Quantitative analysis of terahertz signals using CWT-based spectrogram and Zernike image moments

The combination of terahertz (THz) spectroscopic measurements and multivariate calibration techniques has become a well-established technique in many research fields. However, intentional or unintentional changes in environmental conditions, THz instruments and/or of the substance itself make the established calibration model becoming insufficient and inadequate for the further application. In this article, we introduce, discuss, and evaluate a new multivariate calibration method, the CWT-ZM, that combines the merits of the Zernike moment (ZM) invariance and the continuous wavelet transform (CWT) time-frequency analysis. With the help of a wavelet time-frequency analysis, the THz pulse is expanded into a two-dimensional (2D) time-frequency plane that provides richer and more direct characteristic information in the time and frequency domain simultaneously. In addition, Zernike moments provide linearly independent descriptors for the 2D time-frequency intensity image and are invariant to THz signal affine transformations, such as peak shifting, baseline drifting, and scaling. In this manner, we obtain a set of features that exhibit a high capability to capture the concentrations of the target compounds and a high invariance of the different measuring instruments and the variable environment. This approach results in a more robust regression system with improved generalization properties with respect to standard methods. Experiments were then conducted on a THz dataset of pharmaceutical tablets acquired by two different THz instruments, and these confirmed the effectiveness of the proposed approach. Furthermore, CWT-ZM is an extensible framework that can be combined with various spectral qualitative and quantitative analysis algorithms.