CAREER: An Integrated Approach to the Study of Inverse Methods in Electrical Engineering

这一职业奖项的目标是制定一个完全综合的职业计划，以满足东北大学电气和计算机工程(欧洲经委会)系学生的教育需求。这项工作所有方面背后的基本主题是对逆问题的研究，这是一个在本科生水平上几乎没有的话题，即使在研究生院也不经常考虑，尽管这些问题在工程和应用科学的许多领域无处不在。在教育活动方面，设想了两个项目。在本科阶段，信号处理一般领域的顶峰设计课程正在开发和实施中。在研究生阶段，一门致力于研究围绕线性逆问题的理论和实践问题的课程正在开发中。在研究领域，我们正在探索使用统计和多尺度信号处理方法来解决非线性电磁逆散射问题。这些算法将结合基于矢量Helholtz方程的格林函数公式的散射模型。正在开发一种基于统计的、多网格类型的算法，用于提取图像和目标信息(目标的数量、位置和分类)。将详细的物理模型直接结合到数据处理算法中，使这些技术直接适用于广泛的问题，包括用于成像和目标检测/分类的雷达信号处理、遥感、微波医学成像和地球物理勘探。

The objective of this CAREER award is to develop a fully integrated career plan designed to meet the educational needs of students in the Electrical and Computer Engineering (ECE) Department of Northeastern University. The underlying theme behind all aspects of this work is the study of inverse problems, a topic which is all but absent at the undergraduate level and not often considered even in the graduate school despite the ubiquity of these problems in many fields of engineering and the applied sciences. In the area of educations activities, two projects are envisioned. At the undergraduate level, a capstone design course in the general area of signal processing is being developed and implemented. At the graduate level, a course devoted to the study of the theoretical and practical issues surrounding linear inverse problems is being developed. In the area of research, we are exploring the use of statistical and multiscale signal processing methods for solving non-linear electromagnetic inverse scattering problems. These algorithms will incorporate scattering models based upon a Green's function formulation of the vector Helholtz equation. A statistically-based, multi-grid-type algorithm for extracting image and target information (number of targets, locations, and classifications) is being developed. The incorporation of detailed, physical models directly into the data processing algorithms makes these techniques directly applicable to a wide range of problems including radar signal processing for image formation and target detection/classification, remote sensing, microwave medical imaging, and geophysical exploration.