ROBUST DETECTION AND SPECTRAL ANALYSIS OF SIGNALS WITH APPLICATIONS IN SPECTROSCOPY

Modern spectroscopic techniques, such as nuclear quadrupole resonance (NQR), nuclear magnetic resonance (NMR), and Raman spectroscopy, rely heavily on statistical signal processing systems for decision making and information extraction. The first part of this thesis introduces novel robust algorithms for detection, estimation, and classification of signals obtained through these spectroscopic techniques. More specifically, the problem of NQR-based detection of illicit materials is considered in detail. Several single- and multi-sensor algorithms are introduced that posses many features of practical importance, including: (a) robustness to uncertainties in the assumed spectral amplitudes, (b) exploitation of the polymorphous nature of relevant compounds to improve detection, (c) ability to quantify mixtures, and (d) efficient estimation and cancellation of background noise and radio frequency interference (RFI). For the case of NMR spectroscopy, a subspace-based parameter estimation algorithm is proposed that allows for inclusion of partly uncertain prior knowledge about the spacing between spectral lines, thereby aiding the process of automating the estimation procedure. The final topic in the first part concerns the standoff detection of explosives using Raman spectroscopy. In this regard, a computationally efficient classification scheme is introduced, that can, at a distance of 30 meters, or more, successfully classify measured Raman spectra from several explosive substances, including Nitromethane, TNT, DNT, Hydrogen Peroxide, TATP, and Ammonium Nitrate.

The second part of the thesis addresses the more fundamental problem of estimating high-resolution spectra from non-uniformly sampled sequences with sparse spectra. Estimators are developed for both the power spectral density (PSD) and the magnitude squared coherence (MSC) spectrum. A nonparametric Capon-based MSC estimator is proposed that allows for unevenly sampled data as well as for sequences with arbitrarily missing samples. A high-resolution PSD estimator is also introduced that handles unevenly sampled multidimensional data. Finally, we introduce robust Capon- and APES-based MSC spectral estimators that provide substantially higher resolution as compared to the earlier MSC estimators. The proposed estimators are formulated to allow for an uncertainty in the assumed sampling vector, which can be viewed as a corresponding uncertainty in the sample correlation matrix estimate, and can thus instead, or as well, allow for a poorly conditioned, or even rank-deficient, matrix estimate.