The factorization method for inverse acoustic scattering by a penetrable anisotropic obstacle

Abstract

This paper is devoted to studying the factorization method applied to the inverse problem of reconstructing a penetrable anisotropic obstacle from far field patterns. We proved the validity of the factorization method. Copyright © 2013 John Wiley & Sons, Ltd.

Analysis of new direct sampling indicators for far-field measurements

“…In our analysis, we will consider the time-harmonic acoustic scattering problem for anisotropic media. The LSM and FM have been applied to the inverse scattering problem of recovering the scatterer from the measured far-field pattern in [6] and [19], respectively. We now derive two DSMs for this inverse shape problem.…”

The factorization method for scatterers with different physical properties

“…Here, S 1i denotes the single layer operator S 1 with the wave number k = i. (11), then z ∈ D if, and only if, φ z belongs to the range R(G) of G.…”

“…The case of scattering by obstacles with impedance boundary conditions has been treated in [4,10,13]. In [7] and, more satisfactory, in [2,8,11] it has been extended to the scattering by an inhomogeneous medium. Recently, the factorization method has also been applied to reconstruction of penetrable obstacles with buried objects [1,18] and to reconstruction of impenetrable cavities with interior measurements [15].…”

“…Assume that k 2 is neither a Dirichlet eigenvalue of −∆ in D 1 , Ω 2 nor a Neumann eigenvalue of −∆ in D 2 , Ω 1 . For any z ∈ R n define again φ z ∈ L 2 (S n−1 ) by (11). (a) A point z ∈ R n \Ω 2 belongs to D 1 if, and only if, the function φ z belongs to the range of the operator (H * 1 , H 2 *…”

A modification of the factorization method for scatterers with different physical properties

“…For recent works discussing this case, we refer to previous studies. [5][6][7][8][9] In this paper, we study the factorization method for a scatterer consisting of two objects with different physical properties. Especially, we consider the following two cases: One is the case when each object has the different boundary condition, and the other one is when different penetrability.…”