# Electrical Impedance Tomography with Deep Calder'on Method

arXiv: https://arxiv.org/abs/2304.09074 · HTML: https://mlsanity.com/paper/2304.09074/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 53 references that are in the map.
- First posted on arXiv 18 Apr 2023.

## Builds on (most cited first, 9 of 9)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Deep Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [Deep learning for undersampled MRI reconstruction](https://mlsanity.com/paper/1709.02576/) (2017)
- [A deep convolutional neural network using directional wavelets for low-dose X-ray CT reconstruction](https://mlsanity.com/paper/1610.09736/) (2016)
- [Deep D-bar: Real time Electrical Impedance Tomography Imaging with Deep Neural Networks](https://mlsanity.com/paper/1711.03180/) (2017)
- [Solving Electrical Impedance Tomography with Deep Learning](https://mlsanity.com/paper/1906.03944/) (2019)
- [Unsupervised Knowledge-Transfer for Learned Image Reconstruction](https://mlsanity.com/paper/2107.02572/) (2021)

## Built on by (most cited first, 3 of 3)

- [Electrical Impedance Tomography: A Fair Comparative Study on Deep Learning and Analytic-based Approaches](https://mlsanity.com/paper/2310.18636/) (2023)
- [Stabilizing and Solving Unique Continuation Problems by Parameterizing Data and Learning Finite Element Solution Operators](https://mlsanity.com/paper/2412.04409/) (2024)
- [The learned range test method for the inverse inclusion problem](https://mlsanity.com/paper/2411.00463/) (2024)

## Abstract (arXiv)

Electrical impedance tomography (EIT) is a noninvasive medical imaging modality utilizing the current-density/voltage data measured on the surface of the subject. Calder'on's method is a relatively recent EIT imaging algorithm that is non-iterative, fast, and capable of reconstructing complex-valued electric impedances. However, due to the regularization via low-pass filtering and linearization, the reconstructed images suffer from severe blurring and under-estimation of the exact conductivity values. In this work, we develop an enhanced version of Calder'on's method, using deep convolution neural networks (i.e., U-net) as an effective targeted post-processing step, and term the resulting method by deep Calder'on's method. Specifically, we learn a U-net to postprocess the EIT images generated by Calder'on's method so as to have better resolutions and more accurate estimates of conductivity values. We simulate chest configurations with which we generate the current-density/voltage boundary measurements and the corresponding reconstructed images by Calder'on's method. With the paired training data, we learn the deep neural network and evaluate its performance on real tank measurement data. The experimental results indicate that the proposed approach indeed provides a fast and direct (complex-valued) impedance tomography imaging technique, and substantially improves the capability of the standard Calder'on's method.