Inverse Problems in Passive and Active Remote Sensing

对源辐射的单站(单频)场的观测提供的数据太少，无法唯一地识别源。事实上，有许多非辐射源，它们不以一个或多个频率辐射任何场。然而，首席研究人员已经开发出工具，仅从这些有限和嘈杂的数据中就可以得出关于辐射特定场的一个或多个源的大小和形状的有用结论。特别是，源辐射的远场可以用来计算凸集，该凸集必须包含在真实源的凸壳内(可能更大，但不能更小)。PI继续开发算法来计算这些属性，并根据容易获得的数据开发对源或散射体的其他更详细的描述。PI的方法利用消逝的自然现象来估计来源的大小和位置。许多科学和技术领域，特别是发生在实验室或医学中心的领域，都被数据淹没。遥感技术却没有这种奢侈品。数据通常包括连接到飞机或卫星上的单个雷达天线进行的测量，拖拽在雪地摩托后面，或支撑在两个滑雪者之间。这些数据包含有价值的信息，用于定位地雷、预测雪崩或根据冰雪的特性推断过去气候的变化。然而，在几乎所有的情况下，数据都太有限，无法计算出它正在探测的介质的完整描述。PI的程序是精确地描述人们可以可靠地推断出什么属性，并开发算法来计算它们，即使在存在大量噪声的情况下也是如此。

Observations of the mono-static (single frequency) field radiated by a source provide far too little data to uniquely identify the source. Indeed, there are many non-radiating sources, which do not radiate any field at one or more frequencies. Nevertheless, the principal investigator has developed tools to draw useful conclusions about the size and shape of the source or sources that radiate a particular field from just such limited and noisy data. In particular, the far field radiated by a source can be used to compute a convex set which must be contained within the convex hull of true source (which may be bigger but cannot be smaller). The PI continues to develop algorithms to compute these properties and develop other more detailed descriptions of sources or scatterers from data that is easily acquired. The PI's methods utilize the natural phenomenon of evanescence to estimate the size and location of an source.Many areas of science and technology, especially those that take place in the laboratory or the medical center, are inundated with data. Remote sensing does not share that luxury. Data typically consists of measurements made by a single radar antenna attached to an airplane or a satellite, dragged behind a snowmobile, or supported between two skiers. The data contains valuable information for locating a land mine, predicting an avalanche, or inferring past variations in climate from the properties of snow and ice. However, in virtually all cases, the data is too limited to compute a complete description of the medium it is probing. The PI's program is to describe precisely what properties one can reliably infer, and to develop algorithms to compute them, even in the presence of substantial noise.