Multiple Constrained Reweighted Penalized Least Squares for Spectral Baseline Correction

Baseline drift occurs in various measured spectra, and the existence of a baseline signal will influence qualitative and quantitative analyses. Therefore, it is necessary to perform baseline correction or background elimination before spectral analysis. In this paper, a multiple constrained asymmetric least squares method based on the penalized least squares principle is proposed for baseline correction. The method takes both baseline and peak characteristics into account. Based on the prior knowledge that the left and right boundaries of characteristic peaks should be symmetrical, additional constraints of penalized least squares are added, which ensure the symmetry of spectra. The experimental results of the proposed method on simulated spectra are compared with existing baseline correction methods to verify the accuracy and adaptability of the proposed method. The method is also successfully applied to the baseline correction of real spectra. The results show that it can be effective for estimating the baseline. In addition, this method can also be applied to the baseline correction of other similar spectral signals.

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An Automatic Baseline Correction Method Based on the Penalized Least Squares Method

Sensors ◽

10.3390/s20072015 ◽

2020 ◽

Vol 20 (7) ◽

pp. 2015

Author(s):

Feng Zhang ◽

Xiaojun Tang ◽

Angxin Tong ◽

Bin Wang ◽

Jingwei Wang

Keyword(s):

Least Squares ◽

Least Squares Method ◽

Correction Method ◽

Baseline Correction ◽

Penalized Least Squares ◽

Gaussian Peak ◽

Baseline Drift ◽

Extended Range ◽

Different Types ◽

Smoothness Parameter

Baseline drift spectra are used for quantitative and qualitative analysis, which can easily lead to inaccurate or even wrong results. Although there are several baseline correction methods based on penalized least squares, they all have one or more parameters that must be optimized by users. For this purpose, an automatic baseline correction method based on penalized least squares is proposed in this paper. The algorithm first linearly expands the ends of the spectrum signal, and a Gaussian peak is added to the expanded range. Then, the whole spectrum is corrected by the adaptive smoothness parameter penalized least squares (asPLS) method, that is, by turning the smoothing parameter λ of asPLS to obtain a different root-mean-square error (RMSE) in the extended range, the optimal λ is selected with minimal RMSE. Finally, the baseline of the original signal is well estimated by asPLS with the optimal λ. The paper concludes with the experimental results on the simulated spectra and measured infrared spectra, demonstrating that the proposed method can automatically deal with different types of baseline drift.

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An improved PD-AsLS method of baseline estimated in EDXRF analysis

Analytical Methods ◽

10.1039/d1ay00122a ◽

2021 ◽

Author(s):

Qingxian Zhang ◽

Hui Li ◽

Hongfei Xiao ◽

Jian Zhang ◽

Xiaozhe Li ◽

...

Keyword(s):

Least Squares ◽

Least Squares Method ◽

Fluorescence Analysis ◽

Energy Dispersive ◽

Baseline Correction ◽

Penalized Least Squares ◽

X Ray ◽

Edxrf Analysis ◽

Asymmetric Least Squares

Baseline correction is an important step in energy-dispersive X-ray fluorescence analysis. The asymmetric least squares method (AsLS), adaptive iteratively reweighted penalized least squares method (airPLS), and asymmetrically reweighted penalized least...

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Baseline correction for infrared spectra using adaptive smoothness parameter penalized least squares method

Spectroscopy Letters ◽

10.1080/00387010.2020.1730908 ◽

2020 ◽

Vol 53 (3) ◽

pp. 222-233 ◽

Cited By ~ 2

Author(s):

Feng Zhang ◽

Xiaojun Tang ◽

Angxin Tong ◽

Bin Wang ◽

Jingwei Wang ◽

...

Keyword(s):

Least Squares ◽

Infrared Spectra ◽

Least Squares Method ◽

Baseline Correction ◽

Penalized Least Squares ◽

Smoothness Parameter

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Baseline correction for Raman spectra using an improved asymmetric least squares method

Analytical Methods ◽

10.1039/c4ay00068d ◽

2014 ◽

Vol 6 (12) ◽

pp. 4402-4407 ◽

Cited By ~ 51

Author(s):

Shixuan He ◽

Wei Zhang ◽

Lijuan Liu ◽

Yu Huang ◽

Jiming He ◽

...

Keyword(s):

Least Squares ◽

Raman Spectra ◽

Least Squares Method ◽

Baseline Correction ◽

Asymmetric Least Squares ◽

Raman Spectral

The proposed IAsLS method is successfully applied to practical Raman spectral baseline correction.

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EXPRESS: Baseline Correction Based on a Search Algorithm from Artificial Intelligence

Applied Spectroscopy ◽

10.1177/0003702820977512 ◽

2020 ◽

pp. 000370282097751

Author(s):

Xin Wang ◽

Xia Chen

Keyword(s):

Artificial Intelligence ◽

Objective Function ◽

Least Squares ◽

Least Squares Method ◽

Search Algorithm ◽

Absolute Error ◽

Search Problem ◽

Baseline Correction ◽

Current Spectrum ◽

Data Points

Many spectra have a polynomial-like baseline. Iterative polynomial fitting (IPF) is one of the most popular methods for baseline correction of these spectra. However, the baseline estimated by IPF may have substantially error when the spectrum contains significantly strong peaks or have strong peaks located at the endpoints. First, IPF uses temporary baseline estimated from the current spectrum to identify peak data points. If the current spectrum contains strong peaks, then the temporary baseline substantially deviates from the true baseline. Some good baseline data points of the spectrum might be mistakenly identified as peak data points and are artificially re-assigned with a low value. Second, if a strong peak is located at the endpoint of the spectrum, then the endpoint region of the estimated baseline might have significant error due to overfitting. This study proposes a search algorithm-based baseline correction method (SA) that aims to compress sample the raw spectrum to a dataset with small number of data points and then convert the peak removal process into solving a search problem in artificial intelligence (AI) to minimize an objective function by deleting peak data points. First, the raw spectrum is smoothened out by the moving average method to reduce noise and then divided into dozens of unequally spaced sections on the basis of Chebyshev nodes. Finally, the minimal points of each section are collected to form a dataset for peak removal through search algorithm. SA selects the mean absolute error (MAE) as the objective function because of its sensitivity to overfitting and rapid calculation. The baseline correction performance of SA is compared with those of three baseline correction methods: Lieber and MahadevanâJansen method, adaptive iteratively reweighted penalized least squares method, and improved asymmetric least squares method. Simulated and real FTIR and Raman spectra with polynomial-like baselines are employed in the experiments. Results show that for these spectra, the baseline estimated by SA has fewer error than those by the three other methods.

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