Signal and Information Processing in Analysis and Modeling of Complex Structures

在存储和处理大量复杂结构的数据方面，计算技术的进步不可避免地产生了对快速可靠地将数据转换为关于其底层结构的准确信息的需求。感兴趣的结构范围从现代能源基础设施或高光谱图像等人造结构，到活细胞、人体器官或语言。对这些结构进行建模主要是为了分析、预测和/或控制它们的行为。所有这些目的在很大程度上依赖于建模过程的准确性，而建模过程本身又依赖于我们对系统的先验知识和从中获得的数据。提出实用的数据驱动建模方法以及评估模型的有效方案是关键挑战。这些问题在健康相关的系统和结构建模中变得尤为重要，在这些系统和结构中，使用无法验证的不可靠模型可能会导致不可逆的损害。本研究的预期结果是提供可用于优化数据驱动结构建模的性能和成本效率的知识、理论和算法。这一建议的重点是两个具体领域的发展：(1)线性和非线性系统的系统结构数据驱动建模、参数复杂性、阶数选择和模型评估；(2)从数据中学习，重点是数据去噪、分类和压缩，重点是高光谱成像(HSI)。这项研究计划将使从事数据分析和结构建模的行业受益。通过提供可靠和快速的分析，特别是对医用HSI的新应用领域，将在HSI领域产生立竿见影的影响。

Computational technology advances in storing and processing large amounts of complex-structured data have inevitably created a demand for fast and reliable transformation of data to accurate information about its underlying structure. The structures of interest range from man-made ones such as modern energy infrastructures or hyperspectral images, to living cells, organs of the human body or speech. These structures are modeled mainly for the purpose of analysis, prediction, and/or control of their behavior. All of these purposes heavily rely on the accuracy of the modeling process, which itself depends on our prior knowledge of the system and the data available from it. Proposing practical methods for data-driven modeling as well as efficient schemes for evaluating the models are critical challenges. These issues become vital especially in modeling health-related systems and structures where use of an unreliable model that can not be validated may cause irreversible damages.The intended outcome of this research is to provide knowledge, theory, and algorithms that can be applied to optimize performance and cost efficiency of data-driven structural modeling. The focus of this proposal is developments in two specific areas: (1) system structure data-driven modeling, parametric complexity, order selection, and model evaluation for linear and nonlinear systems; and (2) learning from data with a concentration on data denoising, classification, and compression, with a focus on Hyperspectral Imaging (HSI). This research program will benefit industries involved with data analysis and structural modeling. Immediate impact will be seen in the area of HSI by providing reliable and fast analysis, especially for the new application areas of medical HSI.