Detection of small inhomogeneities via direct sampling method in transverse electric polarization

Park, Won-Kwang

doi:10.1016/j.aml.2017.12.016

Cited by 10 publications

(5 citation statements)

References 19 publications

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“…The indicator function structure (4) implies that the imaging performance is highly dependent on 1) the anomaly's size, permittivity, and conductivity; 2) the antenna configuration (total number and arrangement); and 3) the distance between the transmitter a n and anomaly D m . Observations 1 and 2 have also been made by other studies [3,4,14], but observation 3 is also a significant factor that affects imaging performance in real-world applications, as shown below by the experimental results for Example 4.1.…”

Section: Theoretical Resultssupporting

confidence: 62%

“…Several studies have revealed that the direct sampling method (DSM) is a fast, stable, and effective imaging technique in inverse scattering problems. It has been investigated for imaging small two-dimensional anomalies [1,2,3,4] and retrieving three-dimensional objects [5] for diffusive [6] and electrical impedance [7] tomography applications and for source detection in stratified ocean waveguides [8]. As we have previously observed, DSM only requires one or at most a few incident fields, rather than additional operations, such as singular value decomposition [9,10] or solving ill-posed integral equations [11] or adjoint problems [12,13].…”

Section: Introductionmentioning

confidence: 99%

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Direct sampling method for imaging small anomalies: real-data experiments

Park,

Lee,

Son

2018

Preprint

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In this paper, a direct sampling method (DSM) is designed for a real-time detection of small anomalies from scattering parameters measured by a small number of dipole antennas. Applicability of the DSM is theoretically demonstrated by proving that its indicator function can be represented in terms of an infinite series of Bessel functions of integer order, Hankel function of order zero, and the antenna configurations. Experiments using real-data then demonstrate both the effectiveness and limitations of this method.

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Section: Theoretical Resultssupporting

confidence: 62%

Section: Introductionmentioning

confidence: 99%

Direct sampling method for imaging small anomalies: real-data experiments

Park,

Lee,

Son

2018

Preprint

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“…Then, by testing orthonormality relation between U and W(r), it will be possible to extract r so that the location of D can be identified. To this end, the typical indicator function F DSM (r, m) has been designed as follows (see [29][30][31]33]):…”

Section: Scattering Parameter and Indicator Functions Of Direct Sampling Methodsmentioning

confidence: 99%

“…Direct sampling method (DSM) is a fast, effective, and stable noniterative technique for identifying the location or the outline shape of small or extended targets related to various inverse problems. As such, DSM is currently widely applied in many fields, including the identification of two-and three-dimensional small scatterers [29][30][31][32][33][34] or perfectly conducting cracks [35], diffusive optical tomography [36], electrical impedance tomography [37], detecting sources in a stratified ocean waveguide [38], phaseless inverse source scattering problem [39], and mono-static imaging [40].…”

Section: Introductionmentioning

confidence: 99%

Theoretical Identification of Coupling Effect and Performance Analysis of Single-Source Direct Sampling Method

Park¹

2021

Mathematics

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Although the direct sampling method (DSM) has demonstrated its feasibility in identifying small anomalies from measured scattering parameter data in microwave imaging, inaccurate imaging results that cannot be explained by conventional research approaches have often emerged. It has been heuristically identified that the reason for this phenomenon is due to the coupling effect between the antenna and dipole antennas, but related mathematical theory has not been investigated satisfactorily yet. The main purpose of this contribution is to explain the theoretical elucidation of such a phenomenon and to design an improved DSM for successful application to microwave imaging. For this, we first survey traditional DSM and design an improved DSM, which is based on the fact that the measured scattering parameter is influenced by both the anomaly and the antennas. We then establish a new mathematical theory of both the traditional and the designed indicator functions of DSM by constructing a relationship between the antenna arrangement and an infinite series of Bessel functions of integer order of the first kind. On the basis of the theoretical results, we discover various factors that influence the imaging performance of traditional DSM and explain why the designed indicator function successfully improves the traditional one. Several numerical experiments with synthetic data support the established theoretical results and illustrate the pros and cons of traditional and designed DSMs.

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“…Attempts to address these types of problems have led to a search for fast and effective identification techniques, and various approaches have been developed. Those include the MUltiple SIgnal Classification (MUSIC) algorithm [11][12][13][14][15], the linear [16][17][18][19][20][21] and direct [22][23][24][25][26] sampling methods, and topological derivatives [27][28][29][30][31]. We also refer to various non-iterative imaging techniques [32][33][34][35][36][37].…”

Section: Introductionmentioning

confidence: 99%

Kirchhoff Migration for Identifying Unknown Targets Surrounded by Random Scatterers

Ahn

Park

2019

Applied Sciences

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In this paper, we take into account a two-dimensional inverse scattering problem for localizing small electromagnetic anomalies when they are surrounded by small, randomly distributed electromagnetic scatterers. Generally, subspace migration is considered to be an improved version of Kirchhoff migration; however, for the problem considered here, simulation results have confirmed that Kirchhoff migration is better than subspace migration, though the reasons for this have not been investigated theoretically. In order to explain theoretical reason, we explored that the imaging function of Kirchhoff migration can be expressed by the size, permittivity, permeability of anomalies and random scatterers, and the Bessel function of the first kind of order zero and one. Considered approach is based on the fact that the far-field pattern can be represented using an asymptotic expansion formula in the presence of such anomalies and random scatterers. We also present results of numerical simulations to validate the discovered imaging function structures.

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Detection of small inhomogeneities via direct sampling method in transverse electric polarization

Cited by 10 publications

References 19 publications

Direct sampling method for imaging small anomalies: real-data experiments

Direct sampling method for imaging small anomalies: real-data experiments

Theoretical Identification of Coupling Effect and Performance Analysis of Single-Source Direct Sampling Method

Kirchhoff Migration for Identifying Unknown Targets Surrounded by Random Scatterers

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