Inverse Problems in Passive and Active Remote Sensing

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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.