Frechet derivatives in inverse obstacle scattering

Hettlich, Frank

doi:10.1088/0266-5611/11/2/007

Cited by 151 publications

(150 citation statements)

References 3 publications

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“…• Iterative TD methods allow for topological changes during the iterations, in contrast to classical shape deformation strategies [11,13,19] that require knowledge of the number of objects from the start. Using iterative TD based methods, new objects may be created in the course of the iterations, existing contours may merge and holes inside existing objects may be detected, see [2,3].…”

Section: Iterative Methods To Reconstruct Inclusions and Parametersmentioning

confidence: 99%

Domain and Parameter Reconstruction in Photothermal Imaging

Carpio

Rapún

2016

Mathematics in Industry

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In this work we address the inverse problem of reconstructing inclusions and their thermal parameters given temperature measurements at the accessible side of a material. We describe an iterative descent method that combines topological derivative computations to reconstruct the geometry of the defects with gradient iterations to approximate the material parameters. A numerical experiment showing the ability of the method to obtain reasonable reconstructions in a few iterations is presented.

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Section: Iterative Methods To Reconstruct Inclusions and Parametersmentioning

confidence: 99%

Domain and Parameter Reconstruction in Photothermal Imaging

Carpio

Rapún

2016

Mathematics in Industry

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“…In order to prove the main theoretical result of the paper, we introduce some useful identities (see [2] [12]) without proof.…”

Section: Domain Derivative Methodsmentioning

confidence: 99%

“…Kress proposed a quasi-Newton method to solve inverse scattering problem in [1]. Hettlich solved the inverse obstacle scattering problem for sound obstacles problem [2], and discussed a discontinuity in a conductivity from a single boundary measurement [3].…”

Section: Introductionmentioning

confidence: 99%

Shape Identification for Stokes-Oseen Problem Based on Domain Derivative Method

Yan¹,

Hou²

2015

JAMP

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In this paper, we consider the shape identification problem of a body immersed in the incompressible fluid governed by Stokes-Oseen equations. Based on the domain derivative method, we derive the explicit representation of the derivative of solution with respect to the boundary. Then, according to the boundary parametrization technique, we propose a regularized Gauss-Newton algorithm for the shape inverse problem. Finally, numerical examples indicate that the iterative algorithm is feasible and effective for the practical purpose.

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“…Although the linearization of the homogeneous boundary Neumann condition (see [30]) is slightly more technical than the linearization of the homogeneous Dirichlet condition as described above, it is considerably less involved than the derivation of the boundary condition for the corresponding boundary to far field map F for the sound hard case (see [12]). …”

Section: Decomposition Methods Revisitedmentioning

confidence: 99%

Huygens’ principle and iterative methods in inverse obstacle scattering

2009

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The inverse problem we consider in this paper is to determine the shape of an obstacle from the knowledge of the far field pattern for scattering of time-harmonic plane waves. In the case of scattering from a sound-soft obstacle, we will interpret Huygens' principle as a system of two integral equations, named data and field equation, for the unknown boundary of the scatterer and the induced surface flux, i.e., the unknown normal derivative of the total field on the boundary. Reflecting the ill-posedness of the inverse obstacle scattering problem these integral equations are ill-posed. They are linear with respect to the unknown flux and nonlinear with respect to the unknown boundary and offer, in principle, three immediate possibilities for their iterative solution via linearization and regularization. In addition to presenting new results on injectivity and dense range for the linearized operators, the main purpose of this paper is to establish and illuminate relations between these three solution methods based on Huygens' principle in inverse obstacle scattering. Furthermore, we will exhibit connections and differences to the Communicated by guest editors:

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Frechet derivatives in inverse obstacle scattering

Cited by 151 publications

References 3 publications

Domain and Parameter Reconstruction in Photothermal Imaging

Domain and Parameter Reconstruction in Photothermal Imaging

Shape Identification for Stokes-Oseen Problem Based on Domain Derivative Method

Huygens’ principle and iterative methods in inverse obstacle scattering

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