Background subtract subroutine for spectral data

Goehner, R. P.

doi:10.1021/ac50030a055

Cited by 34 publications

(12 citation statements)

References 6 publications

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“…Problem Modeling. We denote the Raman intensities of an N-point Raman spectrum as y = ( y 1 , …, y N ) and y = b + p + n , in which b is the baseline of the Raman spectrum, which needs to be corrected and is usually modeled as a p -order polynomial because polynomial fitting for the baseline satisfies most spectra; 27,–30 p is the positive gathering peaks in the Raman spectrum, which have different shapes, amplitudes, positions, and widths; and n is the physical noise and model uncertainties, which are modeled here as a white Gaussian and additive noise with variance σ 2 .…”

Section: Methodsmentioning

confidence: 99%

Goldindec: A Novel Algorithm for Raman Spectrum Baseline Correction

et al. 2015

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Raman spectra have been widely used in biology, physics, and chemistry and have become an essential tool for the studies of macromolecules. Nevertheless, the raw Raman signal is often obscured by a broad background curve (or baseline) due to the intrinsic fluorescence of the organic molecules, which leads to unpredictable negative effects in quantitative analysis of Raman spectra. Therefore, it is essential to correct this baseline before analyzing raw Raman spectra. Polynomial fitting has proven to be the most convenient and simplest method and has high accuracy. In polynomial fitting, the cost function used and its parameters are crucial. This article proposes a novel iterative algorithm named Goldindec, freely available for noncommercial use as noted in text, with a new cost function that not only conquers the influence of great peaks but also solves the problem of low correction accuracy when there is a high peak number. Goldindec automatically generates parameters from the raw data rather than by empirical choice, as in previous methods. Comparisons with other algorithms on the benchmark data show that Goldindec has a higher accuracy and computational efficiency, and is hardly affected by great peaks, peak number, and wavenumber.

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Section: Methodsmentioning

confidence: 99%

Goldindec: A Novel Algorithm for Raman Spectrum Baseline Correction

et al. 2015

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“…Many studies have been carried out on baseline shifting, which is one of the most important processes in spectrum analysis. [10][11][12][13][14][15][16][17][18] Although baseline correction methods have improved over time, the total elimination of the residual baseline error is still not guaranteed. The bias from the residual baseline error affects the signal at wavenumbers with low absorbance more than those with high absorbance.…”

Section: Theorymentioning

confidence: 99%

Selective Weighted Least Squares Method for Fourier Transform Infrared Quantitative Analysis

Wang

Wei

et al. 2016

Appl Spectrosc

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Classical least squares (CLS) regression is a popular multivariate statistical method used frequently for quantitative analysis using Fourier transform infrared (FT-IR) spectrometry. Classical least squares provides the best unbiased estimator for uncorrelated residual errors with zero mean and equal variance. However, the noise in FT-IR spectra, which accounts for a large portion of the residual errors, is heteroscedastic. Thus, if this noise with zero mean dominates in the residual errors, the weighted least squares (WLS) regression method described in this paper is a better estimator than CLS. However, if bias errors, such as the residual baseline error, are significant, WLS may perform worse than CLS. In this paper, we compare the effect of noise and bias error in using CLS and WLS in quantitative analysis. Results indicated that for wavenumbers with low absorbance, the bias error significantly affected the error, such that the performance of CLS is better than that of WLS. However, for wavenumbers with high absorbance, the noise significantly affected the error, and WLS proves to be better than CLS. Thus, we propose a selective weighted least squares (SWLS) regression that processes data with different wavenumbers using either CLS or WLS based on a selection criterion, i.e., lower or higher than an absorbance threshold. The effects of various factors on the optimal threshold value (OTV) for SWLS have been studied through numerical simulations. These studies reported that: (1) the concentration and the analyte type had minimal effect on OTV; and (2) the major factor that influences OTV is the ratio between the bias error and the standard deviation of the noise. The last part of this paper is dedicated to quantitative analysis of methane gas spectra, and methane/toluene mixtures gas spectra as measured using FT-IR spectrometry and CLS, WLS, and SWLS. The standard error of prediction (SEP), bias of prediction (bias), and the residual sum of squares of the errors (RSS) from the three quantitative analyses were compared. In methane gas analysis, SWLS yielded the lowest SEP and RSS among the three methods. In methane/toluene mixture gas analysis, a modification of the SWLS has been presented to tackle the bias error from other components. The SWLS without modification presents the lowest SEP in all cases but not bias and RSS. The modification of SWLS reduced the bias, which showed a lower RSS than CLS, especially for small components.

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“…The first step in the separation involved establishing an interference matrix including variance due to other components and instrumental noise. Diffraction patterns from samples having zero concentration of the constituent of interest (j) and background eliminated [29] pure component patterns (from either CLS regression vectors or XRPD scans) were modeled via singular value decomposition (SVD). Loadings explaining high variance in the interference matrix (while exhibiting low correlation to the component of interest (k)) were retained for the interference basis set X −j .…”

Section: Separation Of Multi-component Diffraction Patternsmentioning

confidence: 99%

“…The first interference matrix contains diffraction patterns from samples containing zero concentration of the constituent of interest and background eliminated [29] pure component patterns. The reason for eliminating the background should become apparent when considering the disordered components.…”

Section: Diffraction Pattern Separationmentioning

confidence: 99%