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

Won-Kwang Park

TL;DR

This paper presents a MUSIC-type imaging framework for anomaly detection in microwave imaging without switching devices by exploiting a non-symmetric scattering-parameter matrix. It derives an imaging function from the left- and right-singular vectors and shows that the map can be described as an infinite series of Bessel functions, with imaging quality governed by antenna geometry. Through synthetic and experimental data, the work demonstrates that increasing the total number of transmitters and receivers or employing optimal antenna arrangements can significantly improve anomaly localization and outline recovery. The results extend qualitative microwave imaging to constrained hardware setups and offer practical design insights for antenna placement in non-switching configurations.

Abstract

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.

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

TL;DR

This paper presents a MUSIC-type imaging framework for anomaly detection in microwave imaging without switching devices by exploiting a non-symmetric scattering-parameter matrix. It derives an imaging function from the left- and right-singular vectors and shows that the map can be described as an infinite series of Bessel functions, with imaging quality governed by antenna geometry. Through synthetic and experimental data, the work demonstrates that increasing the total number of transmitters and receivers or employing optimal antenna arrangements can significantly improve anomaly localization and outline recovery. The results extend qualitative microwave imaging to constrained hardware setups and offer practical design insights for antenna placement in non-switching configurations.

Abstract

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.
Paper Structure (6 sections, 2 theorems, 40 equations, 17 figures)

This paper contains 6 sections, 2 theorems, 40 equations, 17 figures.

Table of Contents

  1. Introduction
  2. Scattering Parameter and MUSIC Algorithm
  3. Theoretical Result and Some Properties of Imaging Function
  4. Simulation Results With Synthetic Data
  5. Simulation Results With Experimental Data
  6. Concluding Remarks

Key Result

Theorem 3.1

Let $\boldsymbol{\theta}_n=\mathbf{a}_n/|\mathbf{a}_n|=\mathbf{a}_n/R=(\cos\theta_n,\sin\theta_n)$, $\boldsymbol{\vartheta}_m=\mathbf{b}_m/|\mathbf{b}_m|=\mathbf{b}_m/R=(\cos\vartheta_m,\sin\vartheta_m)$, and $\mathbf{r}-\mathbf{r}_\star=|\mathbf{r}-\mathbf{r}_\star|(\cos\phi,\sin\phi)$. If $M,N>1$ where Here, $J_p$ denotes the Bessel function of integer order $p$ of the first kind and

Figures (17)

  • Figure 1: Illustration of configuration setup.
  • Figure 2: Illustration of the background (left), single (center) and multiple small anomalies (right).
  • Figure 3: (Example \ref{['ex1']}) Maps of $\mathfrak{F}_{\mathop{\mathrm{TX}}\limits}(\mathbf{r})$ (first column), $\mathfrak{F}_{\mathop{\mathrm{RX}}\limits}(\mathbf{r})$ (second column), $\mathfrak{F}(\mathbf{r})$ (third column), and Jaccard index (fourth column). Green and red colored circles describe the location of transmitters and receivers, respectively.
  • Figure 4: (Example \ref{['ex2']}) Maps of $\mathfrak{F}_{\mathop{\mathrm{TX}}\limits}(\mathbf{r})$ (first column), $\mathfrak{F}_{\mathop{\mathrm{RX}}\limits}(\mathbf{r})$ (second column), $\mathfrak{F}(\mathbf{r})$ (third column), and Jaccard index (fourth column). Green and red colored circles describe the location of transmitters and receivers, respectively.
  • Figure 5: (Example \ref{['ex3']}) Maps of $\mathfrak{F}_{\mathop{\mathrm{TX}}\limits}(\mathbf{r})$ (first column), $\mathfrak{F}_{\mathop{\mathrm{RX}}\limits}(\mathbf{r})$ (second column), $\mathfrak{F}(\mathbf{r})$ (third column), and Jaccard index (fourth column). Green and red colored circles describe the location of transmitters and receivers, respectively.
  • ...and 12 more figures

Theorems & Definitions (14)

  • Theorem 3.1: Structure of the Imaging Function for Single Anomaly
  • proof
  • Remark 3.1: Decomposition of the Imaging Function
  • Remark 3.2: Applicability and Limitation
  • Remark 3.3: Optimal Antenna Arrangement
  • Corollary 3.2: Unique Identification
  • Example 4.1: Small Number of Transmitters
  • Example 4.2: Increasing Total Number of Transmitters and Receivers
  • Example 4.3: Effects on the Arrangement of Antennas: Single Anomaly
  • Example 4.4: Imaging of Multiple Anomalies
  • ...and 4 more