研究目的
To develop and validate a full-wave three-dimensional microwave imaging approach for solving the inverse scattering problem using a Newton-conjugate-gradient method in Lp Banach spaces, aiming to improve reconstruction accuracy by reducing over-smoothing effects compared to Hilbert space methods.
研究成果
The proposed Newton-conjugate-gradient method in Lp Banach spaces effectively improves the accuracy of 3D microwave imaging by reducing over-smoothing effects compared to Hilbert space approaches. Numerical results show better shape identification and permittivity reconstruction with optimal p values. Future work should focus on defining a criterion for selecting p and validating the method with experimental data.
研究不足
The study uses synthetic data with added noise, which may not fully represent real-world conditions. The choice of the optimal norm parameter p is not fully defined and requires further analysis. The method has not been validated with experimental data, limiting its applicability to practical scenarios. Computational complexity may be high for large 3D problems.
1：Experimental Design and Method Selection:
The study employs a numerical simulation approach using synthetic data. The inverse scattering problem is solved iteratively with a Newton scheme, where at each step, the problem is linearized and solved using a conjugate-gradient method regularized in Lp Banach spaces. The method is designed to handle the ill-posedness of 3D microwave imaging.
2：Sample Selection and Data Sources:
Synthetic data are generated for a cubic investigation volume containing two dielectric spheres with specified radii, positions, and permittivities. The scattered field is computed using a method-of-moments-based numerical code and corrupted with Gaussian noise (25 dB SNR).
3：List of Experimental Equipment and Materials:
No physical equipment is used; the study is computational. The numerical code is custom-developed based on the method-of-moments.
4：Experimental Procedures and Operational Workflow:
The investigation volume is discretized into subdomains. The inversion procedure involves initializing with a zero contrast function, linearizing the problem at each Newton step, solving the linearized equations with the conjugate-gradient method in Lp spaces, updating the contrast, and iterating until convergence criteria are met (e.g., error reduction below 1% or maximum iterations reached).
5：Data Analysis Methods:
Reconstruction quality is evaluated using normalized root mean square error and mean relative errors for target and background regions. The behavior of errors is analyzed with respect to the norm parameter p in Lp spaces.
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