arXiv subjects

Won-Kwang Park

Publications and source records attributed to Won-Kwang Park.

At least 19 recordsLinked to original sources

arXiv2026

Mathematical and experimental validation of the bifocusing method tailored for bistatic measurement

In this paper, we design a bifocusing-based imaging strategy for the rapid identification of small penetrable dielectric inhomogeneities within a two-dimensional bistatic measurement setup. To address the applicability and limitation, we carefully explore the mathematical structure of the indicator function by establishing a relationship involving the infinite series of Bessel functions, the material characteristics, and the bistatic angle. Through this theoretical result, we rigorously verify that the imaging resolution degrades as the bistatic angle approaches $\SI{180}{\degree}$, and specifically, that target identification becomes impossible when the bistatic angle is $\SI{180}{\degree}$. Conversely, relatively high-resolution results are obtained when the bistatic angle is close to $\SI{0}{\degree}$. The theoretical findings are validated through numerical simulations using the Fresnel experimental dataset, which confirm the applicability and limitations of the proposed method for both dielectric and metallic objects.

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arXiv2025

Topological derivative for a fast identification of short, linear perfectly conducting cracks with inaccurate background information

In this study, we consider a topological derivative-based imaging technique for the fast identification of short, linear perfectly conducting cracks completely embedded in a two-dimensional homogeneous domain with smooth boundary. Unlike conventional approaches, we assume that the background permittivity and permeability are unknown due to their dependence on frequency and temperature, and we propose a normalized imaging function to localize cracks. Despite inaccuracies in background parameters, application of the proposed imaging function enables to recognize the existence of crack but it is still impossible to identify accurate crack locations. Furthermore, the shift in crack localization of imaging results is significantly influenced by the applied background parameters. In order to theoretically explain this phenomenon, we show that the imaging function can be expressed in terms of the zero-order Bessel function of the first kind, the crack lengths, and the applied inaccurate background wavenumber corresponding to the applied inaccurate background permittivity and permeability. Various numerical simulations results with synthetic data polluted by random noise validate the theoretical results.

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arXiv2025

Real-time inversion of two-dimensional Fresnel experimental database using orthogonality sampling method with single and multiple sources: the case of transverse electric polarized waves

This paper concerns an application of the orthogonality sampling method (OSM) for a real-time identification of small objects from two-dimensional Fresnel experimental dataset in transverse electric polarization. First, we apply the OSM with a single source by designing an indicator function based on the asymptotic expansion formula for the scattered field in the presence of small objects. We demonstrate that the indicator function can be expressed by an infinite series of Bessel functions of integer order of the first kind, the range of the signal receiver, and the location of the emitter. Based on this, we then investigate the applicability and limitations of the designed OSM. Specifically, we find that the imaging performance is strongly dependent on the source and the applied frequency. We then apply the OSM with multiple sources to improve imaging performance. Based on the identified structure of the OSM with a single source, we design an indicator function with multiple sources and demonstrate that it can be expressed by an infinite series of the Bessel function of integer order of the first kind, and we explain that objects can be identified uniquely using the designed OSM. Numerical simulation results obtained with the Fresnel experimental dataset demonstrate the advantages and disadvantages of the OSM with a single source and confirm that the designed OSM with multiple sources improves imaging performance.

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arXiv2025

Direct sampling method to retrieve small objects from two-dimensional limited-aperture scattered field data

In this study, we investigated the application of the direct sampling method (DSM) to identify small dielectric objects in a limited-aperture inverse scattering problem. Unlike previous studies, we consider the bistatic measurement configuration corresponding to the transmitter location and design indicator functions for both a single source and multiple sources, and we convert the unknown measurement data to a fixed nonzero constant. To explain the applicability and limitation of object detection, we demonstrate that the indicator functions can be expressed by an infinite series of Bessel functions, the material properties of the objects, the bistatic angle, and the converted constant. Based on the theoretical results, we explain how the imaging performance of the DSM is influenced by the bistatic angle and the converted constant. In addition, the results of our analyses demonstrate that a smaller bistatic angle enhances the imaging accuracy and that optimal selection of the converted constant is crucial to realize reliable object detection. The results of the numerical simulations obtained using a two-dimensional Fresnel dataset validated the theoretical findings and illustrate the effectiveness and limitations of the designed indicator functions for small objects.

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arXiv2024

Application of MUSIC algorithm in real-world microwave imaging of unknown anomalies from scattering matrix

In this contribution, we consider MUltiple SIgnal Classification (MUSIC)-type algorithm for a non-iterative microwave imaging of small and arbitrary shaped extended anomalies located in a homogeneous media from scattering matrix whose elements are scattering parameters measured at dipole antennas. In order to explain the feasibility of MUSIC in microwave imaging, we investigate mathematical structure of MUSIC by establishing a relationship with an infinite series of Bessel function of integer order and antennas setting. This is based on the representation formula of scattering parameters in the presence of small anomalies and the application of Born approximation. Simulation results using real-data at $f=925$MHz of angular frequency are exhibited to show the feasibility of designed algorithm and to support investigated structure of imaging function.

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arXiv2024

A novel study on the MUSIC-type imaging of small electromagnetic inhomogeneities in the limited-aperture inverse scattering problem

We apply MUltiple SIgnal Classification (MUSIC) algorithm for the location reconstruction of a set of {two-dimensional circle-like} small inhomogeneities in the limited-aperture inverse scattering problem. Compared with the full- or limited-view inverse scattering problem, the collected multi-static response (MSR) matrix is no more symmetric (thus not Hermitian), and therefore, it is difficult to define the projection operator onto the noise subspace through the traditional approach. With the help of an asymptotic expansion formula in the presence of small inhomogeneities and the structure of the MSR-matrix singular vector associated with nonzero singular values, we define an alternative projection operator onto the noise subspace and the corresponding MUSIC imaging function. To demonstrate the feasibility of the designed MUSIC, we show that the imaging function can be expressed by an infinite series of integer-order Bessel functions of the first kind and the range of incident and observation directions. Furthermore, we identify that the main factors of the imaging function for the permittivity and permeability contrast cases are the Bessel function of order zero and one, respectively. This further implies that the imaging performance significantly depends on the range of incident and observation directions; peaks of large magnitudes appear at the location of inhomogeneities for permittivity contrast case, and for the permeability contrast case, peaks of large magnitudes appear at the location of inhomogeneities when the range of such directions are narrow, while two peaks of large magnitudes appear in the neighborhood of the location of inhomogeneities when the range is wide enough. The numerical simulation results via noise-corrupted synthetic data also show that the designed MUSIC algorithm can address both permittivity and permeability contrast cases.

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arXiv2024

Unveiling novel insights into Kirchhoff migration for effective object detection using experimental Fresnel dataset

This study investigates the applicability of Kirchhoff migration (KM) for a fast identification of unknown objects in a real-world limited-aperture inverse scattering problem. To demonstrate the theoretical basis for the applicability including unique determination of objects, the imaging function of the KM was formulated using a uniformly convergent infinite series of Bessel functions of integer order of the first kind based on the integral equation formula for the scattered field. Numerical simulations performed using the experimental Fresnel dataset are exhibited to achieve the theoretical results.

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arXiv2024

Real-time tracking of moving objects from scattering matrix in real-world microwave imaging

The problem of the real-time microwave imaging of small, moving objects from a scattering matrix, whose elements are measured scattering parameters, without diagonal elements is considered herein. An imaging algorithm based on a Kirchhoff migration operated at single frequency is designed, and its mathematical structure is investigated by establishing a relationship with an infinite series of Bessel functions of integer order and antenna configuration. This is based on the application of the Born approximation to the scattering parameters of small objects. The structure explains the reason for the detection of moving objects via a designed imaging function and supplies its some properties. To demonstrate the strengths and weaknesses of the proposed algorithm, various simulations with real-data are conducted.

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arXiv2024

Performance analysis of MUSIC-type imaging without diagonal elements of multi-static response matrix

Generally, to apply the MUltiple SIgnal Classification (MUSIC) algorithm for the rapid imaging of small inhomogeneities, the complete elements of the multi-static response (MSR) matrix must be collected. However, in real-world applications such as microwave imaging or bistatic measurement configuration, diagonal elements of the MSR matrix are unknown. Nevertheless, it is possible to obtain imaging results using a traditional approach but theoretical reason of the applicability has not been investigated yet. In this paper, we establish mathematical structures of the imaging function of MUSIC from an MSR matrix without diagonal elements in both transverse magnetic (TM) and transverse electric (TE) polarizations. The established structures demonstrate why the shape of the location of small inhomogeneities can be retrieved via MUSIC without the diagonal elements of the MSR matrix. In addition, they reveal the intrinsic properties of imaging and the fundamental limitations. Results of numerical simulations are also provided to support the identified structures.

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arXiv2024

On the application of subspace migration from scattering matrix with constant-valued diagonal elements in microwave imaging

We consider the application of a subspace migration (SM) algorithm to quickly identify small objects in microwave imaging. In various problems, it is easy to measure the diagonal elements of the scattering matrix if the location of the transmitter and the receiver is the same. To address this issue, several studies have been conducted by setting the diagonal elements to zero. In this paper, we generalize the imaging problem by setting diagonal elements of the scattering matrix as a constant with the application of SM. To show the applicability of SM and its dependence on the constant, we show that the imaging function of SM can be represented in terms of an infinite series of the Bessel functions of integer order, antenna number and arrangement, and applied constant. This result enables us to discover some further properties, including the unique determination of objects. We also demonstrated simulation results with synthetic data to support the theoretical result.

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arXiv2024

Inversion of limited-aperture Fresnel experimental data using orthogonality sampling method with single and multiple sources

In this study, we consider the application of orthogonality sampling method (OSM) with single and multiple sources for a fast identification of small objects in limited-aperture inverse scattering problem. We first apply the OSM with single source and show that the indicator function with single source can be expressed by the Bessel function of order zero of the first kind, infinite series of Bessel function of nonzero integer order of the first kind, range of signal receiver, and the location of emitter. Based on this result, we explain that the objects can be identified through the OSM with single source but the identification is significantly influenced by the location of source and applied frequency. For a successful improvement, we then consider the OSM with multiple sources. Based on the identified structure of the OSM with single source, we design an indicator function of the OSM with multiple sources and show that it can be expressed by the square of the Bessel function of order zero of the first kind an infinite series of the square of Bessel function of nonzero integer order of the first kind. Based on the theoretical results, we explain that the objects can be identified uniquely through the designed OSM. Several numerical experiments with experimental data provided by the Institute Fresnel demonstrate the pros and cons of the OSM with single source and how the designed OSM with multiple sources behave.

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arXiv2023

Application of MUSIC-type imaging for anomaly detection without background information

It has been demonstrated that the MUltiple SIgnal Classification (MUSIC) algorithm is fast, stable, and effective for localizing small anomalies in microwave imaging. For the successful application of MUSIC, exact values of permittivity, conductivity, and permeability of the background must be known. If one of these values is unknown, it will fail to identify the location of an anomaly. However, to the best of our knowledge, no explanation of this failure has been provided yet. In this paper, we consider the application of MUSIC to the localization of a small anomaly from scattering parameter data when complete information of the background is not available. Thanks to the framework of the integral equation formulation for the scattering parameter data, an analytical expression of the MUSIC-type imaging function in terms of the infinite series of Bessel functions of integer order is derived. Based on the theoretical result, we confirm that the identification of a small anomaly is significantly affected by the applied values of permittivity and conductivity. However, fortunately, it is possible to recognize the anomaly if the applied value of conductivity is small. Simulation results with synthetic data are reported to demonstrate the theoretical result.

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arXiv2023

Application and analysis of MUSIC algorithm for anomaly detection in microwave imaging without a switching device

Although the MUltiple SIgnal Classification (MUSIC) algorithm has demonstrated suitability as a microwave imaging technique for detecting anomalies, there is a fundamental limit that it requires a switching device to be used which permits an antenna to transmit and receive signals simultaneously. In this paper, we design a MUSIC-type imaging function using scattering parameter data to find small anomaly and explore its mathematical structure. Considering the investigated structure, we confirm that the imaging performance is highly dependent on the antenna configurations and suggest an arrangement of antennas to enhance imaging performance. Simulation results with synthetic data are displayed to support theoretical result.

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arXiv2019

Analysis and improvement of direct sampling method in the mono-static configuration

The recently introduced non-iterative imaging method entitled \enquote{direct sampling method} (DSM) is known to be fast, robust, and effective for inverse scattering problems in the multi-static configuration but fails when applied to the mono-static one. To the best of our knowledge no explanation of this failure has been provided yet. Thanks to the framework of the asymptotic and the far-field hypothesis in the 2D scalar configuration an analytical expression of the DSM indicator function in terms of the Bessel function of order zero and sizes, shapes and permittivities of the inhomogeneities is obtained and the theoretical reason of the limitation identified. A modified version of DSM is then proposed in order to improve the imaging method. The theoretical results are supported by numerical results using synthetic data.

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arXiv2018

Real-time microwave imaging of unknown anomalies via scattering matrix

We consider an inverse scattering problem to identify the locations or shapes of unknown anomalies from scattering parameter data collected by a small number of dipole antennas. Most of researches does not considered the influence of dipole antennas but in the experimental simulation, they are significantly affect to the identification of anomalies. Moreover, opposite to the theoretical results, it is impossible to handle scattering parameter data when the locations of the transducer and receiver are the same in real-world application. Motivated by this, we design an imaging function with and without diagonal elements of the so-called scattering matrix. This concept is based on the Born approximation and the physical interpretation of the measurement data when the locations of the transducer and receiver are the same and different. We carefully explore the mathematical structures of traditional and proposed imaging functions by finding relationships with the infinite series of Bessel functions of integer order. The explored structures reveal certain properties of imaging functions and show why the proposed method is better than the traditional approach. We present the experimental results for small and extended anomalies using synthetic and real data at several angular frequencies to demonstrate the effectiveness of our technique.

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arXiv2018

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

A direct sampling method (DSM) is designed herein 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 and the antenna locations. Experiments using real-data then demonstrate both the effectiveness and limitations of this method.

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arXiv2018

Direct sampling method for retrieving small perfectly conducting cracks

In this paper, direct sampling method is considered for determining the location of a set of small, linear perfectly conducting cracks from the collected far-field data corresponding to an incident field. To show the feasibility of the direct sampling method, this study proves that the indicator function of the direct sampling method can be represented by the Bessel function of order zero and the crack lengths. The results of the numerical simulations are shown to support the fact that the imaging performance is highly dependent on the crack lengths. To explain the fact that the imaging performance is highly dependent on the rotation of the cracks, the direct sampling method is further analyzed by establishing a representation using Bessel functions of orders zero and one. Based on the derived representation of indicator function, we design improved direct sampling methods by applying incident fields with multiple directions and multiple frequencies. Corresponding analysis of indicator functions and simulation results are shown for demonstrating the effectiveness and improvements.

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arXiv2018

Direct sampling method for imaging small dielectric inhomogeneities: analysis and improvement

The direct sampling method (DSM) has been introduced for non-iterative imaging of small inhomogeneities and is known to be fast, robust, and effective for inverse scattering problems. However, to the best of our knowledge, a full analysis of the behavior of the DSM has not been provided yet. Such an analysis is proposed here within the framework of the asymptotic hypothesis in the 2D case leading to the expression of the DSM indicator function in terms of the Bessel function of order zero and the sizes, shapes and permittivities of the inhomogeneities. Thanks to this analytical expression the limitations of the DSM method when one of the inhomogeneities is smaller and/or has lower permittivity than the others is exhibited and illustrated. An improved DSM is proposed to overcome this intrinsic limitation in the case of multiple incident waves. Then we show that both the traditional and improved DSM are closely related to a normalized version of the Kirchhoff migration. The theoretical elements of our proposal are supported by various results from numerical simulations with synthetic and experimental data.

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