Implicit Solutions of the Electrical Impedance Tomography Inverse Problem in the Continuous Domain with Deep Neural...

Area of Science:

• Medical Imaging
• Computational Science
• Machine Learning

Background:

• Electrical impedance tomography (EIT) is a non-invasive imaging technique for conductivity estimation.
• Existing analytical and numerical methods for EIT inverse problems face challenges with numerical instability and computational time.
• Real-time applications of EIT are limited by the performance of current algorithms.

Purpose of the Study:

• To develop a novel machine learning approach for solving the EIT inverse problem, focusing on shape reconstruction.
• To address numerical instability and computational limitations of existing EIT methods.
• To enable real-time conductivity imaging and shape estimation.

Main Methods:

• A novel neural network architecture is proposed to estimate conductivity distribution in continuous space.
• The model separates the object into homogeneous background and non-homogeneous regions.
• Piece-wise constant and constrained reconstruction methods are developed, inspired by 3D vision techniques.

Main Results:

• The proposed neural network architecture effectively solves the EIT inverse problem, demonstrating improved stability.
• The method allows for real-time inverse problem solving without assumptions on the forward model.
• Numerical experiments show competitive performance compared to established analytical algorithms.

Conclusions:

• The developed machine learning approach offers a stable and efficient solution for EIT shape reconstruction.
• This method advances the potential for real-time applications in conductivity imaging.
• The adaptable architecture can be applied to other ill-posed coefficient inverse problems.