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Contraction Integral Equation for Three-Dimensional Electromagnetic Inverse Scattering Problems.

Yu Zhong1, Kuiwen Xu2

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|August 30, 2021
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Summary
This summary is machine-generated.

This study introduces a new contraction integral equation for inversion (CIE-I) to solve 3D inverse scattering problems (ISPs). The novel method significantly improves inversion performance and speed, especially for complex scattering scenarios.

Keywords:
contraction integral equation for inversion (CIE-I)imaginginverse scatteringnonlinear problem

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Area of Science:

  • Electromagnetics
  • Applied Mathematics
  • Imaging Science

Background:

  • Inverse scattering problems (ISPs) are crucial for applications like geophysical exploration and medical imaging.
  • Traditional methods like the Lippmann-Schwinger integral equation (LSIE) struggle with highly nonlinear ISPs due to multiple scattering effects.
  • Existing methods often converge to local minima, especially with strong scatterers.

Purpose of the Study:

  • To implement a novel contraction integral equation for inversion (CIE-I) for three-dimensional (3D) electromagnetic ISPs.
  • To enhance the performance and convergence speed of inversion algorithms for challenging ISPs.
  • To explore modifications to the contraction mapping condition for further acceleration.

Main Methods:

  • Implementation of the CIE-I for 3D ISPs.
  • Utilizing the FFT-based twofold subspace-based optimization method (TSOM).
  • Relaxing the contraction mapping condition for contrast updates.

Main Results:

  • CIE-I demonstrates superior performance over LSIE for 3D ISPs with strong scatterers, avoiding local minima.
  • The proposed method shows significantly faster convergence for moderate scatterers compared to LSIE.
  • Relaxing contraction mapping conditions further accelerates convergence.

Conclusions:

  • The CIE-I is a powerful tool for solving 3D electromagnetic ISPs, outperforming LSIE.
  • The method offers improved accuracy and speed, particularly for complex and highly nonlinear scattering scenarios.
  • Further optimization of contraction mappings can enhance computational efficiency.