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

高光谱成像系统在科学研究中发挥着重要作用，特别是在行星和陆地地质学、环境监测、军事和安全监视以及矿物学方面。随着当前成像系统技术的进步，正在产生更高分辨率的大型数据集，并且对这些数据集的自动分析的研究变得至关重要。该项目的目标是制定高光谱数据集的数学模型，捕获从业者通常确定的结构类型，作为信息和利用现有的特设方法的语义。重点是基于小波表示的光谱特征的模型，以提供代表所需的多尺度结构信息的功能。这些功能将利用小波的多尺度时频分析特性，并将在多个标签，分类和检索问题上进行测试，这些问题来自广泛的应用领域，预计将吸引工程中代表性不足的群体。该建议的核心是将所提出的模型应用于高光谱信号处理和机器学习。 总体目标是制定和研究用于高维数据的新几何信号模型和用于参数估计的新性能度量，以由新的计算上可行的估计算法来利用，所述新的计算上可行的估计算法（i）由于使用几何结构来捕获相关信号信息而适于压缩信号处理，以及（ii）克服在现有方法中观察到的性能缺点。光谱签名的语义模型的制定，预计将增加普遍表示在应用程序中，由特设规则驱动的过程是司空见惯的接受。该项目通过考虑有可能吸引不同社区和选区的应用领域来扩大代表性不足的群体的参与，以吸引在工程中代表性不足的不同群体的兴趣。学生研究人员将接触到来自不同科学背景和文化的合作者。本科生研究和高中教师研究经验的机会将在这个项目中提供，特别强调场地服务于工程代表性不足的群体。

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.