Studies On The Terahertz Time-domain Spectroscopy Ignal Analysis And Substance Identification Methods Ased On The Geometric Algebra

Terahertz technology is the frontier of the current science and technology studyfields, the terahertz time-domain spectroscopy (THz-TDS) is an important explorationtechnology in the research field of the terahertz science and technology. THz-TDSsignals contain abundant information, and present a unique fingerprint of the material,which can be used for the material identification. How to represent, process and analyzeTHz-TDS signals effectively, and how to utilize the information of signals effectively inthe substance identification, those are the important problems needed to be solved in thestudy of THz-TDS technology.Recent studies show that there are often no obvious peaks in THz-TDS signals, andit is needed to adopt the entire THz-TDS spectra as the substance fingerprint foranalysis and processing. One THz-TDS signal of the entire spectral band can beregarded as a vector in the multi-dimensional vector space. In order to extract andutilize the tremendous information of THz-TDS signals effectively, there is an urgentdemand to develop new signal processing and analysis methods systematically anddeeply. Therefore, the geometric algebra (GA) is brought into the THz-TDS signalanalysis and processing to the characters of THz-TDS signals in this paper, newsubstance identification methods of THz-TDS signals are developed based on GA.Specifically, major contributions of this dissertation are as follows:1. Based on the physical mechanism of the transmission model THz-TDS system,the geometric algebra framework for the THz-TDS signals analysis is constructed, andthe signal analysis method is developed. In the method, both the magnitude and phaseinformation of THz-TDS signals are utilized, and one THz-TDS signal of the entirespectral band is regarded as a vector in the high-dimensional real vector space.Geometrical distribution characteristics and algebraical relations of the THz-TDS signalvectors are studied, which reveal the corresponding relationships between the opticalconstants of the substance and THz-TDS signal vectors.2. Based on the results of the geometric algebra analysis of THz-TDS signals, anouter product similarity function and the Euclidean distance of the THz-TDS signals aredefined respectively using the geometric product. Detailed computation formulas ofthese two similarity measures are derived, with their computational complexitiesdiscussed. The substance classification method based on the THz-TDS signals based on those metrics is proposed. Experiments on the substance classification verify thefeasibility and validity of the similarity function. Other similarity metrics of THz-TDSsignals and their gradient feature vectors using the joint entropy and mutual informationare studied and compared with the metrics defined by the geometric procduct.Comparative experiment shows the advantages of the outer product similarity function.3. The projective split of the THz-TDS signal and its properties are studied. Byanalyzing properties of THz-TDS signals’ metrics under the principle componentanalysis (PCA) and PS, a new dimensionality reduction method of THz-TDS signalsbased on PCA is proposed and applied to signal classification and recognition. Thismethod can effectively realize the dimensionality reduction and the signal denoising,facilitate the feature extraction, contribute to the accurate classification andidentification. Experiments on the classification of THz signals not only verify theeffectiveness of our method, but also show its potential ability in the visualization ofTHz signals and images. The simulated experiments on the signals identification alsoshow that our method is better than the traditional PCA and has better anti-noise ability.4. The conformal split and its properties is studied, the conformal split ofTHz-TDS signal is presented with properties studied. Accordingly, two criteria forsubstance identification are proposed, and a novel substance identification method viathe conformal split is presented. In the method, using the conformal split with respect to2-blades of the “known” substances, one THz-TDS signal is related to vectors insubspaces of substances. The substance can be identified using criteria in the subspaces.The presented methods are applied in experiments of the substance identification, andalso compared with the component spatial pattern analysis (CSPA) method.Experiments show its feasibility and greater accuracy.5. From the signal sparse representation and the results of the THz-TDS analysis,THz-TDS signal vectors can be sparsely represented in an overcomplete dictionary, anda signal classification method via the sparse representation is presented. In the method,an optimal construction of the overcomplete dictionary is developed based on thegeometrical distribution and the algebraic structure properties of signal vectors, thesignal classification model is modified to account for possibly noise, and the test sampleis classified using either the maximized coefficient or the minimized residual.Feasibility and effectiveness of the method is confirmed by experiments presented.Study results in this paper show that the geometric algebra analysis method haspotential ability in the THz-TDS signal analysis and processing, and it will help thedevelopment and application of the substance identification technology based on THz-TDS signals.