Inverse Problems in Remote Sensing

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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.