Direct sampling method for anomaly imaging from S-parameter

In this paper, we develop a fast imaging technique for small anomalies located in homogeneous media from S-parameter data measured at dipole antennas. Based on the representation of S-parameters when an anomaly exists, we design a direct sampling method (DSM) for imaging an anomaly and establishing a relationship between the indicator function of DSM and an infinite series of Bessel functions of integer order. Simulation results using synthetic data at f=1GHz of angular frequency are illustrated to support the identified structure of the indicator function.Comment: 6 pages, 6 figure

Biholomorphic mapping on the boundary I

We study on the biholomorphic equivalence of a strongly pseudoconvex bounded domain with differentiable spherical boundary to an open ball, and we study on the biholomorphicity of a proper holomorphic self mapping of a strongly pseudoconvex domain with real analytic boundary.Comment: This is a preliminary version. Any comment is greatly appreciated

A novel study on subspace migration for imaging of a sound-hard arc

In this study, the influence of a test vector selection used in subspace migration to reconstruct the shape of a sound-hard arc in a two-dimensional inverse acoustic problem is considered. In particular, a new mathematical structure of imaging function is constructed in terms of the Bessel functions of the order 0, 1, and 2 of the first kind based on the structure of singular vectors linked to the nonzero singular values of a Multi-Static Response (MSR) matrix. This structure indicates that imaging performance of subspace migration is highly related to the unknown shape of arc. The simulation results with noisy data indicate support for the derived structure.Comment: 9 pages, 12 figure

Appearance of inaccurate results in the MUSIC algorithm with inappropriate wavenumber

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.Comment: 16 pages, 20 figure

Analysis of a multi-frequency electromagnetic imaging functional for thin, crack-like electromagnetic inclusions

Recently, a non-iterative multi-frequency subspace migration imaging algorithm was developed based on an asymptotic expansion formula for thin, curve-like electromagnetic inclusions and the structure of singular vectors in the Multi-Static Response (MSR) matrix. The present study examines the structure of subspace migration imaging functional and proposes an improved imaging functional weighted by the frequency. We identify the relationship between the imaging functional and Bessel functions of integer order of the first kind. Numerical examples for single and multiple inclusions show that the presented algorithm not only retains the advantages of the traditional imaging functional but also improves the imaging performance.Comment: 15 pages, 20 figure

Topological derivative-based technique for imaging thin inhomogeneities with few incident directions

Many non-iterative imaging algorithms require a large number of incident directions. Topological derivative-based imaging techniques can alleviate this problem, but lacks a theoretical background and a definite means of selecting the optimal incident directions. In this paper, we rigorously analyze the mathematical structure of a topological derivative imaging function, confirm why a small number of incident directions is sufficient, and explore the optimal configuration of these directions. To this end, we represent the topological derivative based imaging function as an infinite series of Bessel functions of integer order of the first kind. Our analysis is supported by the results of numerical simulations.Comment: 14 pages, 29 figure

Asymptotic properties of MUSIC-type imaging in two-dimensional inverse scattering from thin electromagnetic inclusions

The main purpose of this paper is to study the structure of the well-known non-iterative MUltiple SIgnal Classification (MUSIC) algorithm for identifying the shape of extended electromagnetic inclusions of small thickness located in a two-dimensional homogeneous space. We construct a relationship between the MUSIC-type imaging functional for thin inclusions and the Bessel function of integer order of the first kind. Our construction is based on the structure of the left singular vectors of the collected multistatic response matrix whose elements are the measured far-field pattern and the asymptotic expansion formula in the presence of thin inclusions. Some numerical examples are shown to support the constructed MUSIC structure.Comment: 19 pages, 7 figure

Structure and properties of linear sampling method for perfectly conducting, arc-like cracks

We consider the imaging of arbitrary shaped, arc-like perfectly conducting cracks located in the two-dimensional homogeneous space via linear sampling method. Based on the structure of eigenvectors of so-called Multi Static Response (MSR) matrix, we discover the relationship between imaging functional adopted in the linear sampling method and Bessel function of integer order of the first kind. This relationship tells us that why linear sampling method works for imaging of perfectly conducting cracks in either Transverse Magnetic (Dirichlet boundary condition) and Transverse Electric (Neumann boundary condition), and explains its certain properties. Furthermore, we suggest multi-frequency imaging functional, which improves traditional linear sampling method. Various numerical experiments are performed for supporting our explores.Comment: 17 pages, 16 figure

Subspace migration for imaging of thin, curve-like electromagnetic inhomogeneities without shape information

It is well-known that subspace migration is stable and effective non-iterative imaging technique in inverse scattering problem. But, for a proper application, geometric features of unknown targets must be considered beforehand. Without this consideration, one cannot retrieve good results via subspace migration. In this paper, we identify the mathematical structure of single- and multi-frequency subspace migration without any geometric consideration of unknown targets and explore its certain properties. This is based on the fact that elements of so-called Multi-Static Response (MSR) matrix can be represented as an asymptotic expansion formula. Furthermore, based on the examined structure, we improve subspace migration and consider the multi-frequency subspace migration. Various results of numerical simulation with noisy data support our investigation.Comment: 15 pages, 32 figures. arXiv admin note: text overlap with arXiv:1404.237

Multi-frequency topological derivative for approximate shape acquisition of curve-like thin electromagnetic inhomogeneities

In this paper, we investigate a non-iterative imaging algorithm based on the topological derivative in order to retrieve the shape of penetrable electromagnetic inclusions when their dielectric permittivity and/or magnetic permeability differ from those in the embedding (homogeneous) space. The main objective is the imaging of crack-like thin inclusions, but the algorithm can be applied to arbitrarily shaped inclusions. For this purpose, we apply multiple time-harmonic frequencies and normalize the topological derivative imaging function by its maximum value. In order to verify its validity, we apply it for the imaging of two-dimensional crack-like thin electromagnetic inhomogeneities completely hidden in a homogeneous material. Corresponding numerical simulations with noisy data are performed for showing the efficacy of the proposed algorithm.Comment: 25 pages, 28 figure