Inverse obstacle scattering with limited-aperture data

Masaru Ikehata; Esa Niemi; Samuli Siltanen

doi:10.3934/ipi.2012.6.77

Article Contents

2012, Volume 6, Issue 1: 77-94. Doi: 10.3934/ipi.2012.6.77

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Inverse obstacle scattering with limited-aperture data

1.
Department of Mathematics, Graduate School of Engineering, Gunma University
2.
Department of Mathematics and Statistics, University of Helsinki

Received: February 28, 2011

Revised: September 30, 2011

Published: January 2012

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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.

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Mathematics Subject Classification: 65N21, 35J25, 78A46.

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