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Deep D-bar: Real time Electrical Impedance Tomography Imaging with Deep Neural Networks (1711.03180v2)

Published 8 Nov 2017 in math.NA, cs.NE, and math.AP

Abstract: The mathematical problem for Electrical Impedance Tomography (EIT) is a highly nonlinear ill-posed inverse problem requiring carefully designed reconstruction procedures to ensure reliable image generation. D-bar methods are based on a rigorous mathematical analysis and provide robust direct reconstructions by using a low-pass filtering of the associated nonlinear Fourier data. Similarly to low-pass filtering of linear Fourier data, only using low frequencies in the image recovery process results in blurred images lacking sharp features such as clear organ boundaries. Convolutional Neural Networks provide a powerful framework for post-processing such convolved direct reconstructions. In this study, we demonstrate that these CNN techniques lead to sharp and reliable reconstructions even for the highly nonlinear inverse problem of EIT. The network is trained on data sets of simulated examples and then applied to experimental data without the need to perform an additional transfer training. Results for absolute EIT images are presented using experimental EIT data from the ACT4 and KIT4 EIT systems.

Citations (239)

Summary

  • The paper enhances EIT reconstruction by integrating D-bar methods with a U-net CNN to mitigate blurring from low-pass filtering.
  • It demonstrates significant image clarity improvements validated by SSIM across experiments on ACT4 and KIT4 systems.
  • This hybrid approach paves the way for reliable, real-time EIT imaging in medical diagnostics and potential 3D applications.

Deep D-bar: Enhancing Real-Time Electrical Impedance Tomography Imaging with Deep Neural Networks

The paper "Deep D-bar: Real-Time Electrical Impedance Tomography Imaging with Deep Neural Networks" presents an innovative integration of D-bar methods with convolutional neural networks (CNNs) to tackle the challenges inherent in Electrical Impedance Tomography (EIT). Specifically, this paper addresses the limitations posed by EIT's ill-posed nonlinear inverse problem, notably its tendency to produce blurred images due to low-pass filtering of the nonlinear Fourier data. This development is significant within the context of medical imaging, where EIT's non-invasiveness and high contrast potential are often offset by difficulties in interpreting undersampled, noisy data.

Technical Overview

The authors focus on the D-bar method, known for its robust direct reconstructions for EIT. This approach is unique in its capacity to transform the EIT problem into a Schrödinger equation framework, facilitating the use of complex geometrical optics (CGO) solutions for reconstruction. The primary drawback of D-bar methods is the blurring resultant from low-pass filtering to handle the nonlinear inverse problem's instability. Therefore, the authors propose incorporating a CNN to counteract this blurring by enhancing the sharpness and reliability of EIT images.

Contribution and Results

The paper demonstrates that using a CNN as a post-processing tool on D-bar reconstructions substantially improves the image quality. The CNN employed is based on the U-net architecture, which has been particularly effective in segmentation tasks, making it apt for the image refinement needed in EIT. The network is trained with simulated datasets and demonstrates a noteworthy generalization capability, evidenced by its application to real experimental data without additional transfer training.

The experiments conducted on two EIT systems, ACT4 and KIT4, serve as validation for the method. The results indicate that the 'Deep D-bar' approach significantly enhances image clarity compared to traditional D-bar methods. The use of Structural Similarity Index Measures (SSIM) underscores the improved fidelity of the CNN post-processed images. Importantly, these findings suggest that real-time application is viable, aligning with the processing speed required in clinically relevant settings.

Implications and Future Directions

The implications of this research are multifold. Practically, it offers an effective method for improving the applicability of EIT in medical diagnostics by addressing long-standing issues related to image sharpness and detail. Theoretically, it showcases the potential of hybrid approaches in solving complex inverse problems by leveraging the strengths of both direct mathematical methods and deep learning.

Future developments may include extending this methodology to three-dimensional EIT imaging, where D-bar frameworks are still in a nascent stage. Moreover, exploration into different neural network architectures and varying input conditions could further enhance the robustness of this method. The adaptability of this approach to other forms of imaging and different types of feature extraction remains an intriguing possibility.

In summary, the marriage of the D-bar method with CNNs introduces a nuanced approach to EIT, which could significantly advance its utility in medical and industrial settings. By systematically mitigating the blurring issue, this paper paves the way for more reliable, real-time imaging solutions that can ultimately improve patient diagnostics and outcomes.