Adaptive Kaczmarz method for image reconstruction in electrical impedance tomography

Area of Science:

• Medical Imaging
• Computational Electromagnetics
• Applied Mathematics

Background:

• Electrical Impedance Tomography (EIT) reconstructs internal conductivity from surface measurements.
• Solving the inverse problem in EIT is computationally intensive, especially for large-scale applications.
• Traditional methods like Kaczmarz and Gauss-Newton can be memory-demanding and less accurate.

Purpose of the Study:

• To present an adaptive Kaczmarz method for solving the inverse problem in EIT.
• To improve the accuracy and stability of conductivity distribution reconstruction.
• To reduce computational cost and memory requirements for large-scale EIT problems.

Main Methods:

• An adaptive Kaczmarz method is proposed, integrating optimal current pattern generation.
• A novel subset scheme is employed for memory efficiency.
• The method iteratively refines conductivity estimates using optimal current patterns between Kaczmarz algorithm steps.

Main Results:

• The proposed adaptive Kaczmarz method yields more accurate and stable solutions compared to traditional Kaczmarz and Gauss-Newton methods.
• The novel subset scheme enhances memory efficiency.
• The algorithm effectively characterizes unknown conductivity distributions.

Conclusions:

• The adaptive Kaczmarz method offers a computationally efficient and accurate approach for EIT inverse problems.
• Optimal current pattern selection is crucial for distinguishing conductivity estimates.
• This method provides a robust alternative for reconstructing conductivity distributions in EIT.