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

Won-Kwang Park

Abstract

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.

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

Abstract

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 MHz of angular frequency are exhibited to show the feasibility of designed algorithm and to support investigated structure of imaging function.

Paper Structure

This paper contains 10 sections, 3 theorems, 50 equations, 14 figures, 1 table.

Table of Contents

  1. Introduction
  2. Forward Problem and MUSIC Algorithm
  3. Forward Problem and Scattering Parameter
  4. Introduction to MUSIC Algorithm
  5. MUSIC Algorithm Without Diagonal Elements of the Scattering Matrix
  6. Analysis of the Imaging Function
  7. Simulation Results With Synthetic Data: CST STUDIO SUITE
  8. Real-Data Experiments
  9. Concluding Remarks
  10. Proof of the Theorem \ref{['StructureImaging']}

Key Result

Theorem 3.1

Let $\boldsymbol{\theta}_n=\mathbf{a}_n/|\mathbf{a}_n|=\mathbf{a}_n/R=[\cos\theta_n,\sin\theta_n]^{\mathtt{T}}$ and $\mathbf{r}-\mathbf{r}_\star=|\mathbf{r}-\mathbf{r}_\star|[\cos\phi_\star,\sin\phi_\star]^{\mathtt{T}}$. If $\mathbf{a}_n$ satisfies $|\mathbf{a}_n-\mathbf{r}|\gg1/4|k|$ for $n=1,2,\cd where $J_\nu$ denotes the Bessel function of integer order $\nu$ of the first kind and $\mathrm{Re}

Figures (14)

  • Figure 1: (Examples \ref{['Example4-1']} and \ref{['Example4-2']}) Test configurations with (left) and without (right) anomaly $\Gamma_\mathrm{S}$ for calculating $\mathrm{S}_{\mathop{\mathrm{tot}}\limits}(m,n)$ and $\mathrm{S}_{\mathop{\mathrm{inc}}\limits}(m,n)$, respectively.
  • Figure 2: (Example \ref{['Example4-1']}) Distribution of singular values of scattering matrix $\mathbb{K}$ (left column) and map of $\mathfrak{F}_{\mathop{\mathrm{TM}}\limits}(\mathbf{r})$ (right column).
  • Figure 3: (Example \ref{['Example4-2']}) Distribution of singular values of scattering matrix $\mathbb{D}$ (left) and map of $\mathfrak{F}_{\mathop{\mathrm{DM}}\limits}(\mathbf{r})$ (right).
  • Figure 4: (Example \ref{['Example4-3']}) Same as Figure \ref{['Setting-Small']} except the anomaly is $\Gamma_\mathrm{E}$.
  • Figure 5: (Example \ref{['Example4-3']}) Distribution of singular values of scattering matrix (left column) and map of $\mathfrak{F}_{\mathop{\mathrm{TM}}\limits}(\mathbf{r})$ (top, right column) and $\mathfrak{F}_{\mathop{\mathrm{DM}}\limits}(\mathbf{r})$ (bottom, right).
  • ...and 9 more figures

Theorems & Definitions (19)

  • Remark 2.1: Linearization
  • Remark 2.2: 2D approximation
  • Remark 2.3: Total number of nonzero singular values
  • Remark 2.4: Extended anomaly
  • Theorem 3.1: Structure of imaging function for single anomaly
  • Remark 3.1: Applicability
  • Corollary 3.2: Unique determination of anomaly
  • Remark 3.2: Appearance of unexpected artifacts and resolution
  • Remark 3.3: Ideal condition for a better imaging performance
  • Remark 3.4: Experimental configuration for a better imaging performance
  • ...and 9 more