A linear sampling method for inverse scattering from an open arc

Kirsch, Andreas; Ritter, Stefan

doi:10.1088/0266-5611/16/1/308

Cited by 132 publications

(125 citation statements)

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“…As an attempt to improve the linear sampling method, the so-called Factorization method has been developed in [18,21]. The latter method has rigorous justification, keeps the previous advantages and of course is an interesting tool for reconstruction problems in inverse scattering.…”

Section: Introductionmentioning

confidence: 99%

Factorization Method for Electromagnetic Inverse Scattering from Biperiodic Structures

Lechleiter¹,

Nguyen²

2013

SIAM J. Imaging Sci.

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This paper is concerned with the inverse scattering problem of electromagnetic waves from penetrable biperiodic structures in three dimensions. We study the Factorization method as a tool for reconstructing the periodic media from measured data consisting of scattered electromagnetic waves for incident plane electromagnetic waves. We propose a rigorous analysis for the method. A simple criterion is provided to reconstruct the biperiodic structures. We also provide three-dimensional numerical experiments to indicate the performance of the method.

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Section: Introductionmentioning

confidence: 99%

Factorization Method for Electromagnetic Inverse Scattering from Biperiodic Structures

Lechleiter¹,

Nguyen²

2013

SIAM J. Imaging Sci.

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“…Since F Γ is injective, so is G * Γ as S * Γ is injective, whence (i) follows. Properties (ii)-(iii) are the content of [18,Theorem 3.7]; property (iv) is established by [18,Theorem 3.8].…”

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confidence: 99%

MUSIC for Extended Scatterers as an Instance of the Factorization Method

Arens¹,

Lechleiter²,

Lüke³

2009

SIAM J. Appl. Math.

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Abstract. Recent work of Luke and Devaney showed that there exists an implementation of a modified linear sampling method that is equivalent to a MUSIC algorithm for scattering from sound soft obstacles. The correspondence is independent of the size of the scatterer or the wavelength of the incident field. As the proof was not constructive, an explicit implementation could not be justified. In the present work, we show that MUSIC is an instance of the factorization method applied to any nonabsorbing scatterer, thus providing a justification for the MUSIC algorithm at arbitrary illuminating frequency for arbitrary nonabsorbing scatterers. These results are also extended to scattering from cracks. With explicit constructions in hand, we are also able to provide error and stability estimates for practical implementations in noisy environments with limited data and to explain a curious behavior of the factorization method in the case of noisy data.Key words. inverse problems, scattering theory, factorization method, image processing, MU-SIC AMS subject classifications. 35R30, 35P25, 94A081. Introduction. The Multiple Signal Classification (MUSIC) algorithm is a well-known method for determining the location of emitters from sensors with arbitrary locations and arbitrary directional characteristics such as gain, phase or polarization in a noise/interference environment [27]. The method is based on the observation that the far field patterns of point sources with centers near the true signal source are nearly orthogonal to the noise subspace of the far field operator, or the multi-static response matrix, as it is known in the signal and image processing literature. The connection between the MUSIC algorithm and other inverse scattering techniques has been explored by several authors [5,16,23]. Earlier studies are limited to point-like scatterers. More recent studies [11,2,12,8,9, 1] approach an application of the MU-SIC algorithm to scatterers of some specified size, relative to the wavelength, and are based on the finite-dimensional multi-static response matrix for point-like scatterers. An anonymous referee brought to our attention [3] dealing with closely related questions for linearized scattering. In [23] Luke and Devaney combine the linear sampling method of Colton and Kirsch [6] with the point source method of Potthast [26] to show the existence of a field that is orthogonal to the far field patterns of point sources centered on the boundary of the scatterers. This extends the MUSIC algorithm to obstacles of arbitrary size, independent of the frequency. Missing from their analysis, however, is a concrete way to construct such a field. Numerical experiments indicate that fields constructed from elements of the noise subspace of the far field operator (that is, the subspace corresponding to small eigenvalues of the far field operator) yield the desired properties. In the present work we use Kirsch's factorization method [14] to prove this to be the case, thus yielding a constructive proof of the MUSIC algorithm...

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“…Motivated from this, non-iterative techniques for retrieving the location of such inhomogeneities have been investigated. Those include the MUltiple SIgnal Classification (MUSIC) algorithm [5,6,7], the linear sampling method [8,9,10], and Kirchhoff and subspace migrations [11,12,13]. Although these techniques are confirmed to be fast, stable, and effective, they still require observations from a significant number of directions of the incident and scattered field or far-field data to obtain an acceptable result.…”

Section: Introductionmentioning

confidence: 99%

A Novel Study on Direct Sampling Method for Imaging Multiple Targets

Park¹

2017

dtetr

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Abstract. The Direct Sampling Method (DSM) is well known to be a fast, stable, and effective detection technique in inverse scattering problems, but its analysis is restricted to imaging of a single target. Motivated by this, we investigate the mathematical structure of DSM for imaging small multiple dielectric targets by establishing a relationship with the radii and permittivities of targets, and Bessel function of order zero. This structure explains why DSM can be applied to the imaging of multiple targets. Numerical results support our findings.

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A linear sampling method for inverse scattering from an open arc

Cited by 132 publications

References 6 publications

Factorization Method for Electromagnetic Inverse Scattering from Biperiodic Structures

Factorization Method for Electromagnetic Inverse Scattering from Biperiodic Structures

MUSIC for Extended Scatterers as an Instance of the Factorization Method

A Novel Study on Direct Sampling Method for Imaging Multiple Targets

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