Mathematical and Statistical Methods for Multistatic Imaging

Ammari, Habib; Garnier, Josselin; Jing, Wenjia; Kang, Hyeonbae; Lim, M. W.; Sølna, Knut; Wang, Han

doi:10.1007/978-3-319-02585-8

Cited by 146 publications

(193 citation statements)

References 109 publications

(193 reference statements)

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“…Following [26] (see also [23]), we can prove that where ∂/∂τ is the tangential derivative on ∂B, v and w periodic with respect to x 1 of period 1 and satisfy…”

Section: Lemma 43mentioning

confidence: 99%

Mathematical and numerical framework for metasurfaces using thin layers of periodically distributed plasmonic nanoparticles

Ammari

Ruiz

et al. 2016

Proc. R. Soc. A.

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In this paper, we derive an impedance boundary condition to approximate the optical scattering effect of an array of plasmonic nanoparticles mounted on a perfectly conducting plate. We show that at some resonant frequencies the impedance blows up, allowing for a significant reduction of the scattering from the plate. Using the spectral properties of a Neumann-Poincaré type operator, we investigate the dependency of the impedance with respect to changes in the nanoparticle geometry and configuration.

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“…Following [26] (see also [23]), we can prove that where ∂/∂τ is the tangential derivative on ∂B, v and w periodic with respect to x 1 of period 1 and satisfy…”

Section: Lemma 43mentioning

confidence: 99%

Mathematical and numerical framework for metasurfaces using thin layers of periodically distributed plasmonic nanoparticles

Ammari

Ruiz

et al. 2016

Proc. R. Soc. A.

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“…The inverse source problem of reconstructing f from u for fixed frequency is well known to be ill-posed for general sources; see, for instance, [6,15,16]. While there are many methods of reconstructing f from u, we concentrate on the following three most common ones in the literature: …”

Section: Inverse Source Problemsmentioning

confidence: 99%

“…The ill-posedness of the inverse source problem is due to the fast decay of the singular values to zero; see, for instance, [15,17]. By a direct calculation, one can show that the minimum L 2 -norm solution to (2.4) is given by…”

Section: (B) Minimum L 2 -Norm Solutionmentioning

confidence: 99%

Super-resolution in high-contrast media

Ammari

Zhang

2015

Proc. R. Soc. A.

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“…Note that 4) where in order to obtain the latter identity, expression (5.2) has been invoked. Assuming, z, z ′ ∈ Ω far from ∂Ω and utilizing the Helmholtz-Kirchhoff identities, we obtain Similarly, third term E 3 (z, z ′ ) can be evaluated and appears to be…”

Section: B Proof Of Lemma 51mentioning

confidence: 99%

“…Soon after its emergence [24], the idea was embraced for imaging of diametrically small anomalies [18] and inverse scattering problems; see, for example, [2,4,15,22,23,25,27] and articles cited therein.…”

Section: Introductionmentioning

confidence: 99%

Stability and Resolution Analysis of Topological Derivative Based Localization of Small Electromagnetic Inclusions

Wahab

2015

SIAM J. Imaging Sci.

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The aim of this article is to elaborate and rigorously analyze a topological derivative based imaging framework for locating an electromagnetic inclusion of diminishing size from boundary measurements of the tangential component of scattered magnetic field at a fixed frequency. The inverse problem of inclusion detection is formulated as an optimization problem in terms of a filtered discrepancy functional and the topological derivative based imaging functional obtained therefrom. The sensitivity and resolution analysis of the imaging functional is rigorously performed. It is substantiated that the Rayleigh resolution limit is achieved. Further, the stability of the reconstruction with respect to measurement and medium noises is investigated and the signal-to-noise ratio is evaluated in terms of the imaginary part of free space fundamental magnetic solution.

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Mathematical and Statistical Methods for Multistatic Imaging

Cited by 146 publications

References 109 publications

Mathematical and numerical framework for metasurfaces using thin layers of periodically distributed plasmonic nanoparticles

Mathematical and numerical framework for metasurfaces using thin layers of periodically distributed plasmonic nanoparticles

Super-resolution in high-contrast media

Stability and Resolution Analysis of Topological Derivative Based Localization of Small Electromagnetic Inclusions

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