Fast reconstruction of Raman spectra based on global weighted linear regression
Introduction
Raman spectroscopy has the advantages of no damage, no marking and no interference from water [1,2], etc. It can obtain the spectral information on tissues or cells under the close physiological conditions. Therefore, it has become a diagnostic or analytic tool for various diseases [3,4]. However, slow data acquisition of Raman spectra has seriously hindered the expansion of its application. In order to improve the speed of data acquisition of Raman spectra and the high resolution of Raman imaging, the researchers have done a lot research.
In order to settle this problem, several methods [5] have been explored. The first one is line scanning: a laser spot is concentrated on the surface of the sample by scanning along a line and the corresponding Raman spectral signals are imaged on the CCD of the spectrometer. It has achieved the purpose of simultaneously collecting multiple spectra, and effectively improved the speed of scanning. However, it is still time-consuming. Simultaneously, the resolution of Raman imaging can only reach the level of a few microns. The other one is Wide-Field imaging. By exciting the sample in a Wide-Field, the Raman scattering is directly coupled to the surface of CCD, and wavelength of the passed signal is converted to single wavelength imaging by using a Liquid crystal tunable filter (LCTF) [6]. Compared to line scanning, Wide-Field imaging can achieve a higher resolution and a better dynamic performance. However, it can only collect spectra of single wavelength at two spatial dimensions.
Therefore, it is important to develop an algorithm which is cost-effective and fast in data acquisition of Raman spectra. In this paper, an algorithm based on the fast reconstruction of Raman spectra has been put forward: Firstly, we get the Raman spectra set R of the sample A and the corresponding multi-channel measurements set U. Secondly, the transform Matrix W between R and U is established. Finally, the Raman spectrum of sample A is reconstructed by the multi-channel measurements u and W. All the above are shown in Fig. 1. In the process of fast reconstruction of Raman spectra, the solution to the transform matrix W is particularly critical. In 2005, D. R. Connah etc. [7] applied polynomial regression to multi-spectral imaging systems and achieved rapidly reconstruction of spectral reflectance. In 2013, Shuo Chen etc. [8] proposed a fast reconstruction of Raman spectra from narrow-band measurements based on Wiener estimate.
In the above algorithms, the solution to the transform matrix W, either ignores the influence of nonlinear factors, or disregard the optimization of the training samples. Therefore, a new algorithm is proposed in this paper. Firstly, the polynomial regression is performed on the multi-channel measurements in order to reduce the influence of nonlinear factors. Secondly, a linear regression function is established by optimizing the training samples and making a global assignment weighted to the optimizing samples. Finally, the reconstruction of Raman spectra is quickly achieved, by introducing the normalization and cross-validation algorithms. In addition, the quality of the reconstruction of Raman spectra will be determined based on the root mean square error (RMSE).
Section snippets
Reconstructed spectra based on global weighted linear regression
The Raman spectra set R of sample A (A is shown in Fig. 1) is obtained by taking a conventional Raman spectrometer(composed of QE65Pro, Raman fiber probe, and 785 nm laser illumination), which are used as training samples. The corresponding multi-channel measurements set U are achieved by calculating the inner product between each Raman spectrum of R and the spectral response function matrix of the band-pass filters at the wavenumbers of the characteristic peak. And so far, the preparation for
Spectral preprocessing
In this paper, ethanol and lactic acid are used as experimental samples. Measuring the concentration of 50% ethanol solution by a conventional Raman spectrometer and obtaining a training sample set of ethanol, k represents the number of measurement. The concentration of 45%, 55% ethanol solution and lactic acid solution are measured ten times. Taking the best one from ten as the spectra to be detected and setting as,and, respectively. In order to improve the
Conclusion
In this paper, a fast algorithm for the reconstruction of Raman spectra based on Global weighted linear regression from multi-channel measurements is developed. This algorithm improves the accuracy of reconstruction by optimizing the training samples and making a global assignment weighted to the optimizing samples. According to the RMSE, it proves that this algorithm is 78.2% higher than the Pseudo-inverse Method in the accuracy of the Raman spectrum reconstructed. Simultaneously, it can be
CRediT authorship contribution statement
Xian-guang Fan: Resources, Supervision. Long Liu: Conceptualization, Methodology, Validation, Formal analysis, Writing - original draft, Writing - review & editing. Zhe-ming Kang: Investigation. Ying-jie Zeng: Writing - review & editing. Yu-liang Zhi: Writing - review & editing. Ying-jie Xu: Writing - review & editing. Jia-jie Zhang: Writing - review & editing. Xin Wang: Resources, Funding acquisition, Project administration, Supervision.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgement
The authors would like to acknowledge financial support from Natural Science Foundation of China (No.21874113).
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