Comparison of algorithms for non-linear inverse 3D electrical tomography reconstruction

Area of Science:

• Medical Imaging
• Computational Electromagnetics
• Biomedical Engineering

Background:

• Non-linear electrical impedance tomography (EIT) reconstruction typically uses the Newton-Raphson method.
• This approach faces challenges with large matrices and high storage demands in complex 3D scenarios.
• Existing methods are computationally intensive for 3D imaging.

Purpose of the Study:

• To evaluate a conjugate gradient (CG) based reconstruction algorithm as an alternative to Newton-Raphson for 3D EIT.
• To assess the feasibility of CG for 3D tomographic imaging with adaptive mesh refinement.
• To compare the storage and computational efficiency of CG versus Newton-Raphson.

Main Methods:

• Developed and implemented a conjugate gradient reconstruction algorithm for 3D EIT.
• Incorporated adaptive mesh refinement into the CG algorithm.
• Compared the CG algorithm against the Newton-Raphson scheme using a simple 3D head model.
• Evaluated reconstruction speed, accuracy, and storage requirements.

Main Results:

• The conjugate gradient algorithm demonstrated suitability for 3D EIT reconstruction.
• The CG method requires significantly less storage space compared to the Newton-Raphson scheme.
• A speed increase of approximately 30% was achieved with the CG method.
• Reconstruction accuracy was maintained without loss.

Conclusions:

• The conjugate gradient algorithm is a viable and efficient alternative for 3D non-linear EIT reconstruction.
• CG-based methods offer practical advantages in terms of speed and storage for complex 3D imaging problems.
• Adaptive mesh refinement enhances the performance of CG algorithms in EIT.