Abstract
The number of data points of digitally recorded spectra have been limited by the number of multichannel detectors employed, which sometimes impedes the precise characterization of spectral peak shape. Here we describe a methodology to increase the number of data points as well as the signal-to-noise (S/N) ratio by applying Bayesian super-resolution in the analysis of spectroscopic data. In our present method, first, the hyperparameters for the Bayesian super-resolution are determined by a virtual experiment imitating actual experimental data, and the precision of the super-resolution reconstruction is confirmed by the calculation of errors from the ideal values. For validation of the super-resolution reconstruction of spectroscopic data, we applied this method to the analysis of Raman spectra. From 200 Raman spectra of a reference Si substrate with a data interval of about 0.8 cm−1, super-resolution reconstruction with a data interval of 0.01 cm−1 was successfully achieved with the promised precision. From the super-resolution spectrum, the Raman scattering peak of the reference Si substrate was estimated as 520.55 (+0.12, −0.09) cm−1, which is comparable to the precisely determined value reported in previous works. The present methodology can be applied to various kinds of spectroscopic analysis, leading to increased precision in the analysis of spectroscopic data and the ability to detect slight differences in spectral peak positions and shapes.
Highlights
Spectroscopy is utilized in various research fields such as physics, chemistry, agriculture and medical science, and delivers valuable insights and knowledge
The average error of the reconstructed spectrum with a narrow data interval from the Lorentz function was as low as 3.31, which is almost the same as the estimated standard deviation obtained with 200 measurements (σ200 = 3.01), which indicates that the Bayesian super-resolution succeeded in achieving both high resolution by Bayesian super-resolution and the reduction of noise by data accumulation
The current results indicate that by applying Bayesian super-resolution to data from multiple measurements of Raman spectra obtained by a commercial chargecoupled device (CCD) Raman apparatus, one can estimate the Raman shift with similar precision to that obtained by high-reliability methods
Summary
Spectroscopy is utilized in various research fields such as physics, chemistry, agriculture and medical science, and delivers valuable insights and knowledge. Bayesian image super-resolution is a method to combine a set of low-resolution images of the same view with sub-pixel displacements relative to each other using Bayes’ rule in order to obtain a single image of higher resolution. In the field of digital image processing, “resolution” means the pixel interval length, which is calculated by dividing the width of the image into the number of pixels. This is totally different from the meaning of spectral resolution, which is defined as the minimum wavenumber, wavelength, or frequency difference between two lines in a spectrum that can be distinguished. The word “super-resolution” is used to mean not that the spectral resolution is increased, but that the data interval is narrowed
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