Inverse obstacle scattering with limited-aperture data

Abstract

Inverse obstacle scattering aims to extract information about distant and unknown targets using wave propagation. This study concentrates on a two-dimensional setting using time-harmonic acoustic plane waves as incident fields and taking the obstacles to be sound-hard with smooth or polygonal boundary. Measurement data is simulated by sending one incident wave towards the area of interest and computing the far field pattern (1) on the whole circle of observation directions, (2) only in directions close to backscattering, and (3) only in directions close to forward-scattering. A variant of the enclosure method is introduced, based on applying the far field operator to an explicitly constructed density, yielding information about the convex hull of the obstacle. The numerical evidence presented suggests that the convex hull of obstacles can be approximately recovered from noisy limited-aperture far field data.

Data recovery in inverse scattering: From limited-aperture to full-aperture

“…Various reconstruction algorithms using limited-aperture data have been developed [1,3,10,12,14,17,20,21,25]. Although uniqueness of the inverse problems can be proved in some cases [8], the quality of the reconstructions are not satisfactory.…”

A novel study on subspace migration for imaging of a sound-hard arc

“…The main subject of this paper is the imaging of sound-hard arc in homogeneous space. An extension to limited-aperture problem [17,18,19] or the half-space problem [20,21,22,23] will be an interesting research subject. Finally, we expect the analysis presented in this paper could be extended to three-dimensional problems [24,25,26] and real-world application such as biomedical imaging [27,28,29].…”

Localization of small obstacles from back-scattered data at limited incident angles with full-waveform inversion

“…Recall that the single-layer operator S J and the Fourier nodes w J,l are defined in (7) and (6). At each index k, the quantities in the parentheses of (40) are row vectors of size N par . The contraction · (J,l)…”

“…In this subsection, we consider a structured configuration of twelve soft-scattering obstacles centered at (22,32), (26,32), (30,32), (34,32), (22,36), (26,36), (30,36), (34,36), (22,40), (26,40), (30,40), (34,40), inside a domain of size 56 × 72. We use four angles of radiation for the data, sending planewaves from all four sides of the domain.…”