Microwave imaging using the finite-element method and a sensitivity analysis approach.

Area of Science:

• Electromagnetics and computational physics
• Inverse problems and numerical methods

Background:

• Reconstructing constitutive parameters of penetrable scatterers from scattered field data is crucial for various applications.
• Existing methods often struggle with ill-posed inverse problems and computational efficiency.

Discussion:

• A differential formulation of the forward scattering problem is solved using the finite-element method (FEM).
• A cost function, incorporating measurement error and Tikhonov regularization, is minimized using a nonlinear conjugate gradient algorithm.
• Sensitivity analysis via FEM and adjoint state vector methodology enhance computational efficiency and accuracy.

Key Insights:

• The proposed method effectively reconstructs scatterer parameters from scattered field measurements.
• The integration of FEM and Tikhonov regularization addresses the ill-posed nature of inverse scattering problems.
• The technique demonstrates robustness against noise and varying regularization levels.

Outlook:

• The method holds promise for applications in microwave medical imaging, such as detecting proliferated bone marrow.
• Further research could explore extensions to more complex scatterer geometries and different measurement modalities.