularization is introduced. To improve the spectral resolution, spectral structure information is incorporated into regularization by using the adaptive term to distinguish the spectral structure from other regions. The proposed algorithm can effectively suppress Poisson noise as well as preserve the spectral structure and detailed information. Moreover, it becomes more robust with the change of the regularization parameter. Comparative results on simulated and real degraded Raman spectra are reported. The recovered Raman spectra can easily extract the spectral features and interpret the unknown chemical mixture.

© 2014 Chinese Laser Press

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References

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2014 (1)

L. Z. Deng, L. Cao, and H. Zhu, “Spectral semi-blind deconvolution with hybrid regularization,” Infrared Phys. Technol. 64, 91–96 (2014).
[Crossref]

2013 (1)

2012 (2)

L. Yan, H. Liu, S. Zhong, and H. Fang, “Semi-blind spectral deconvolution with adaptive Tikhonov regularization,” Appl. Spectrosc. 66, 1334–1346 (2012).
[Crossref]

H. Liu, T. Zhang, L. Yan, H. Fang, and Y. Chang, “A MAP-based algorithm for spectroscopic semi-blind deconvolution,” Analyst 137, 3862–3873 (2012).
[Crossref]

2010 (2)

2007 (1)

2005 (3)

1997 (1)

1981 (1)

1967 (1)

Buslov, D. K.

Cameron, D. G.

Cao, L.

L. Z. Deng, L. Cao, and H. Zhu, “Spectral semi-blind deconvolution with hybrid regularization,” Infrared Phys. Technol. 64, 91–96 (2014).
[Crossref]

Chang, Y.

H. Liu, T. Zhang, L. Yan, H. Fang, and Y. Chang, “A MAP-based algorithm for spectroscopic semi-blind deconvolution,” Analyst 137, 3862–3873 (2012).
[Crossref]

Deng, L. Z.

L. Z. Deng, L. Cao, and H. Zhu, “Spectral semi-blind deconvolution with hybrid regularization,” Infrared Phys. Technol. 64, 91–96 (2014).
[Crossref]

Fang, H.

H. Liu, T. Zhang, L. Yan, H. Fang, and Y. Chang, “A MAP-based algorithm for spectroscopic semi-blind deconvolution,” Analyst 137, 3862–3873 (2012).
[Crossref]

L. Yan, H. Liu, S. Zhong, and H. Fang, “Semi-blind spectral deconvolution with adaptive Tikhonov regularization,” Appl. Spectrosc. 66, 1334–1346 (2012).
[Crossref]

Héberger, K.

Helstrom, C. W.

Hu, Z.

Kalivas, J. H.

Katrasnik, J.

Kauppinen, J. K.

Likar, B. T.

Liu, H.

H. Liu, T. Zhang, L. Yan, H. Fang, and Y. Chang, “A MAP-based algorithm for spectroscopic semi-blind deconvolution,” Analyst 137, 3862–3873 (2012).
[Crossref]

L. Yan, H. Liu, S. Zhong, and H. Fang, “Semi-blind spectral deconvolution with adaptive Tikhonov regularization,” Appl. Spectrosc. 66, 1334–1346 (2012).
[Crossref]

Lórenz-Fonfría, V. A.

Mantsch, H. H.

Moffatt, D. J.

Nikonenko, N. A.

Padrós, E.

Pernu, F.

Song, K. Y.

Stout, F.

Sun, J.

Wang, G.

Weber, J. J.

Xu, Z.

Yan, L.

H. Liu, T. Zhang, L. Yan, H. Fang, and Y. Chang, “A MAP-based algorithm for spectroscopic semi-blind deconvolution,” Analyst 137, 3862–3873 (2012).
[Crossref]

L. Yan, H. Liu, S. Zhong, and H. Fang, “Semi-blind spectral deconvolution with adaptive Tikhonov regularization,” Appl. Spectrosc. 66, 1334–1346 (2012).
[Crossref]

Yavuz, D. D.

Yoon, H. J.

Yuan, J.

Zhang, T.

H. Liu, T. Zhang, L. Yan, H. Fang, and Y. Chang, “A MAP-based algorithm for spectroscopic semi-blind deconvolution,” Analyst 137, 3862–3873 (2012).
[Crossref]

Zhong, S.

Zhu, H.

L. Z. Deng, L. Cao, and H. Zhu, “Spectral semi-blind deconvolution with hybrid regularization,” Infrared Phys. Technol. 64, 91–96 (2014).
[Crossref]

Analyst (1)

H. Liu, T. Zhang, L. Yan, H. Fang, and Y. Chang, “A MAP-based algorithm for spectroscopic semi-blind deconvolution,” Analyst 137, 3862–3873 (2012).
[Crossref]

Appl. Opt. (1)

Appl. Spectrosc. (6)

Chin. Opt. Lett. (1)

Infrared Phys. Technol. (1)

L. Z. Deng, L. Cao, and H. Zhu, “Spectral semi-blind deconvolution with hybrid regularization,” Infrared Phys. Technol. 64, 91–96 (2014).
[Crossref]

J. Opt. Soc. Am. (1)

Opt. Lett. (2)

Other (2)

NASA, “Absorption spectral data of Cr:LiSAF crystal,” http://aesd.larc.nasa.gov/gl/laser/spectra/spectra.htm .

S. B. Engelson, “Raman spectral of (D+)-glucopyranose,” http://www.models.life.ku.dk/specarb .

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Figures (6)

Fig. 1.
Fig. 1. Illustration of TR and MTR constraints on three types: flat region, noise region, and structure region. (a) Tikhonov regularization. (b) Modified Tikhonov regularization can distinguish different regions.
Fig. 2.
Fig. 2. Simulation experiment. (a) Raman spectrum of methyl formate ( C 2 H 4 O 2 ) from 400 to 1500 cm 1 . (b) Overlap spectrum. (c) Contaminated by Poisson noise. (d) RL. (e) TR-RL. (f) MTR-RL.
Fig. 3.
Fig. 3. NMSE versus regularization parameter of TR-RL and MTR-RL for the Raman spectrum of methyl formate ( C 2 H 4 O 2 ).
Fig. 4.
Fig. 4. NMSE versus the iteration number of the three methods for the Raman spectrum [methyl formate ( C 2 H 4 O 2 )].
Fig. 5.
Fig. 5. Real Raman spectrum experiment. (a) Cr:LisAF crystal [13] from 300 to 900 nm, deconvolution by (b) TR-RL and (c) MTR-RL. (d) Estimated instrument function.
Fig. 6.
Fig. 6. Real Raman deconvolution experiment. (a) Raman spectrum of (D+)-glucopyranose [14] from 10 to 700 cm 1 . (b) MTR-RL result.

Tables (2)

Tables Icon

Table 1. NMSE of Measured Spectrum and the Best Deconvolution Spectrum (with the Lowest NMSE by Different Algorithms)

Tables Icon

Table 2. FWHMR and NSR (in Brackets) Values of Different Deconvolution Methods on the Real Raman Spectra a

Equations (9)

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g ( v ) = Poisson ( s ( v ) h ( v ) ) ,
p ( g | s , h ) = v L ( s ( v ) h ( v ) ) g ( v ) g ( v ) ! exp { ( s ( v ) h ( v ) ) } ,
E 1 ( s ) = v ( g ( v ) log [ s ( v ) h ( v ) ] + s ( v ) h ( v ) ) .
E 2 ( s ) = v ( g ( v ) log [ s ( v ) h ( v ) ] + s ( v ) h ( v ) ) + α | s | 2 ,
w ( | s | ) = 1 1 + ( s / k ) 2 ,
MTR = w ( | s | ) | s | 2 ,
E ( s , h ) = v L [ g ( v ) log ( s ( v ) h ( v ) ) + s ( v ) h ( v ) ] + α w ( | s | ) | s | 2 .
s ^ t ( k + 1 ) = s ^ ( k ) { h ^ ( k ) ( v ) [ g s ^ ( k ) h ^ ( k ) ] } , s ^ ( k + 1 ) = s ^ t ( k + 1 ) v s ^ t ( k + 1 ) ,
h ^ t ( k + 1 ) = h ^ ( k ) { s ^ ( k + 1 ) ( v ) [ g s ^ ( k + 1 ) h ^ ( k ) ] } × 1 { 1 α w ( | s ^ | ) ( 2 s ^ ) } ,

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