Detection of multiple impedance obstacles by non-iterative topological gradient based methods

Abstract

We investigate a fast, one-step imaging method of multiple 2D and 3D acoustic obstacles fully-coated by a complex surface impedance with either monochromatic or multi-frequency noisy data. Introducing the topological gradient of the misfit functional as a limit of shape derivatives, closed-form expressions of the obstacle indicator are derived using Fourier and Mie series expansions of the radiating solution. We provide a wide variety of numerical experiments that assesses the performance and limitations of the one step single and multi-frequency imaging strategies when dealing both with full and limited aperture measurements.