Using the linear sampling method and an improved maximum product criterion for the solution of the electromagnetic inverse medium problem

Bazán, Fermín S. V.; Francisco, Juliano B.; Leem, Koung Hee; Pelekanos, George

doi:10.1016/j.cam.2014.06.003

Cited by 8 publications

(5 citation statements)

References 12 publications

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“…Here, the definitions of first kind of spherical Bessel functions are used to go from (38) to (39) and from ( 40) to (41), respectively. The combination of ( 35) and ( 37) for s = 1, 2, 3, leads to…”

Section: Introduction Of Direct Sampling Methods and Its Structure Analysismentioning

confidence: 99%

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Structure analysis of direct sampling method in 3D electromagnetic inverse problem: near- and far-field configuration

Kang

Lambert

2021

Inverse Problems

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In this paper, we study the structure analysis of the Direct Sampling Method (DSM) in the threedimensional inverse electromagnetic scattering problem. Even though the DSM is well-known to the robust, fast, and efficient non-iterative type algorithm to estimate the support and shape of unknown inhomogeneities from scattered data, the inhomogeneities might not be detected in the DSM with improper test polarization. To explain the reason for the phenomenon, we carefully analyze the indicator function of DSM using the asymptotic formula of the scattered field under a small volume hypothesis of well-separated inhomogeneities. The analytic representation formula of the indicator function of DSM is presented by establishing the relationship of spherical Bessel functions, the polarization of the incident wave and the test dipole, and the polarization tensor of the inhomogeneities, which depends on their sizes, permittivity, etc. Through such theoretical results, we also show the validity of the guideline to choose the test polarization given by other work. Furthermore, we propose our method to select the polarization of the test dipole for better efficiency. With a similar path of derivation, we also introduce and analyze the indicator function of DSM in far-field configurations. Various numerical simulations with synthetic and experimental data validate our theoretical results and proposals.

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Section: Introduction Of Direct Sampling Methods and Its Structure Analysismentioning

confidence: 99%

“…where υ is an isosurface parameter and I is either I DSM (z; y, q) or I DSMP (z; y). According to [40], we choose the parameter υ such as…”

Section: Numerical Simulationsmentioning

confidence: 99%

Structure analysis of direct sampling method in 3D electromagnetic inverse problem: near- and far-field configuration

Kang

Lambert

2021

Inverse Problems

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“…. For convergence details and practical implementation of IMPC the reader is referred to [8]. The goal of this subsection is to give further insight into the theoretical properties of IMPC to fully understand why it work so well.…”

Section: Revisiting Impc and Gdpmentioning

confidence: 99%

“…It is well known however that Morozov's discrepancy principle is time-consuming and requires an a priori knowledge of the noise level in the data, something that is unavoidable in real life applications. Therefore we employ an Improved Maximum Product Criterion (IMPC), developed by Bazán et al [8], which via a fast and efficient algorithm chooses as regularization parameter, the critical point associated with the largest local maximum, of a product created by the regularized solution norm and the corresponding residual norm. The IMPC is an improved version of the Maximum Product Criterion (MPC) that originally appeared in [9].…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, Journal of Applied Mathematics and Physics as with MPC, IMPC does not depend on user specified input parameters (like subspace dimension or truncating parameter) and requires no a priori knowledge of the noise level [9]. As we mentioned before, IMPC extends in a very elegant way the maximum product criterion, and it is worth mentioning that has been applied with great success in reconstructing obstacles in acoustics [9], electromagnetics [8] as well as applications in elastic scattering [10]. In addition to employing IMPC, the introduction of the mixed reciprocity relation avoids the computation of the far field of the Green function by replacing it with the total wave, and therefore renders the resulting algorithm even more attractive with respect to the computational point of view [3].…”

Section: Introductionmentioning

confidence: 99%

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On an Application of the Improved Maximum Product Criterion to Inverse Acoustic Scattering in a Layered Medium

Bazán¹,

Francisco²,

Leem³

et al. 2021

JAMP

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In this paper, we consider the numerical treatment of an inverse acoustic scattering problem that involves an impenetrable obstacle embedded in a layered medium. We begin by employing a modified version of the well known factorization method, in which a computationally effective numerical scheme for the reconstruction of the shape of the scatterer is presented. This is possible, due to a mixed reciprocity principle, which renders the computation of the Green function at the background medium unnecessary. Moreover, to further refine our inversion algorithm, an efficient Tikhonov parameter choice technique, called Improved Maximum Product Criterion (IMPC) is exploited. Our regularization parameter is computed via a fast iterative algorithm which requires no a priori knowledge of the noise level in the far-field data. Finally, the effectiveness of IMPC is illustrated with various numerical examples.

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A numerical comparison of different qualitative algorithms for solving 2D inverse elastic scattering problems

Leem

Pelekanos

2021

Comp. Appl. Math.

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Using the linear sampling method and an improved maximum product criterion for the solution of the electromagnetic inverse medium problem

Cited by 8 publications

References 12 publications

Structure analysis of direct sampling method in 3D electromagnetic inverse problem: near- and far-field configuration

Structure analysis of direct sampling method in 3D electromagnetic inverse problem: near- and far-field configuration

On an Application of the Improved Maximum Product Criterion to Inverse Acoustic Scattering in a Layered Medium

A numerical comparison of different qualitative algorithms for solving 2D inverse elastic scattering problems

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