In this paper, we consider the inverse scattering problem of recovering the shape of a cavity or the surface impedance from one source and a knowledge of measurements placed on a curve inside the cavity. Based on a potential approach the inverse problem is equivalent to a system of nonlinear and ill-posed integral equations, a regularized Newton iterative approach is applied to reconstruct the boundary and the injectivity for the linearized system is established. Numerical examples are provided showing the viability of our method.
"Reconstruction for cavities with impedance boundary condition." J. Integral Equations Applications 25 (3) 431 - 454, FALL 2013. https://doi.org/10.1216/JIE-2013-25-3-431