Multi-resolution subspace-based optimization method for solving three-dimensional inverse scattering problems.

Area of Science:

• Electromagnetics and Applied Physics
• Computational Imaging
• Inverse Problems

Background:

• Quantitative three-dimensional microwave imaging is crucial for various applications.
• Inverse scattering problems often suffer from local minima and ambiguity.
• The contrast source framework is a common approach for microwave imaging.

Purpose of the Study:

• To propose an innovative methodology for solving quantitative 3D microwave imaging problems.
• To address the challenges of local minima and ambiguity in inverse scattering.
• To accurately retrieve both deterministic and ambiguous parts of unknown contrast currents.

Main Methods:

• A combination of an iterative multiscaling strategy and a subspace-based optimization method (SOM).
• A nested iteration process: outer loop refines the region of interest (ROI), inner loop retrieves dielectric properties.
• Utilizing the contrast source framework for problem formulation.

Main Results:

• The proposed algorithm effectively mitigates local minimum issues.
• It accurately retrieves both deterministic and ambiguous components of contrast currents.
• Numerical examples demonstrate the algorithm's validity and robustness compared to existing methods.

Conclusions:

• The developed methodology offers a robust solution for quantitative 3D microwave imaging.
• The combination of multiscaling and SOM provides enhanced accuracy in scatterer detection and property retrieval.
• This approach shows significant promise for advancing microwave imaging techniques.