Blind spectral deconvolution algorithm for Raman spectrum with Poisson noise

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.

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Fig. 2. Simulation experiment. (a) Raman spectrum of methyl formate (C2H4O2) from 400 to 1500 cm−1. (b) Overlap spectrum. (c) Contaminated by Poisson noise. (d) RL. (e) TR-RL. (f) MTR-RL.

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Fig. 3. NMSE versus regularization parameter of TR-RL and MTR-RL for the Raman spectrum of methyl formate (C2H4O2).

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Fig. 4. NMSE versus the iteration number of the three methods for the Raman spectrum [methyl formate (C2H4O2)].

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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.

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Fig. 6. Real Raman deconvolution experiment. (a) Raman spectrum of (D+)-glucopyranose [14] from 10 to 700 cm−1. (b) MTR-RL result.

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Table 1. NMSE of Measured Spectrum and the Best Deconvolution Spectrum (with the Lowest NMSE by Different Algorithms)
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Table 1. NMSE of Measured Spectrum and the Best Deconvolution Spectrum (with the Lowest NMSE by Different Algorithms)
Spectral Deconvolution by
Spectra Degraded Spectrum FSD [4] RL [9] TR-RL MTR-RL
$C_{2} H_{4} O_{2}$ 0.0451 0.0272 0.0231 0.0240 0.0219
$C_{9} H_{10} O_{2}$ 0.0223 0.0195 0.0136 0.0105 0.0092
$C_{4} H_{4} S$ 0.0480 0.0315 0.0231 0.0198 0.0184

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

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

Spectrum	FSD[4]	RL[9]	TR-RL	MTR-RL
Raman 1	1.47	1.50	3.61	3.98
Raman 1	(1.10)	(1.32)	(2.20)	(2.35)
Raman 2	1.67	2.28	4.50	4.71
Raman 2	(1.18)	(1.91)	(2.18)	(2.46)
Raman 3	1.25	1.78	3.61	3.81
Raman 3	(1.68)	(1.71)	(2.22)	(2.31)
Raman 4	1.87	2.21	2.90	3.04
Raman 4	(1.41)	(1.75)	(2.31)	(2.40)
Raman 5	1.45	2.16	2.85	3.29
Raman 5	(1.02)	(1.01)	(1.80)	(1.96)
Raman 6	1.88	2.43	3.01	3.21
Raman 6	(1.10)	(1.22)	(1.56)	(1.76)
Raman 7	1.71	1.98	2.50	2.61
Raman 7	(1.24)	(1.31)	(1.68)	(2.01)
Raman 8	1.42	1.68	2.31	2.58
Raman 8	(1.89)	(2.11)	(2.48)	(2.86)

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Hai Liu, Zhaoli Zhang, Jianwen Sun, and Sanya Liu, "Blind spectral deconvolution algorithm for Raman spectrum with Poisson noise," Photonics Res. 2, 168 (2014)

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Paper Information

Category: Spectroscopy

Received: Aug. 8, 2014

Accepted: Sep. 11, 2014

Published Online: May. 21, 2015

The Author Email: and Sanya Liu (lsy5918@gmail.com)

DOI:10.1364/PRJ.2.000168

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

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

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

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

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