Machine learning enhanced electrical impedance tomography for 2D materials

Abstract

Electrical Impedance Tomography (EIT) is a non-invasive imaging technique that reconstructs the interior conductivity distribution of samples from a set of voltage measurements performed on the sample boundary. EIT reconstruction is a non-linear and ill-posed inverse problem. Consequently, the non-linearity results in a high computational cost of solution, while regularisation and the most informative measurements must be used to overcome ill-posedness. To build the foundation of future research into EIT applications for 2D materials, such as graphene, we designed and implemented a novel approach to measurement optimisation via a machine learning adaptive electrode selection algorithm (A-ESA). Furthermore, we modified the forward solver of a python-based EIT simulation software, pyEIT, to include the complete electrode model (CEM) and employed it on 2D square samples [1, 2]. In addition, the Deep D-Bar U-Net convolutional neural network architecture was applied to post-process conductivity map reconstructions from the GREIT algorithm [3, 4]. The A-ESA offered around 20% lower reconstruction losses in fewer measurements than the standard opposite-adjacent electrode selection algorithm, on both simulated data and when applied to a real graphene-based device. The CEM enhanced forward solver achieved a 3% lower loss compared to the original pyEIT forward model. Finally, an experimental evaluation was performed on a graphene laminate film. Overall, this work demonstrates how EIT could be applied to 2D materials and highlights the utility of machine learning in both the experimental and analytical aspects of EIT.

Sensitivity volume as figure-of-merit for maximizing data importance in electrical impedance tomography

“…Other EIT literature has sought to increase contact number (Coxson et al 2022) and vary contact placement (Yan et al 2006, Smyl and Liu 2020, Karimi et al 2021 to optimize results. Additional works have used two-point measurements or electrode segmentation schemes to select contacts (Polydorides and McCann 2002, Kantartzis et al 2013, Zhang et al 2016, Ma et al 2020 that may have some strict mathematical advantage, but are disadvantageous for use in biomedical applications (Putensen et al 2019) or with existing EIT hardware.…”

“…In the optimization of EIT methods, it becomes necessary to develop figures of merit for quantitative comparisons. A wide variety of metrics have been proposed within the EIT literature that are often case specific (Graham and Adler 2006, Adler et al 2009, Yasin et al 2011, Grychtol et al 2016, Wagenaar and Adler 2016, Thürk et al 2019 or cannot be applied until after an inverse solve is completed (Yorkey et al 1987, Tang et al 2002, Coxson et al 2022. In comparison, the sensitivity volume figure-of-merit is unique, unambiguous, consistent, and broadly applicable.…”

“…Data space selection has been referred to as an 'electrode selection algorithm' (Coxson et al 2022), a measurement 'protocol' (Holder 2005), an 'electrode stimulation and measurement configuration' (Grychtol et al 2016), or an 'electrode placement configuration' (Graham and Adler 2007). These prior works often take trial and error approaches (Adler et al 2011), are limited to highly specific cases (Ma et al 2020), or require optimization of multi-step machine learning algorithms (Coxson et al 2022).…”

“…Data space selection has been referred to as an 'electrode selection algorithm' (Coxson et al 2022), a measurement 'protocol' (Holder 2005), an 'electrode stimulation and measurement configuration' (Grychtol et al 2016), or an 'electrode placement configuration' (Graham and Adler 2007). These prior works often take trial and error approaches (Adler et al 2011), are limited to highly specific cases (Ma et al 2020), or require optimization of multi-step machine learning algorithms (Coxson et al 2022). In addition to the adjacent measurement protocol mentioned in the introduction, skip measurements have grown in popularity as a data space standard based on an empirical extrapolation of adjacent data space (Adler et al 2011, de Castro Martins et al 2019, Adler and Zhao 2023.…”

The Trade-off in Machine Learning Application for Electrical Impedance Tomography

“…In order to bypass the problem of conventional reconstruction processing, the ML predicts the true conductivity distribution by governing a neural network trained in the initial condition of EIT measurement. Some promising studies show the performance of ML, such as prediction of the most optimum scanning measurement pattern [14] , restoration of reconstructed image [15] , estimation of the object of interest without an image [16] , and recognition of hand prosthesis control [17] .…”