# Hyperspectral Imaging Sorting of Refurbishment Plasterboard Waste
## 2 Materials and Methods
### HSI-Based Sorting System  
Automated in-line sorting of plasterboard contained in refurbishment plasterboard waste was carried out at laboratory scale by means of a table-top setup based on an HSI system. The HSI system included an advanced HSI camera that provides the complete spectral footprint of every pixel of a sample image, air-cooled tubular halogen lamps and a sliding scanning table. The HSI camera (HySpex short-wavelength infrared-384 model, Norsk Elektro Optikk) was the main component of this experimental setup and worked in the spectral range of shortwave infrared (930-2500 nm). The camera is based on the push-broom scanning method for data recording, by which all spectral wavelengths from a narrow line of a spatial scene are simultaneously measured. Table 1 presents the main characteristics of the camera. The illumination system comprised two halogen 100W/12V lamps, one on each side of the camera, oriented at 45\({}^{\circ}\). The sample moving system consisted of a translation stage with a 1040 mm lab rack and controller. The experimental setup was controlled with a Bre freeze software package (Prediktera) that allowed the recording of hyperspectral images of materials, training and validation of classification models based on machine learning algorithms, and ultimately, running of sorting applications in real-time. The principal component analysis (PCA) and the partial least square discriminant analysis (PLS-DA) algorithms are the multivariate data analysis tools that were applied to build the classification models [6; 11; 16; 17; 18; 19]. On one side, PCA is a statistical tool for exploratory data analysis and attempts to find the hidden structure in large and complex \begin{table}
\begin{tabular}{l l} \hline \hline
**Description** & **Specification** \\ \hline Spectral range & 930–2500 nm \\ Spatial pixels & 384 \\ Spectral channels & 288 \\ Spectral sampling & 5.45 nm \\ Field of view (FOV) & 16\({}^{\circ}\) \\ Pixel FOV across/along & 0.73/0.73 mrad \\ Resolution & 16 bits \\ Maximum speed (at full resolution) & 400 ps \\ Working distance & 21.1 cm \\ Lens & 30 cm close-up lens \\ \hline \hline \end{tabular}
\end{table} 
Table 1: HSI camera characteristics. Figure 1: Collected refurbishment plasterboard waste in Nottingham (United Kingdom). data sets. Hidden structure results from the influence of all variables acting simultaneously and extracting this information reveals, for example, patterns or groupings. Basically, PCA is used to investigate the relationships between samples and measured variables in order to find patterns or groups in the data. It searches for common features, but not for differences between classes. On the other hand, PLS-DA is an algorithm used for the elaboration of linear classification models able to predict the class of unknown samples. The PLS-DA approach consists of building a classification model of all classes, where discrimination is achieved based on inherent class-wise differences. It assumes that any new sample has to belong to just one of the defined classes. For instance, a sample that belongs to class A when the PLS-DA algorithm is applied cannot belong to any other class. The main advantage of PLS-DA is that the relevant sources of data variability are modelled by latent variables, which are a linear combination of the original variables. This allows graphical visualization and understanding of the different data patterns and relations by latent variables scores and loadings [16]. The PLS-DA algorithm for developing classification models of refurbishment plasterboard waste was the only algorithm used in this work because it assigns only one of the available categories, based on its spectral signature, to each unknown sample in the hyperspectral image, making the interpretation of the results easier [17]. Furthermore, this machine learning method has also provided satisfactory results at the laboratory scale with other construction and demolition waste fractions [11; 13; 14; 16].