Combination of machine learning and electrical impedance tomography

The reconstruction of electrical impedance tomography is a nonlinear and ill-posed reverse problem. Due to the non-linearity, the computational costs of a method are high, and regularization and the most relevant observations must be used to minimize bad condition.

Combination of machine learning and electrical impedance tomography

Study: Machine learning enhanced electrical impedance tomography for 2D materials† Image Credit: Peshkova/

In an article published in the magazine Inverse problems, an adaptive electrode selection technique for machine learning was used to build and apply a unique approach to measurement enhancement. Overall, this study showed how electrical impedance tomography (EIT) can be used for 2D materials and emphasized the importance of machine learning in both the numerical and computational components of electrical impedance tomography.

What is EIT?

Electrical Impedance Tomography (EIT) is a visualization technique that uses a series of four measurements along the sample edge to rebuild the conductivity dispersion in an object.

Electrical impedance tomography is a non-invasive imaging technology developed in geophysics for subsurface scanning and medical physics to investigate differences in body tissues by measuring conductivity changes.

Because the reverse problem in electrical impedance tomography image reconstruction is ill-posed, much work has been done from the outset to increase the integrity and precision of electrical impedance tomography. Many methods, including methods using artificial neural networks (ANNs), have been presented thus far in an attempt to address the reverse problem.

Deep learning and EIT

Recent studies have used deep learning to develop and evaluate an ANN on numerically generated data for the two-dimensional (2D) D-Bar reconstruction approach. They effectively created the conductivity of artificial agar objects and illustrated how neural networks could increase the restoration precision of electrical impedance tomography.

Machine learning is not only important for evaluating EIT images, but can also be used to optimize the placement of electrodes around the sample rather than simply spacing electrodes at regular intervals. Several regularly used flow patterns are available today, including the adjacent drive design and the opposite (polar) drive pattern.

A series of studies have assessed these patterns or provided a theoretical study on how to optimize electrode choice; machine-learned electrode selection models can replace most common computational procedures, and the adjacent pattern is still commonly used in the literature, even after it has been shown to be particularly inaccurate,

EIT use with graphene

Electrical impedance tomography has recently been used to investigate the 2D conduction patterns of thin films and graphene. The EIT reconstruction was coupled to a conductivity map obtained using time-domain spectroscopy (TDS), a low-resolution approach performed in a power-off state using rather expensive equipment when using graphene for the first time.

Only a 4% difference was detected between the TDS and EIT maps, indicating the applicability of electrical impedance tomography for the characterization of 2D materials. Although 2D EIT is often researched because it often involves simpler procedures, it does not reflect use cases in conventional medical applications.

The basic principles of EIT with machine learning for use on 2D materials were established here. A unique adaptive electrode selection technique for machine learning was devised and a strategy was developed to produce conductance restorations of 2D materials by integrating it with a forward solver complemented by the complete electrode model (CEM).

The EIT measurements were performed on a square sample mold using the pyEIT python-based program. This program originally only used a simple forward solver, but it was upgraded in this study to include the CEM.

Study Highlights

Taking into account the electrode width, the CEM-enhanced forward solver outperformed the base solution from the initial pyEIT program. More complicated modeling improved restoration precision, while GPU acceleration cut computation time in half.

Such properties are of crucial importance for future applications of 2D materials, where the limited width of connections becomes more and more relevant. In addition, creating a machine learning A-ESA was useful, as it regularly yielded fewer reconstructive losses and better performance than the usual opposite-adjacent and adjacent-adjacent techniques.

The use of U-Net CNN for the post-processing of the reconstruction produced encouraging initial results, highlighting the value of deep learning, which is increasingly being used in several domains, including EIT.

This study showed the potential application of EIT for the characterization of 2D materials and illustrated how the integration of machine learning approaches could significantly improve both the experimental and analytical parts of such work.

Future Directions

One of the next stages would be to examine rectangular samples, as the algorithm currently supports it: creating mesh, GREIT pixel images, and the general map matrix can all be of nx x ny shape. Future research could look at different morphologies, such as an ellipse or a jagged shape.

Rather than just periodically inserting electrodes, machine learning can be used to optimize their spatial placement around the sample.

One can even envision a recursive robotic solution that includes adaptive electrode selection and adaptive electrode in situ placement, where one set of data is taken, the electrodes are moved to more optimized locations, and then another set of data is retrieved at the new contact spots.


Coxson, A., Mihov, I., Wang, Z., Avramov, V., Barnes, F.B., & Slizovskiy, S. (2022). Machine learning enhanced electrical impedance tomography for 2D materials. Inverse problems† Available at:

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