Comparison of total variation algorithms for electrical impedance tomography

Area of Science:

• Medical Imaging
• Computational Electromagnetics
• Image Reconstruction

Background:

• Electrical Impedance Tomography (EIT) reconstructs internal conductivity distributions using boundary measurements.
• Traditional l2 norm regularization smooths sharp conductivity changes, limiting EIT resolution.
• Total Variation (TV) regularization preserves discontinuities but requires specialized algorithms due to non-differentiability.

Purpose of the Study:

• To compare the performance of three advanced Total Variation (TV) algorithms for Electrical Impedance Tomography (EIT).
• To evaluate noise performance, spatial resolution, and convergence rates of PDIPM, LADMM, and SB methods in EIT.
• To assess the effectiveness of these algorithms on different phantoms and noise levels.

Main Methods:

• Simulations were conducted on 2D cylindrical meshes and phantoms, including a 3D head-shaped phantom.
• Three TV algorithms were implemented and compared: primal dual interior point method (PDIPM), linearized alternating direction method of multipliers (LADMM), and split Bregman (SB).
• Performance metrics included calculation speed, spatial resolution, noise handling, convergence rate, and image error under varying noise conditions.

Main Results:

• LADMM exhibited the fastest computation but the poorest spatial resolution.
• PDIPM achieved the sharpest conductivity reconstruction but with lower contrast compared to SB.
• SB demonstrated a faster convergence rate than PDIPM and resulted in the lowest overall image errors.

Conclusions:

• Each TV algorithm presents unique advantages and disadvantages for EIT reconstruction.
• The split Bregman method offers a favorable balance of convergence speed and image accuracy for time-difference EIT.
• Algorithm selection in EIT depends on specific application requirements regarding speed, resolution, and accuracy.