On the recovery of boundary impedance for 3-dimensional obstacle by acoustic wave scattering using modified Kaczmarz iteration algorithm

The boundary impedance coefficient for an impenetrable obstacle represents its absorption ability for the incident waves, and consequently its indirect detection is of great importance in remote sensing, with the aim of detecting the property of obstacle boundary. We address an inverse acoustic scattering problem for a three-dimensional obstacle, focusing on the reconstruction of boundary impedance using the far-field pattern of the scattered wave corresponding to given incident plane waves. A two-point gradient method combined with the Kaczmarz type scheme is proposed to obtain satisfactory reconstruction. The iteration scheme is formulated by applying the adjoint operator for the forward scattering, based on the potential representation of the scattered wave. The convergence property of the iteration process is rigorously proved. To address the computational scheme for the surface potentials, we use an efficient numerical scheme tailored for three-dimensional geometries. Numerical experiments are presented to demonstrate the validity and robustness of our proposed approach.