**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
*F*1 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
*F*1, 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.