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

Objective:
The inverse problem of computing conductivity distributions in 2D and 3D objects interrogated by low-frequency electrical signals, which is called Electrical Impedance Tomography (EIT), is treated using a Method-of-Moment technique.
Methods:
A Point-Matching-Method-of-Moment technique is used to formulate a global integral equation solver. Radial Basis Functions are adopted to express the conductivity distribution. Single-step quadratic-norm (
$L^2$
) and iterative total variation (
$L^1$
) regularization techniques are exploited to solve the inverse problem.
Results:
Simulation and experimental tests on a circular reconstruction domain show satisfactory performance in deriving conductivity distribution, achieving a Correlation Coefficient (
$CC$
) up to 0.863 for 70 dB voltage
$SNR$
and 0.842 for 40 dB voltage
$SNR$
. The proposed methodology with
$L^2$
-norm regularization provided better results than traditional iterative Gauss-Newton's approach, whereas with
$L^1$
-norm regularization it showed promising performance. Moreover, 3D reconstructions on a cylindrical cavity demonstrated superior results near the electrodes’ planes compared to those of the conventional linearized approach. Finally, application to EIT medical data for dynamic lung imaging successfully revealed the breath-cycle conductivity changes.
Conclusion:
The results show that the proposed method can be effective for both 2D and 3D EIT and applicable to many applications.
Significance:
Strong conductivity variations are successfully tackled with a very good Correlation Coefficient. In contrast to conventional EIT solutions based on weak-form and linearization on small conductivity changes, the proposed method requires only one step to converge with
$L^2$
-norm regularization. The proposed method with
$L^1$
-norm regularization also achieves good reconstruction quality with a low number of iterations.