A fast progressive spectrum denoising combined with partial least squares algorithm and its application in online Fourier transform infrared quantitative analysis.

Fourier transform infrared (FTIR) spectroscopy is an important method in analytical chemistry. A material can be qualitatively and quantitatively analyzed from its FTIR spectrum. Spectrum denoising is commonly performed before online FTIR quantitative analysis. The average method requires a long time to collect spectra, which weakens real-time online analysis. The Savitzky-Golay smoothing method makes peaks smoother with the increase of window width, causing useful information to be lost. The sparse representation method is a common denoising method, that is used to reconstruct spectrum. However, for the randomness of noise, we can't achieve the sparse representation of noise. Traditional sparse representation algorithms only perform denoising once, and the noise can not be removed completely. FTIR spectrum denoising should therefore be performed in a progressive way. However, it is difficult to determine to what degree of denoising is required. Here, a fast progressive spectrum denoising combined with partial least squares method was developed for online FTIR quantitative analysis. Two real sample data sets were used to test the performance of the proposed method. The experimental results indicated that the progressive spectrum denoising method combined with the partial least squares method performed markedly better than other methods in terms of root mean squared error of prediction and coefficient of determination in the FTIR quantitative analysis.

Simultaneous spectrum fitting and baseline correction using sparse representation.

Sparse representation has been applied in many domains, such as signal processing, image processing and machine learning. In this paper, a redundant dictionary with each column composed of a Voigt-like lineshape is constructed to represent the pure spectrum of the sample. With the prior knowledge that the baseline is smooth and sparse representation coefficient for a pure spectrum, a method simultaneously fitting the pure spectrum and baseline is proposed. Since the pure spectrum is nonnegative, the representation coefficients are also made to be nonnegative. Then through alternating optimization, a surrogate function based algorithm is used to obtain the sparse coefficients. Finally, we adopt one simulated data set and two real data sets to evaluate our method. The results of quantitative analysis show that our method successfully estimates the baseline and pure spectrum and is superior compared to other baseline correction and preprocessing methods.