Multi-frequency based location search algorithm of small electromagnetic inhomogeneities embedded in two-layered medium

Journal of Computational Physics

2015

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Multi-frequency subspace migration imaging technique are usually adopted for the noniterative imaging of unknown electromagnetic targets such as cracks in the concrete walls or bridges, anti-personnel mines in the ground, etc. in the inverse scattering problems. It is confirmed that this technique is very fast, effective, robust, and can be applied not only full-but also limited-view inverse problems if suitable number of incident and corresponding scattered field are applied and collected. But in many works, the application of such technique is somehow heuristic. Under the motivation of such heuristic application, this contribution analyzes the structure of imaging functional employed in the subspace migration imaging technique in two-dimensional full-and limited-view inverse scattering when the unknown target is arbitrary shaped, arc-like perfectly conducting cracks located in the homogeneous two-dimensional space. Opposite to the Statistical approach based on the Statistical Hypothesis Testing, our approach is based on the fact that subspace migration imaging functional can be expressed by a linear combination of Bessel functions of integer order of the first kind. This is based on the structure of the Multi-Static Response (MSR) matrix collected in the far-field at nonzero frequency in either Transverse Magnetic (TM) mode (Dirichlet boundary condition) or Transverse Electric (TE) mode (Neumann boundary condition). Explored expression of imaging functionals gives us certain properties of subspace migration and an answer of why multi-frequency enhances imaging resolution. Particularly, we carefully analyze the subspace migration and confirm some properties of imaging when a small number of incident field is applied. Consequently, we simply introduce a weighted multi-frequency imaging functional and confirm that which is an improved version of subspace migration in TM mode. Various results of numerical simulations via the far-field data affected by large amount of random noise are well matched with the analytical results derived herein, and give some ideas of future studies.

Section: Introductionmentioning

confidence: 99%

Multi-frequency subspace migration for imaging of perfectly conducting, arc-like cracks in full- and limited-view inverse scattering problems

Journal of Computational Physics

2015

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“…Based on explored structures, we confirmed that the shapes of small anomalies can be retrieved by imaging function without diagonal elements of the scattering matrix, and this is a considerable improvement over the traditional technique. Following several works [39,43,53,59], it has been shown that subspace migration is effective in a limitedaperture inverse scattering problem. The application and development of a microwave imaging technique to the limited-aperture problem is an interesting problem.…”

Section: Resultsmentioning

confidence: 99%

Real-time microwave imaging of unknown anomalies via scattering matrix

Mechanical Systems and Signal Processing

2019

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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.

“…Our current research considers cracks with Dirichlet boundary conditions; we plan to extend our research to cracks with Neumann boundary conditions (soundhard arc in inverse acoustic scattering problem), refer to [11,12]. Furthermore, motivated by [2,7,10,18,20], extending our research to the limited-view inverse scattering problem will be an interesting research topic. …”

Section: Results Of Numerical Simulations and Finding Exact Locationsmentioning

confidence: 99%

Appearance of inaccurate results in the MUSIC algorithm with inappropriate wavenumber

Journal of Inverse and Ill-Posed Problems

2017

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Abstract. MUltiple SIgnal Classification (MUSIC) is a well-known non-iterative location detection algorithm for small, perfectly conducting cracks in inverse scattering problems. However, when the applied wavenumbers are unknown, inaccurate locations of targets are extracted by MUSIC with inappropriate wavenumbers, a fact that has been confirmed by numerical simulations. To date, the reason behind this phenomenon has not been theoretically investigated. Motivated by this fact, we identify the structure of MUSIC-type imaging functionals with inappropriate wavenumbers by establishing a relationship with Bessel functions of order zero of the first kind. This result explains the reasons for inaccurate results. Various results of numerical simulations with noisy data support the identified structure of MUSIC.