Abstract
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.
Highlights
The main purpose of microwave imaging is to retrieve the parameter distribution in a domain from scattering parameter data
To compare the imaging performance of FDSM (r, m) and FDSE (r, m), we established a mathematical structure of the indicator functions, as outlined below
To demonstrate the theoretical results and to compare the imaging performance of FDSM (r, m) and FDSE (r, m), simulation results with synthetic data are presented
Summary
The main purpose of microwave imaging is to retrieve the parameter (permittivity or conductivity) distribution in a domain from scattering parameter data. It is natural to consider the generation of a good initial guess before the iteration procedure Due to this reason, various noniterative techniques have been investigated and applied to inverse scattering problems and microwave imaging, for example, MUltiple SIgnal Classification (MUSIC) algorithm [19,20], Kirchhoff and subspace migrations [21,22], Factorization method [23,24], topological sensitivity [25,26], and linear sampling method [27,28]. A related mathematical theory of this phenomenon has yet to be satisfactorily established because previous studies do not consider the coupling effect between teh anomaly and antennas Motivated by this issue, we attempted to identify the factors that influence the measurement data and correspondingly introduced another indicator function of DSM for a better imaging performance by removing certain scattering parameter data influenced by the coupling effect.
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