George C. PAPANICOLAOU
Department of Mathematics, Stanford University
Imaging in complex environments

Abstract: Imaging in its many forms is a very rapidly advancing interdisciplinary science that is deeply rooted in modern applied mathematics: In wave propagation (migration or back-propagation methods), diffusion, impedance and x-ray tomography, statistical denoising and classification, as well as in fast computational methods for dealing with very large data sets. I will present some recently developed methods for imaging with array and distributed sensors when the environment between the objects to be imaged and the sensors is complex and only partially known to the imager. This brings in modelling and analysis in random media, and the need for statistical algorithms that increase the computational complexity of imaging. I will illustrate the theory with applications from non-destructive testing and from other areas.