Sensor Imaging
Monday January 28, 2008
11:00AM - 12:00PM
Speakers:
George Papanicolaou
Abstract:
Imaging to a mathematician is a special class of inverse problems in analysis, differential equations and probability, which are typically ill-posed.
They have played an important role in the development of mathematical methods that turned out to have broader significance and applicability.
But in the sciences and in engineering imaging can mean many different things, including the recovery of the approximate location and properties of an object from the echoes of waves received at various sensors placed in the environment of the object.
Seismic imaging, sonar, radar, diagnostic imaging with ultrasound, etc., are examples. There is now an emerging interdisciplinary science of sensor imaging that has an interesting mathematical theory. In this lecture I will describe the basic elements of this theory. I will also compare the theoretical performance of some special ultrasonic imaging systems to the actual performance of similar systems in nature, the ones used by the dolphin and by the bat.
Not surprisingly, evolution has created bio-sonar systems that perform much better than current theories predict. What is missing in our theoretical understanding?
George Papanicolaou
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