Dual-Domain Deep D-bar Method for Solving Electrical Impedance Tomography
<|reference_start|>Dual-Domain Deep D-bar Method for Solving Electrical Impedance Tomography: The regularized D-bar method is one of the most prominent methods for solving Electrical Impedance Tomography (EIT) problems due to its efficiency and simplicity. It provides a direct approach by applying low-pass filtering to the scattering data in the non-linear Fourier domain, thereby yielding a smoothed conductivity approximation. However, D-bar images often present low contrast and low resolution due to the absence of accurate high-frequency information and ill-posedness of the problem. In this paper, we proposed a dual-domain neural network architecture to retrieve high-contrast D-bar image sequences from low-contrast D-bar images. To further accentuate the spatial features of the conductivity distribution, the widely adopted U-net has been tailored for conductivity image calibration from the predicted D-bar image sequences. We call such a hybrid approach by Dual-Domain Deep D-bar method due to the consideration of both scattering data and image information. Compared to the single-scale structure, our proposed multi-scale structure exhibits superior capabilities in reducing artifacts and refining conductivity approximation. Additionally, solving discrete D-bar systems using the GMRES algorithm entails significant computational complexity, which is extremely time-consuming on CPU-based devices. To remedy this, we designed a surrogate GPU-based Richardson iterative method to accelerate the data enhancement process by D-bar. Numerical results are presented for simulated EIT data from the KIT4 and ACT4 systems to demonstrate notable improvements in absolute EIT imaging quality when compared to existing methodologies.<|reference_end|>
@article{cao2024dual-domain,
    title={Dual-Domain Deep D-bar Method for Solving Electrical Impedance
  Tomography},
    author={Xiang Cao, Qiaoqiao Ding, Xiaoqun Zhang},
    journal={arXiv preprint arXiv:2407.03335},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.03335},
    primaryClass={math.NA cs.CV cs.NA eess.IV}
}