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In-depth resolution for a strip source in the Fresnel zone
R Pierri1, A Liseno, F Soldovieri
1Seconda Università di Napoli, Dipartimento di Ingegneria dell'Informazione, Aversa, Italy. pierri@unina.it
Summary
This study analyzes resolution limits for reconstructing electric current distributions. Regularization is essential for stable solutions due to the ill-posed nature of inverse problems in the Fresnel zone.
Area of Science:
- Electromagnetics
- Inverse Problems
- Computational Physics
Background:
- Determining resolution limits in current distribution reconstruction is crucial for electromagnetic imaging.
- The study focuses on a 1D, scalar, rectilinear electric current distribution.
- Data collection occurs in the Fresnel zone over a finite rectilinear observation domain.
Purpose of the Study:
- To analyze the achievable resolution limits in reconstructing a current distribution.
- To investigate the ill-posed nature of the inverse problem and propose regularization methods.
- To determine depth-resolving power using Rayleigh's criterion.
Main Methods:
- Analytical singular-value decomposition (SVD) of the radiation operator.
- Introduction of suitable scalar products in data and unknown spaces.
- Utilizing results concerning prolate spheroidal wave functions.
- Applying truncated SVD for regularization.
Main Results:
- The inverse problem is severely ill-posed for high space-bandwidth products.
- Singular value behavior indicates the ill-posedness.
- Truncated SVD provides a stable solution via regularization.
- Rayleigh's criterion was used to determine depth-resolving power.
Conclusions:
- Regularization is mandatory for stable solutions in current distribution reconstruction.
- The study provides insights into the resolution limits and depth-resolving power.
- Geometric parameters of the measurement configuration impact resolution.