Inverse scattering reconstruction of a three dimensional sound-soft axis-symmetric impenetrable object

Abstract

In this work, we consider the problem of reconstructing the shape of a three dimensional impenetrable sound-soft axis-symmetric obstacle from measurements of the scattered field at multiple frequencies. This problem has important applications in locating and identifying obstacles with axial symmetry in general, such as, land mines. We present a two-part framework for recovering the shape of the obstacle. In part 1, we introduce an algorithm to find the axis of symmetry of the obstacle by making use of the far field pattern. In part 2, we recover the shape of the obstacle by applying the recursive linearization algorithm (RLA) with multifrequency measurements of the scattered field. In the RLA, a sequence of inverse scattering problems using increasing single frequency measurements are solved. Each of those problems is ill-posed and nonlinear. The ill-posedness is treated by using a band-limited representation for the shape of the obstacle, while the nonlinearity is dealt with by applying the damped Gauss-Newton method. When using the RLA, a large number of forward scattering problems must be solved. Hence, it is paramount to have an efficient and accurate forward problem solver. For the forward problem, we apply separation of variables in the azimuthal coordinate and Fourier decompose the resulting problem, leaving us with a sequence of decoupled simpler forward scattering problems to solve. Numerical examples for the inverse problem are presented to show the feasibility of our two-part framework in different scenarios, particularly for objects with non-smooth boundaries.

arXiv comment23 pages, 10 figures

References in corpus (7)

• Efficient numerical solution of acoustic scattering from doubly-periodic arrays of axisymmetric objects
• An explicit kernel-split panel-based Nyström scheme for integral equations on axially symmetric surfaces
• A high-order Nystrom discretization scheme for boundary integral equations defined on rotationally symmetric surfaces
• An inverse acoustic-elastic interaction problem with phased or phaseless far-field data
• An FFT-accelerated direct solver for electromagnetic scattering from penetrable axisymmetric objects
• Inverse Obstacle scattering in two dimensions with multiple frequency data and multiple angles of incidence
• Robust integral formulations for electromagnetic scattering from three-dimensional cavities

Cited by in corpus (3)

• A Neural Network Warm-Start Approach for the Inverse Acoustic Obstacle Scattering Problem
• On the robustness of inverse scattering for penetrable, homogeneous objects with complicated boundary
• A highly efficient iterative approach for inverse acoustic obstacle scattering problems in three dimensions