Data recovery in inverse scattering: From limited-aperture to full-aperture

Liu, Xiaodong; Sun, Jiguang

doi:10.1016/j.jcp.2018.10.036

Cited by 29 publications

(24 citation statements)

References 31 publications

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“…As expected, the reconstruction for the object closer to the observation points is sharper than for the other one, which underestimates its size. The obtained results are in accordance to limited aperture experiments obtained for other model problems by either using topological derivative-based methods (see [2,14,15,34,42]) or by other techniques like the (generalized) linear sampling, factorization, or MUSIC algorithms (see [3,4,6,37])…”

Section: Some Test Casessupporting

confidence: 86%

“…Then, by Theorem 4 we deduce now that f (ε) must behave as ε d−2 , and by choosing f (ε) = (d − 1)2 d−1 πε d−2 , namely, defining f as in (15), we find formula (37).…”

Section: =1mentioning

confidence: 94%

“…iκλu r ,0 (x)w r ,0 (x) , (37) where u r ,0 is the solution to (1) with = app for the incident field u inc r , and w r ,0 solves (27) with u 0 = u r ,0 and u meas = u meas,r .…”

Section: =1mentioning

confidence: 99%

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Topological Imaging Methods for the Iterative Detection of Multiple Impedance Obstacles

Louër

Rapún

2022

J Math Imaging Vis

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In this paper, we investigate shape inversion algorithms based on the computation of iterated topological derivatives for the detection of multiple particles coated by a complex surface impedance in two- and three-dimensional acoustic media. New closed-form formulae for the topological derivative of the misfit functional are derived when an approximate set of unknown particles has already been recovered. Proofs rely on the computation of shape derivatives followed by the topological asymptotic analysis of a boundary integral equation formulation of the forward and adjoint problems. The relevance of the theoretical results is illustrated by various 2D and 3D experiments using monochromatic imaging algorithms either fully or partially based on topological derivatives.

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Section: Some Test Casessupporting

confidence: 86%

“…Then, by Theorem 4 we deduce now that f (ε) must behave as ε d−2 , and by choosing f (ε) = (d − 1)2 d−1 πε d−2 , namely, defining f as in (15), we find formula (37).…”

Section: =1mentioning

confidence: 94%

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Topological Imaging Methods for the Iterative Detection of Multiple Impedance Obstacles

Louër

Rapún

2022

J Math Imaging Vis

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“…In Figures 6 and 7, we see that W FF (z) and W TDSM (z) seem to give better reconstructions than W CD (z) for partial aperture data. Recently, in [24,25], some data completion methods were used to compute the missing scattering data, which were then used by a qualitative method to recover the scatterer. Applying these data completion methods can possibly be employed to provide better reconstructions with partial aperture data.…”

Section: Numerical Examplesmentioning

confidence: 99%

Direct Sampling for Recovering Sound Soft Scatterers from Point Source Measurements

Harris

2021

Computation

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In this paper, we consider the inverse problem of recovering a sound soft scatterer from the measured scattered field. The scattered field is assumed to be induced by a point source on a curve/surface that is known. Here, we propose and analyze new direct sampling methods for this problem. The first method we consider uses a far-field transformation of the near-field data, which allows us to derive explicit bounds in the resolution analysis for the direct sampling method’s imaging functional. Two direct sampling methods are studied, using the far-field transformation. For these imaging functionals, we use the Funk–Hecke identities to study the resolution analysis. We also study a direct sampling method for the case of the given Cauchy data. Numerical examples are given to show the applicability of the new imaging functionals for recovering a sound soft scatterer with full and partial aperture data.

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“…Subsequently, methods using full aperture data can be employed. We refer to [13,17] for some data retrieval techniques along these lines.…”

mentioning

confidence: 99%

Inverse electromagnetic obstacle scattering problems with multi-frequency sparse backscattering far field data

Arens

Liu

2020

Inverse Problems

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This paper is dedicated to design a direct sampling method of inverse electromagnetic scattering problems, which uses multi-frequency sparse backscattering far field data for reconstructing the boundary of perfectly conducting obstacles. We show that a smallest strip containing the unknown object can be approximately determined by the multi-frequency backscattering far field data at two opposite observation directions. The proof is based on the Kirchhoff approximation and Fourier transform. Such a strip is then reconstructed by an indicator, which is the absolute value of an integral of the product of the data and some properly chosen function over the frequency interval. With the increase of the number of the backscattering data, the location and shape of the underlying object can be reconstructed. Numerical examples are conducted to show the validity and robustness of the proposed sampling method. The numerical examples also show that the concave part of the underlying object can be well reconstructed, and the different connected components of the underlying object can be well separated.

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Data recovery in inverse scattering: From limited-aperture to full-aperture

Cited by 29 publications

References 31 publications

Topological Imaging Methods for the Iterative Detection of Multiple Impedance Obstacles

Topological Imaging Methods for the Iterative Detection of Multiple Impedance Obstacles

Direct Sampling for Recovering Sound Soft Scatterers from Point Source Measurements

Inverse electromagnetic obstacle scattering problems with multi-frequency sparse backscattering far field data

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