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Friday, November 2, 2007 - 2:00pm

George Papanicolaou

Stanford U

Location

University of Pennsylvania

337 Towne

I will describe how reflectors can be imaged from echoes received at an array of sensors. I will then describe ways in which the edges of the reflectors can be imaged so that their shape can be visualized. It turns out that the best way to image edges is by illuminating the reflectors from the edges of the array. The mathematical framework for analyzing this problem is the singular value decomposition, which in a certain high frequency regime can be determined explicitly using generalized prolate spheroidal functions. These functions have some interesting properties that are particularly useful in assessing image resolution. I will also show the results of extensive numerical simulations. This is joint work with L. Borcea and F. Guevara Vasquez.