Inverse Problems in Remote Sensing

PI的目标是为遥感应用开发新的多维数学工具。这个项目的一个主要重点是从既有限又有噪音的数据中得出准确和有用的结论。PI和合作者已经开发了并继续开发基于可以用单个移动天线获得的多个测量来寻找一个或多个物体的位置和凸起几何形状的方法。在固定的波数下，消逝现象限制了传播波(远场)的线性空间的维度，这取决于源(支撑)的大小。这个项目利用这种维度标记作为一种工具来定位源或散射体，对其辐射的信号进行滤波，估计其大小，甚至估计其(良好分离的)组件的数量。渐变是指这样一个事实，即携带高空间分辨率所需信息的波的分量随着距离物体的距离衰减得如此迅速，以至于它们实际上在远处是看不见的。在这个项目中，我们正在开发将消逝作为一种工具的方法，而不是接受它作为一种限制。根据我们在雷达或声纳阵列的辐射方向图中看不到的频率(消失模式)，我们可以计算发射或反射该辐射方向图的对象的位置和大小。

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.