Methods based on wavelet transform such as denoising, compression, and multiscale analysis were developed for near infrared (NIR) analysis model transfer of an amine mixture to improve the precision of piecewise direct standardization (PDS). Transfer samples and correlative parameters based on wavelet denoising and piecewise direct standardization (WDPDS), wavelet compression and piecewise direct standardization (WCPDS), and wavelet multiscale and piecewise direct standardization (WMPDS) were studied, and the optimal conditions were confirmed.
Near infrared (NIR) spectroscopy analysis has many advantages: It has a high analysis speed and high accuracy, it provides simultaneous determination of multiple components, it is nondestructive, and it causes zero pollution. It has been widely used in the food, medicine, and petrochemical industries. NIR spectra are susceptible to noise and background interference because of the broad and overlapped bands and smaller absorption coefficients. So, it is very important to adopt appropriate methods to reduce noise, compress variables, and improve NIR model speed and precision. Wavelet transform is already an important tool in signal processing because of its property of time-frequency localization. It is widely used in noise reduction, data compression, and background subtraction of NIR spectra (1–3).
Calibration transfer is a technique for transferring a NIR calibration model from a reference analytical instrument to a target analytical instrument that may be a different instrument, or the same instrument at a later time (4,5). Piecewise direct standardization (PDS) is a general and successful model-transfer algorithm; it can select the optimized window width of the spectral range for correction (6). However, the PDS algorithm is only dependent on a fixed-size window width in the entire spectral range, and there are too many transfer data variables. Consequently, the precision of calibration transfer needs to be further improved.This study uses an amine mixture as an example to discuss the combination of wavelet and PDS algorithms, which will improve the precision of NIR model transfer. Also, the transfer effects are compared among the denoising, compression, and multiscale wavelet transform methods.
Fundamentals and Algorithms
Wavelet Denoising and Piecewise Direct Standardization
The wavelet denoising and piecewise direct standardization (WDPDS) algorithm (7) combines wavelet denoising and PDS. First, the signal NIR spectra are decomposed with wavelet transform and the smaller absolute value of coefficients are removed. Then, the rest of the wavelet coefficients are directly used in PDS transfer. Lastly, the spectra are reconstructed based upon the calibrated wavelet coefficients. The specific steps are as follows:
Wavelet Compression and Piecewise Direct Standardization
The wavelet compression and piecewise direct standardization (WCPDS) algorithm (8,9) combines wavelet compression with PDS. Wavelet compression participates in both the establishment of the NIR model in the reference instrument and NIR model transfer. The concrete steps are as follows:
Wavelet Multiscale and Piecewise Direct Standardization
The wavelet multiscale and piecewise direct standardization (WMPDS) algorithm (10) takes advantage of the multiresolution analysis features of wavelet transformation. Wavelet function and decomposition level are determined according to needs, the difference between instruments is decomposed into wavelet coefficients of each layer, and the window widths of PDS algorithm are adjusted to the changes of wavelet coefficients. The specific steps are as follows: