Piecewise Fractional Differential Asymmetric Least Squares Baseline Correction Algorithm for ATR-FTIR of Complex Mixed Solutions

Peng Shan; Menghao Zhi; Teng Liang; Di He; Zhigang Li; Zhonghai He

doi:10.3788/AOS241700

Acta Optica Sinica, Volume. 45, Issue 4, 0430003(2025)

Piecewise Fractional Differential Asymmetric Least Squares Baseline Correction Algorithm for ATR-FTIR of Complex Mixed Solutions

Peng Shan^1,2, Menghao Zhi^1,2、*, Teng Liang^1,2, Di He^1,2, Zhigang Li^1,2, and Zhonghai He^1,2

Author Affiliations

¹Hebei Key Laboratory of Micro-Nano Precision Optical Sensing and Measurement Technology, Qinhuangdao 066004, Hebei , China

²College of Information Science and Engineering, Northeastern University, Shenyang 110819, Liaoning , China

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Figures & Tables(18)

$Segmented fractional order based asymmetric least squares baseline correction algorithm$

Fig. 1. Segmented fractional order based asymmetric least squares baseline correction algorithm

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Fig. 2. Simulated spectra. (a) Baseline of simulated spectrum; (b) simulated peak signal; (c) overall spectrum

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Fig. 3. Real data spectra and division lines. (a) γ-PGA; (b) whole blood

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Fig. 4. Baseline correction experimental results on simulated spectrum. (a) FdAsLS correction; (b) PFdAsLS correction

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Fig. 5. Scatter plots of predicted glucose concentrations. (a) Original spectra; (b) AsLS corrected spectra; (c) FdAsLS corrected spectra; (d) PFdAsLS corrected spectra

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Fig. 6. Scatter plots of predicted sodium glutamate concentrations. (a) Original spectra; (b) AsLS corrected spectra; (c) FdAsLS corrected spectra; (d) PFdAsLS corrected spectra

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Fig. 7. Spectra of γ-PGA (glucose) after baseline correction and fitted baseline. (a) FdAsLS-corrected spectra; (b) FdAsLS-fitted baselines; (c) PFdAsLS-corrected spectra; (d) PFdAsLS-division line and fitted baselines

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Fig. 8. Spectra of γ-PGA (sodium glutamate) after baseline correction and fitted baseline. (a) FdAsLS-corrected spectra; (b) FdAsLS-fitted baselines; (c) PFdAsLS-corrected spectra; (d) PFdAsLS-division line and fitted baselines

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Fig. 9. Scatter plots of predicted blood glucose values. (a) Original spectra; (b) AsLS corrected spectra; (c) FdAsLS corrected spectra; (d) PFdAsLS corrected spectra

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Fig. 10. Spectra of whole blood (blood glucose) after baseline correction and fitted baselines. (a) FdAsLS-corrected spectra; (b) FdAsLS-fitted baselines; (c) PFdAsLS-corrected spectra; (d) PFdAsLS-division lines and fitted baselines

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Table 1. Peak signal data
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Table 1. Peak signal data
Peak wavenumber r_o_i Full width at half-maximum w_o_i Peak area A_o_i
300 30 9900
600 23 11000
990 10 2900
1200 20 5200
2000 40 14000

Table 2. FdAsLS-correction experimental results of simulated data
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Table 2. FdAsLS-correction experimental results of simulated data
$α$ $λ$ RMSE $α$ $λ$ RMSE
0.1 1 201.000 2.0 10^7.5 3.983
0.8 1 27.702 2.5 10^3.5 28.755
0.9 10² 21.223 3.0 10⁹ 7.262
1.0 10³ 3.739 4.0 10⁹ 17.631
1.5 10² 27.067

Table 3. PFdAsLS-correction experimental results of simulated data
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Table 3. PFdAsLS-correction experimental results of simulated data
Division interval /cm^-1 $α$ $λ$ RMSE
[0, 1280) 2 10⁸ 1.381
[1280, 1700) 1 10² 1.381
[1700, 2300) 2 10^8.5 1.381
[2300, 3000] 1 10^1.5 1.381

Table 4. FdAsLS correction experimental results for γ-PGA spectra

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Table 4. FdAsLS correction experimental results for γ-PGA spectra

$α$	RMSEP of glucose	RMSEC of glucose	RMSEP of sodium glutamate	RMSEC of sodium glutamate	$α$	RMSEP of glucose	RMSEC of glucose	RMSEP of sodium glutamate	RMSEC of sodium glutamate
0	2.703	2.059	0.937	0.386	1.2	2.812	1.005	0.954	0.563
0.2	2.587	1.918	0.923	0.385	1.4	2.608	1.712	0.904	0.407
0.4	2.356	1.772	0.896	0.382	1.6	2.538	1.643	0.927	0.355
0.6	2.436	1.650	0.873	0.418	1.8	2.692	2.153	0.941	0.411
0.8	2.607	1.425	0.922	0.422	2.0	2.648	2.109	0.930	0.318
1.0	2.424	2.006	0.961	0.413

Table 5. Subsection division, parameter configuration, and quantitative analysis results of PFdAsLS correction experiments for γ-PGA spectra

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Table 5. Subsection division, parameter configuration, and quantitative analysis results of PFdAsLS correction experiments for γ-PGA spectra

Ingredient	Glucose	Sodium glutamate
Division interval /cm^-1	[4000, 2244), [2244, 1273), [1273, 400]	[4000, 2244), [2244, 1273), [1273, 400]
$α$	1.3; 3.0; 1.3	1.3; 3.0; 0.8
$λ$	10^0.5; 1; 10^0.5	10^0.5; 10²; 1
RMSEP	2.086	0.792
RMSEC	1.510	0.406

Table 6. FdAsLS correction experimental results for whole blood spectra
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Table 6. FdAsLS correction experimental results for whole blood spectra
$α$ RMSEP RMSEC $α$ RMSEP RMSEC
0 2.150 2.370 1.2 1.547 1.678
0.2 1.437 1.584 1.4 1.658 1.810
0.4 1.482 1.591 1.6 1.633 1.731
0.6 1.427 1.565 1.8 1.606 1.913
0.8 1.418 1.582 2.0 1.508 1.727
1.0 1.520 1.684

Table 7. Subsection division, parameter configuration, and quantitative analysis results of PFdAsLS correction experiments for whole blood spectra
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Table 7. Subsection division, parameter configuration, and quantitative analysis results of PFdAsLS correction experiments for whole blood spectra
Parameter Value
Division
interval /cm^-1
[4000, 3660), [3660, 2725), [2725,1717), [1717, 1477), [1477, 400]
$α$ 1.3, 0.9, 1.7, 0.7, 0.8
$λ$ 10^1.5, 1, 10^2.5, 10^1.5, 10^2.5
RMSEP 1.175
RMSEC 1.404

Table 8. Experimental results of different baseline correction algorithms

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Table 8. Experimental results of different baseline correction algorithms

Algorithm	RMSEC of glucose	RMSEP of glucose	RMSEC of sodium glutamate	RMSEP of sodium glutamate	RMSEC of blood glucose	RMSEP of blood glucose
None	2.059	2.703	0.386	0.936	2.370	2.150
AsLS	2.006	2.424	0.318	0.930	1.727	1.508
asPLS	1.497	2.624	0.480	0.964	2.507	2.317
SBL	1.644	2.479	0.593	0.990	1.589	1.704
airPLS	1.576	2.413	0.535	0.995	1.731	1.878
SSFBCSP	1.902	2.448	0.444	0.969	1.777	2.049
FdAsLS	1.772	2.356	0.418	0.873	1.418	1.351
PFdAsLS	1.510	2.086	0.406	0.792	1.404	1.175

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Peng Shan, Menghao Zhi, Teng Liang, Di He, Zhigang Li, Zhonghai He. Piecewise Fractional Differential Asymmetric Least Squares Baseline Correction Algorithm for ATR-FTIR of Complex Mixed Solutions[J]. Acta Optica Sinica, 2025, 45(4): 0430003

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