Recovering piecewise constant refractive indices by a single far-field pattern

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http://hdl.handle.net/10138/320394

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Blasten , E & Liu , H 2020 , ' Recovering piecewise constant refractive indices by a single far-field pattern ' , Inverse Problems , vol. 36 , no. 8 , 085005 . https://doi.org/10.1088/1361-6420/ab958f

Title: Recovering piecewise constant refractive indices by a single far-field pattern
Author: Blasten, Emilia; Liu, Hongyu
Contributor: University of Helsinki, Department of Mathematics and Statistics
Date: 2020-08
Number of pages: 16
Belongs to series: Inverse Problems
ISSN: 0266-5611
URI: http://hdl.handle.net/10138/320394
Abstract: We are concerned with the inverse scattering problem of recovering an inhomogeneous medium by the associated acoustic wave measurement. We prove that under certain assumptions, a single far-field pattern determines the values of a perturbation to the refractive index on the corners of its support. These assumptions are satisfied, for example, in the low acoustic frequency regime. As a consequence if the perturbation is piecewise constant with either a polyhedral nest geometry or a known polyhedral cell geometry, such as a pixel or voxel array, we establish the injectivity of the perturbation to far-field map given a fixed incident wave. This is the first unique determinancy result of its type in the literature, and all of the existing results essentially make use of infinitely many measurements.
Subject: inverse medium scattering
uniqueness
single far-field pattern
value at corner
piecewise constant
polyhedral
CAUCHY DATA
CORNERS
UNIQUENESS
111 Mathematics
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