III: Small: Wavelet-Based Representations for Hyperspectral Data Processing and Interpretation

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Hyperspectral imaging systems play an important role in scientific research, especially in planetary and terrestrial geology, environmental monitoring, military and security surveillance, and mineralogy. With current advances in imaging systems technology, large datasets at higher resolutions are being produced and research on automated analysis of these datasets is becoming critical. The goal of this project is to formulate mathematical models for hyperspectral datasets that capture the types of structure commonly identified by practitioners as informative and leveraged semantically in existing ad-hoc methods. The focus is on models based on wavelet representations for spectral signatures in order to provide features that represent the desired multiscale structural information. The features will leverage the wavelet's multiscale time-frequency analysis properties, and will be tested on several labeling, classification, and retrieval problems from a broad range of application areas that are expected to attract underrepresented groups in engineering. This proposal is centered on the application of the proposed models to hyperspectral signal processing and machine learning. The overall goal is to formulate and study new geometric signal models for high-dimensional data and new performance metrics for parameter estimation to be leveraged by new computationally feasible estimation algorithms that (i) are amenable to compressive signal processing due to the use of geometric structure to capture relevant signal information and (ii) overcome the performance shortcomings observed in existing approaches. The formulation of a semantic model for spectral signatures is expected to increase the acceptance of universal representations in applications where processes driven by ad-hoc rules are commonplace. The project broadens participation of underrepresented groups by considering applications areas that have the potential to appeal to diverse communities and constituencies in order to attract interest from a diverse class of populations underrepresented in engineering. Student researchers will be exposed to collaborators from a diverse set of scientific backgrounds and cultures. Opportunities for undergraduate research and high-school teacher research experience will be offered in this project with a particular emphasis on venues serving groups underrepresented in engineering.