Image reconstruction and unique continuation properties
University of Sydney
Date: Tuesday 11 June 2019
Time: 11:00 a.m.
Place: Room 241, 2nd floor, Science III building
A classical result of Jerison-Kenig showed that the optimal assumption for unique continuation properties for elliptic PDE. In this talk we will explore its connection to image reconstruction with impedance tomography. We will develop an analogous theory in the context of partial data inverse problems to obtain the same sharp regularity assumption as Jerison-Kenig. The method we use involves explicit microlocal construction of the Dirichlet Green's function which on its own may be of interest for partial data image reconstruction.