  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.
