Parsimonious calibration models for near-infrared spectroscopy using wavelets and scaling functions

In this study, the utility of Haar wavelet and Haar scaling function preprocessing of near-infrared (NIR) spectra was investigated in view of obtaining more parsimonious calibration models than using single wavelength selection algorithms. To evaluate these processing schemes, three data sets were analyzed. The first consisted of a previously well-studied set of wheat spectra, with known moisture content values. Also, myoglobin oxygen saturation or sample temperature were quantified from NIR spectra of tissue phantoms. For all of the above spectra, a genetic algorithm was used to choose a simple combination of either wavelengths or wavelets to parsimoniously estimate the property of interest. Since each data set analyzed was known to have different preprocessing requirements to yield low errors of prediction, it was possible to show how adaptable Haar wavelets and scaling functions are under different conditions. The need for trial and error preprocessing to obtain good calibrations was reduced. Furthermore, it was found that multiresolution analysis preprocessing before variable selection led to simpler models with lower errors than single-wavelength selection. In particular, scaling functions (or “son” Haar wavelets) gave the most parsimonious models. Since son wavelet models are easy to interpret and are straightforward to implement in an instrument, Haar scaling function preprocessing is a useful tool for building simplified NIR instrumentation. In the long term, these simplified instruments could be used to improve the speed and accuracy of quantification in on-line processes or clinical measurements.