Monotonicity in inverse obstacle scattering on unbounded domains

Uniqueness Theorems for Inverse Obstacle Scattering Problems in Lipschitz Domains

For the Neumann and Robin boundary conditions the uniqueness theorems for inverse obstacle scattering problems are proved in Lipschitz domains. The role of non-smoothness of the boundary is analyzed.

Inverse obstacle scattering in the time domain

This work is a study of the extension of an inverse obstacle scattering algorithm for fixed, single-frequency data to multi-frequency time-dependent settings. The inversion algorithm is based on the point source method, which reconstructs scattered fields pointwise with respect to frequency. We use Fourier transforms to obtain the time-dependent scattered fields as superpositions of single-freq...

Inverse obstacle scattering for elastic waves

Complex Spherical Waves and Inverse Problems in Unbounded Domains

This work is motivated by the inverse conductivity problem of identifying an embedded object in an infinite slab. The novelty of our approach is that we use complex spherical waves rather than classical Calderón type functions. For Calderón type functions, they are growing exponentially on one side of a hyperplane and decaying exponentially on the other side. Without extra modifications, they a...

Huygens' principle and iterative methods in inverse obstacle scattering

The main purpose of this paper is to establish relations between three iterative numerical methods based on Huygen’s principle that arose almost simultaneously to solve a particular inverse problem. The inverse problem we consider in this paper is to determine the shape of an obstacle from the knowledge of the far field pattern for scattering of time-harmonic plane waves. In the case of scatter...