An Efficient Point-Matching Method-of-Moments for 2D and 3D Electrical Impedance Tomography Using Radial Basis...

Area of Science:

• Electrical Engineering
• Biomedical Imaging
• Computational Physics

Background:

• Electrical Impedance Tomography (EIT) is a non-invasive imaging technique used to reconstruct internal conductivity distributions.
• Traditional EIT methods often rely on linearization and weak-form formulations, which can be limited in handling strong conductivity variations.
• Accurate conductivity reconstruction is crucial for various applications, including medical diagnostics and material science.

Purpose of the Study:

• To develop and validate a novel Method-of-Moment (MoM) technique for solving the inverse problem in 2D and 3D Electrical Impedance Tomography (EIT).
• To evaluate the performance of the proposed MoM technique using both L2 (quadratic-norm) and L1 (total variation) regularization methods.
• To demonstrate the applicability and effectiveness of the developed EIT method across different domains, including simulations, experimental tests, and medical imaging.

Main Methods:

• A Point-Matching-Method-of-Moment technique was employed to formulate a global integral equation solver.
• Radial Basis Functions were utilized to represent the conductivity distribution within the objects.
• Both single-step L2-norm and iterative L1-norm regularization techniques were applied to solve the inverse problem.

Main Results:

• Simulations and experimental tests on a circular domain achieved high Correlation Coefficients (CC) up to 0.863 (70 dB SNR) and 0.842 (40 dB SNR).
• The L2-norm regularization provided superior results compared to the traditional Gauss-Newton approach.
• 3D reconstructions showed improved performance near electrodes, and dynamic lung imaging successfully captured breath-cycle conductivity changes.

Conclusions:

• The proposed Method-of-Moment technique is effective for both 2D and 3D EIT, showing broad applicability.
• The method successfully reconstructs strong conductivity variations, outperforming conventional linearized approaches.
• Both L2 and L1 regularization strategies offer efficient and accurate solutions for EIT inverse problems.