Resolution and stability analysis in full-aperture, linearized conductivity and wave imaging (Q2845419)

The inverse conductivity problem is to find a conductivity inclusion from boundary measurements. The problem lays a mathematical foundation to electrical impedance tomography. The same mathematical model works in a variety of applications, such as breast cancer imaging and mine detection. The main objective of this paper is to introduce the notion of resolution in solving the inverse conductivity problem and to precisely quantify some important non-intuitive facts in imaging. The paper provides explicit formulas for the resolving power of the measurements in the presence of measurement noise. Resolution estimates in both the linearized conductivity problem and in the wave imaging problem are considered. It is demonstrated that the low-frequency regime in wave imaging and the inverse conductivity problem are very sensitive to measurement noise, while high frequencies increase stability in wave imaging.