NIR Model Transfer Based on Wavelet Transform Algorithms - - Spectroscopy
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NIR Model Transfer Based on Wavelet Transform Algorithms


Spectroscopy
Volume 28, Issue 6, pp. 36-41

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:

  • Select transfer samples and obtain their spectra from the reference and the target instruments, respectively.
  • Determine the wavelet function and decomposition level.
  • Calculate wavelet coefficients of transfer samples from the two instruments, sort the absolute value in descending order, and determine the number (m) of wavelet coefficients for calibration. (This step is the process of noise reduction.)
  • Use the PDS algorithm to calculate the transfer matrixes F1 of selected wavelet coefficients (m) for calibration.
  • Pretreat the spectra signal of unknown samples from the target instrument in the same way, select the same number of wavelet coefficients and correct them with transfer matrixes F1, and lastly, reconstruct the calibrated spectra.
  • Predict the corrected spectra of unknown samples and get the corresponding results, using the NIR model established in the reference instrument.

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:

  • Decompose the NIR spectral data of calibration samples from the reference instrument with wavelet transform, and set the wavelet transform decomposition level. Select wavelet coefficients that are relevant to sample quality, and use the partial least squares (PLS) regression method to set the model.
  • Select transfer samples and obtain their spectra from the reference and the target instruments, respectively.
  • Process the signals of the transfer samples with the same wavelet transform, and select the same wavelet coefficients.
  • Use the PDS algorithm to calculate the transfer matrixes F2 of selected wavelet coefficients.
  • Process signals of unknown samples from the target instrument in the same way, and correct them with transfer matrixes F2.
  • Predict the reconstructed spectra of unknown samples and get the corresponding results, using the NIR model established in the reference instrument.

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:

  • Select transfer samples and obtain their spectra from the reference and target instruments, respectively.
  • Determine mother wavelet and decomposition level n, then process the above-mentioned spectra with wavelet transform.
  • Optimize the window width of the PDS algorithm; the window width of wavelet coefficients in the first level is w, and in the level i is 2 i w. Calculate the transfer matrixes F3 of wavelet coefficients with the PDS algorithm.
  • Obtain NIR spectra of unknown samples from the target instrument. Pretreat them in the same way and calibrate the spectra data with F3.
  • Predict the reconstructed spectra of unknown samples and get the corresponding results, using the NIR model established in the reference instrument.


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