Inverse Problems in Remote Sensing

摘要 PI 的目标是为遥感应用开发新的多维数学工具。该项目的主要重点是从有限且嘈杂的数据中得出精确且有用的结论。 PI 和合作者已经开发并继续开发基于多个测量值来查找一个或多个物体的位置和凸几何形状的方法，这些测量可以通过单个移动天线获得。 在固定波数下，消逝现象根据源（支持）的大小限制了传播波（远场）的线性空间的尺寸。 该项目利用这种维度标记作为工具来定位源或散射体、过滤其辐射的信号、估计其大小，甚至可能估计其（良好分离的）组件的数量。消失现象使我们无法使用低频电磁波获得高度详细的图像。 消逝是指携带高空间分辨率所需信息的波的成分随着距物体的距离而快速衰减，以至于从远处看它们实际上是不可见的。在这个项目中，我们正在开发使用消失作为工具的方法，而不是接受它作为限制。根据我们在雷达或声纳阵列的辐射图案中看不到的频率（渐逝模式），我们可以计算位置并估计发射或反射该辐射图案的物体的大小。

AbstractThe PI's goals are to develop new multi-dimensional mathematical tools for remote sensing applications. A primary emphasis of this project is to draw precise and useful conclusions from data that is both limited and noisy. The PI and collaborators have developed and continue to develop methods for finding the location and convex geometry of one or more objects based on multiple measurements that can be obtained with a single mobile antenna. At a fixed wave number, the phenomenon of evanescence limits the dimension of the linear space of propagating waves (far fields) in terms of the size of the (support of the) source. This project utilizes this dimensional marker as a tool for locating a source or scatterer, filtering the signal it radiates, estimating its size and possibly even the number of its (well-separated) components.The phenomenon of evanescence prevents us from obtaining highly detailed images using low frequency electro-magnetic waves. Evanescence refers to the fact that the components of the wave which carry the information necessary for high spatial resolution decay so rapidly with distance from an object, that they are effectively invisible from afar. In this project, we are developing methods to use evanescence as a tool, rather than accepting it as a limitation. Based on the frequencies that we do not see (the evanescent modes) in a radiation pattern at a radar or sonar array, we can calculate the position and estimate the size of the object that emitted or reflected that radiation pattern.