Overview

Target detection and classification is a fundamental problem in many applications. The main aim in this problem is to determine the existence of certain targets that might be corrupted with both interferences and noises. The target may be a specific known signal, or signals from a given candidate set. The traditional detection approaches are based on the perfect knowledge of interferences. In practice, however, it is most often difficult to obtain reliable prior information on the interferences embedded in the observed data. Hence, detectors that do not rely on the information about the interference are more desirable in general. In this dissertation, we focus on data-driven methods for target detection and classification that use only the observed data and develop a class of detectors for the detection of both a specific target and targets from a set. We also present a subspace partitioning scheme to enhance the performance of all subspace-based detectors by improving the conditioning of the target subspace. The proposed methods are implemented for Raman spectroscopy in the joint contaminated surface detection (JCSD) system, as well as the appropriate pre-processing and spectral matching techniques for the JCSD system. They have been shown to work effectively in simulations, experiments, and on the field data. For the first problem, detection of a specified target, we develop two data-driven detection methods. The first one uses a constrained independent component analysis (c-ICA) approach. We derive constrained version of the Infomax algorithm and show that a decision can be made on the existence of a certain target by defining a suitable measure of closeness. Then, we develop a second method that uses the upper bound of the correlation between the target and mixing components as the detection index (DCB), and derive the expression for this correlation bound using the observed data. A more common and challenging problem is that of determining the presence of targets in a given mixture without the explicit information on the targets themselves, other than a candidate set. We present a novel detection approach, detection with canonical correlation (DCC) for this problem where we also assume that there is no prior information on the interference. We use the maximum canonical correlations between the target set and the observation data set as the detection statistic, and the coefficients of the canonical vector to determine the indices of components from a given target library, thus enabling both detection and classification of the target components that might be present in the mixture. We derive an approximate distribution of the maximum canonical correlation when targets are present. For applications where the contributions of components are non-negative, non-negativity constraints are incorporated into the canonical correlation analysis framework and a recursive algorithm is derived. The performance of detectors can severely degrade when the target and interference subspace are either singular or have strong linear dependence among its elements. Considering the fact that an ill-conditioned subspace implies the existence of high correlations between linear combinations of the data set components, we propose a subspace partitioning scheme to improve the conditioning of the target subspace by reducing the inner correlations among the linear combinations of the target components. As a result, detection can be performed in a number of better-conditioned subspaces instead of the original ill-conditioned subspace, hence significantly enhancing the detection performance. Finally, the proposed data-driven detection approaches and...

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