Optimal Mesh Size for Inverse Medium Scattering Problems

Ammari, Habib; Chow, Yat Tin; Liu, Keji

doi:10.1137/18m122159x

Cited by 7 publications

(6 citation statements)

References 35 publications

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“…We have also checked that the method is very robust in connection with this issue. For a discussion about the selection of optimal meshes for the evaluation of indicator functions, we refer to [41]. These results provide the initial stage to implement iterative corrections, as we explain in Section 5.…”

Section: Multifrequency Methodsmentioning

confidence: 99%

Multifrequency Topological Derivative Approach to Inverse Scattering Problems in Attenuating Media

Carpio

Rapún

2021

Symmetry

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Detecting objects hidden in a medium is an inverse problem. Given data recorded at detectors when sources emit waves that interact with the medium, we aim to find objects that would generate similar data in the presence of the same waves. In opposition, the associated forward problem describes the evolution of the waves in the presence of known objects. This gives a symmetry relation: if the true objects (the desired solution of the inverse problem) were considered for solving the forward problem, then the recorded data should be returned. In this paper, we develop a topological derivative-based multifrequency iterative algorithm to reconstruct objects buried in attenuating media with limited aperture data. We demonstrate the method on half-space configurations, which can be related to problems set in the whole space by symmetry. One-step implementations of the algorithm provide initial approximations, which are improved in a few iterations. We can locate object components of sizes smaller than the main components, or buried deeper inside. However, attenuation effects hinder object detection depending on the size and depth for fixed ranges of frequencies.

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Section: Multifrequency Methodsmentioning

confidence: 99%

Multifrequency Topological Derivative Approach to Inverse Scattering Problems in Attenuating Media

Carpio

Rapún

2021

Symmetry

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“…We fixed M 5 100 for 2D simulations and M 5 40 for the 3D ones since these values provide clear visualizations. For the selection of optimal meshes for evaluating indicator functions, we refer to Ammari et al (2020).…”

Section: Implementation Of the Iterative Algorithmmentioning

confidence: 99%

Topological sensitivity analysis revisited for time-harmonic wave scattering problems. Part II: recursive computations by the boundary integral equation method

Louër

Rapún

2021

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PurposeThe purpose of this paper is to revisit the recursive computation of closed-form expressions for the topological derivative of shape functionals in the context of time-harmonic acoustic waves scattering by sound-soft (Dirichlet condition), sound-hard (Neumann condition) and isotropic inclusions (transmission conditions).Design/methodology/approachThe elliptic boundary value problems in the singularly perturbed domains are equivalently reduced to couples of boundary integral equations with unknown densities given by boundary traces. In the case of circular or spherical holes, the spectral Fourier and Mie series expansions of the potential operators are used to derive the first-order term in the asymptotic expansion of the boundary traces for the solution to the two- and three-dimensional perturbed problems.FindingsAs the shape gradients of shape functionals are expressed in terms of boundary integrals involving the boundary traces of the state and the associated adjoint field, then the topological gradient formulae follow readily.Originality/valueThe authors exhibit singular perturbation asymptotics that can be reused in the derivation of the topological gradient function in the iterated numerical solution of any shape optimization or imaging problem relying on time-harmonic acoustic waves propagation. When coupled with converging Gauss−Newton iterations for the search of optimal boundary parametrizations, it generates fully automatic algorithms.

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“…In general, the selection of suitable meshes for the evaluation of indicator functions is not a trivial step, specially when data correspond to different frequencies. For details on this topic we refer to [2]. However, we checked that for the multifrequency data available in the Fresnel databases our method is robust in connection with the mesh selection and only a slight calibration was needed.…”

Section: Topological Sensitivity Based Imagingmentioning

confidence: 99%

“…Indeed, as already mentioned, the definition of the approximated domain Ω app,λ depends on the selected grid. In principle, suitable grids depend on the frequency (see [2]). However, we have checked that for the multifrequency measurements available in the Fresnel databases our method is very robust in connection with the mesh selection.…”

Section: Target Reconstructionmentioning

confidence: 99%

Processing the 2D and 3D Fresnel experimental databases via topological derivative methods

Carpio¹,

Peña²,

Rapún³

2021

Inverse Problems

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This paper presents reconstructions of homogeneous targets from the 2D and 3D Fresnel databases by one-step imaging methods based on the computation of topological derivative and topological energy fields. The electromagnetic inverse scattering problem is recast as a constrained optimization problem, in which we seek to minimize the error when comparing experimental microwave measurements with computer-generated synthetic data for arbitrary targets by approximating a Maxwell forward model. The true targets are then characterized by combining the topological derivatives or energies of such shape functionals for all available receivers and emitters at different frequencies. Our approximations are comparable to the best approximations already obtained by other methods. However, these topological fields admit easy to evaluate closed-form expressions, which speeds up the process.

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Optimal Mesh Size for Inverse Medium Scattering Problems

Cited by 7 publications

References 35 publications

Multifrequency Topological Derivative Approach to Inverse Scattering Problems in Attenuating Media

Multifrequency Topological Derivative Approach to Inverse Scattering Problems in Attenuating Media

Topological sensitivity analysis revisited for time-harmonic wave scattering problems. Part II: recursive computations by the boundary integral equation method

Processing the 2D and 3D Fresnel experimental databases via topological derivative methods

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