Liliana Borcea
Noah G. Harding Professor of Computational and Applied Mathematics
Rice University
Edge illumination and imaging of extended reflectors
Abstract:
I will talk about an inverse scattering problem for the acoustic wave equation, where the goal is to image reflectors given measurements of echoes at a remote, finite aperture array of receivers. In such problems it is important to recover well the shape of the reflectors, and in particular to emphasize their edges. I will discuss how to use the singular value decomposition of the array response matrix, frequency by frequency, to image selectively the edges of extended reflectors in a homogeneous medium. I will present theory in the Fraunhofer diffraction regime, which explains that information about the edges is contained in the singular vectors for singular values that are intermediate between the large ones and zero. These transition singular vectors beamform selectively from the array onto the edges of the reflector cross-section facing the array, so that these edges are enhanced in imaging with travel time migration. I will also show numerical simulations that illustrate the behavior of our algorithms in an extended Fraunhofer regime, which is more appropriate for ultrasound applications.
This is joint work with George Papanicolaou (Stanford) and Fernando Guevara Vasquez (University of Utah).
Refreshments immediately following in Ewing 536.