A decoupling-based imaging method for inverse medium scattering for Maxwell's equations

Lakhal, A

doi:10.1088/0266-5611/26/1/015007

Cited by 14 publications

(9 citation statements)

References 32 publications

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“…Many inverse problems arising from applications in the natural sciences, engineering and other fields are nonlinear. One field of interest is inverse scattering with its many different applications for example in medical and nondestructive testing ( [1], [3], [14], [13]).…”

mentioning

confidence: 99%

Sequential subspace optimization for nonlinear inverse problems

Wald

Schuster

2016

Journal of Inverse and Ill-Posed Problems

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In this work we discuss a method to adapt sequential subspace optimization (SESOP), which has so far been developed for linear inverse problems in Hilbert and Banach spaces, to the case of nonlinear inverse problems. We start by revising the well-known technique for Hilbert spaces. In a next step, we introduce a method using multiple search directions that are especially designed to fit the nonlinearity of the forward operator. To this end, we iteratively project the initial value onto stripes whose shape is determined by the search direction, the nonlinearity of the operator and the noise level. We additionally propose a fast algorithm that uses two search directions. Finally we will show convergence and regularization properties for the presented method.

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mentioning

confidence: 99%

Sequential subspace optimization for nonlinear inverse problems

Wald

Schuster

2016

Journal of Inverse and Ill-Posed Problems

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“…Equation ( 5) was rigorously justified in suitable function spaces in [27] and it is very convenient for solving related inverse problems; see [27] for an application to the inverse source problem and [26] for inverse medium scattering. Compared with the whole-space Maxwell system, equation ( 5) is defined only over the scatterer support , since the induced electrical current J vanishes identically outside .…”

Section: Integral Representation Of Maxwell Systemmentioning

confidence: 99%

“…In contrast, the latter provides a distributed estimate of the refractive index n 2 by applying regularization techniques. We just mention the adjoint-based method [17,26,33], recursive linearization (for multi-frequency data) [6], Gauss-Newton method [15,20,21], contrasted source inversion [2] and level set method [18] for an incomplete list. Generally, the estimates by a method from the latter group can provide more details of inclusions/inhomogeneities, but at the expense of much increased computational efforts, especially when the forward model is the full threedimensional Maxwell system.…”

Section: Introductionmentioning

confidence: 99%

A direct sampling method for inverse electromagnetic medium scattering

2013

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In this paper, we study the inverse electromagnetic medium scattering problem of estimating the support and shape of medium scatterers from scattered electric or magnetic near-field data. We shall develop a novel direct sampling method based on an analysis of electromagnetic scattering and the behavior of the fundamental solution. The method is applicable even with one incident field and needs only to compute inner products of the measured scattered field with the fundamental solutions located at sampling points. Hence it is strictly direct, computationally very efficient, and highly tolerant to the presence of noise in the data. Two-and three-dimensional numerical experiments indicate that it can provide reliable support estimates of one single and multiple scatterers in case of both exact and highly noisy data.

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“…We apply a regularisation method to stabilise the solution (Lakhal and Louis, 2008;Lakhal, 2010Lakhal, , 2013. We apply a regularisation method to stabilise the solution (Lakhal and Louis, 2008;Lakhal, 2010Lakhal, , 2013.…”

Section: Introductionmentioning

confidence: 99%

A stable numerical algorithm for the design of anti-reflection coating for solar cells

Abazid

Lakhal

Louis

2016

IJRET

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We present an efficient numerical algorithm for the design of anti-reflection coating (ARC). In contrast to the widely used direct design where the behaviour of the field is investigated, we consider the inverse problem. Our purpose is to determine the best material for the ARC which matches with some sought values of the field at the surface. Mathematically, we solve an inverse scattering problem to identify the refractive index of the ARC. For modelling, the light propagation throughout a stratified ARC the time-harmonic Maxwell equations are reduced into one dimensional Helmholtz equation with prescribed boundary conditions. From this BVP, we derive an equivalent formulation as a Fredholm integral equation. The problem is nonlinear and ill-posed. We apply Born approximation for linearisation. To obtain stable solutions, we present numerical results using the method of approximate inverse (AI). We also carry out numerical tests to compare AI to Tikhonov-Phillips method.

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A decoupling-based imaging method for inverse medium scattering for Maxwell's equations

Cited by 14 publications

References 32 publications

Sequential subspace optimization for nonlinear inverse problems

Sequential subspace optimization for nonlinear inverse problems

A direct sampling method for inverse electromagnetic medium scattering

A stable numerical algorithm for the design of anti-reflection coating for solar cells

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