A Regularized Sampling Method for Solving Three-Dimensional Inverse Scattering Problems

Colton, David; Giebermann, Klaus; Monk, Peter

doi:10.1137/s1064827598340159

Cited by 84 publications

(67 citation statements)

References 19 publications

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“…In this respect, the achieved results against 2D anthropomorphic head phantoms motivate the ongoing studies aimed at extending the proposed tool in the more realistic 3D case, wherein the well assessed effectiveness of the LSM to tackle the full vectorial imaging problem [28,29] will be exploited. Also, we will consider the assessment of the proposed imaging strategy against other kind of uncertainties, such as for instance inaccurate positioning of the measurement probes.…”

Section: Discussionmentioning

confidence: 70%

A Feasibility Study on Microwave Imaging for Brain Stroke Monitoring

Scapaticci¹,

Donato²,

Catapano³

et al. 2012

PIER B

241

160

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Abstract-The adoption of microwave imaging as a tool for noninvasive monitoring of brain stroke has recently gained increasing attention. In this respect, the paper aims at providing a twofold contribution. First, we introduce a simple design tool to devise guidelines to properly set the working frequency as well as to choose the optimum matching medium needed to facilitate the penetration of the probing wave into the head. Second, we propose an imaging strategy based on a modified formulation of the linear sampling method, which allows a quasi real time monitoring of the disease's evolution. The accuracy of the design guidelines and performance of the imaging strategy are assessed through numerical examples dealing with 2D anthropomorphic phantoms.

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Section: Discussionmentioning

confidence: 70%

A Feasibility Study on Microwave Imaging for Brain Stroke Monitoring

Scapaticci¹,

Donato²,

Catapano³

et al. 2012

PIER B

241

160

View full text Add to dashboard Cite

show abstract

“…their positions and external supports), have also been proposed. The linear sampling [40], the factorization, and the MUltiple SIgnal Classification (MUSIC) methods [41] belong to this class of inversion algorithms.…”

Section: Other Gpr Imaging Techniquesmentioning

confidence: 99%

Advanced Inversion Techniques for Ground Penetrating Radar

Fedeli¹,

Pastorino²,

Randazzo³

2017

JTIT

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Abstract-Ground Penetrating Radar (GPR) systems are nowadays standard inspection tools in several application areas, such as subsurface prospecting, civil engineering and cultural heritage monitoring. Usually, the raw output of GPR is provided as a B-scan, which has to be further processed in order to extract the needed information about the inspected scene. In this framework, inverse-scattering-based approaches are gaining an ever-increasing interest, thanks to their capabilities of directly providing images of the physical and dielectric properties of the investigated areas. In this paper, some advances in the development of such inversion techniques in the GPR field are revised and discussed.

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“…Then the idea, introduced first by Colton and Kirsch [20] (sampling method) and by Kirsch [29] (factorization method) in the context of inverse obstacle scattering problems, is to characterize the support of an obstacle by the range of some operator related to M . These methods have since then been applied to a variety of different applications; cf., e.g., the papers [17][18][19]26] (sampling method) and [25,28,31,32,34] (factorization method), and the many references therein.…”

Section: Introductionmentioning

confidence: 99%

Identification of small inhomogeneities: Asymptotic factorization

2007

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Abstract. We consider the boundary value problem of calculating the electrostatic potential for a homogeneous conductor containing finitely many small insulating inclusions. We give a new proof of the asymptotic expansion of the electrostatic potential in terms of the background potential, the location of the inhomogeneities and their geometry, as the size of the inhomogeneities tends to zero. Such asymptotic expansions have already been used to design direct (i.e. noniterative) reconstruction algorithms for the determination of the location of the small inclusions from electrostatic measurements on the boundary, e.g. MUSIC-type methods. Our derivation of the asymptotic formulas is based on integral equation methods. It demonstrates the strong relation between factorization methods and MUSIC-type methods for the solution of this inverse problem.

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A Regularized Sampling Method for Solving Three-Dimensional Inverse Scattering Problems

Cited by 84 publications

References 19 publications

A Feasibility Study on Microwave Imaging for Brain Stroke Monitoring

A Feasibility Study on Microwave Imaging for Brain Stroke Monitoring

Advanced Inversion Techniques for Ground Penetrating Radar

Identification of small inhomogeneities: Asymptotic factorization

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