Automated filtering in the nonlinear Fourier domain of systematic artifacts in 2D electrical impedance tomography

Figure 1.  Top row: a sample difference reconstruction $ \sigma $ (left) of one frame from Human Dataset 1, reconstructed with no priors, and the corresponding segmented lung region (right) compared against the lung region extracted from CT data, which we take to be ground truth. Note the large conductive artifacts on the left and right sides of the reconstruction (indicated by arrows) which distort the lung boundary. Bottom row: the reconstruction $ \sigma' $ which now includes a priori data, and corresponding segmented lung boundaries, showing improved sharpness of organ boundaries, but still exhibiting large artifacts

Figure 2.  A flowchart illustrating the main steps of the proposed algorithm. Fourier data is represented by colored regions plotted in the (real or imaginary) $ k $-plane, with the origin at the center. The sets $ \mathcal{R}_1^{{ \mbox{Re}}} $ and $ \mathcal{R}_1^{{ \mbox{Im}}} $ are denoted by the general notation $ \mathcal{R}_1 $

Figure 3.  Sample sequence of left and right artifact boundaries corresponding to each of 5 total iterations of Brown linear temporal smoothing, plotted on the same axes. The original extracted artifact boundaries are plotted in lightest gray, with subsequent iterations plotted in incrementally darker grayscale. The final artifact boundaries are plotted boldly, in black.

Figure 4.  Original a priori boundaries with no artifacts (left), the reconstruction $ \sigma $ containing artifacts (center), and the modified boundaries which now include automatically extracted artifacts (right), for a sample frame from Human Dataset 1

Figure 5.  Top row: Conductivity phantoms for Simulated Datasets A, B, and C, with added artifacts, used to generate simulated data. Bottom row: the corresponding phantoms with no artifacts, considered ground truth for quantitative validation purposes. The conductivity values used in the forward solution were $ \sigma_{\mathrm{heart}} = 0.75, \sigma_{\mathrm{lungs}} = 0.25, \sigma_{\mathrm{artifacts}} = 0.9, \sigma_{\mathrm{background}} = 0.5 $ S/m.

Figure 6.  FEM meshes for Simulated Datasets A, B, and C, with added artifacts. Electrode centers are plotted using dots on the boundary

Figure 7.  Results from simulated data. Normalized reconstructions $ \sigma $ (no priors or artifact filtering, top row), $ \sigma' $ (with priors, no artifact filtering, center row), and $ \tilde\sigma' $ (with priors and artifact filtering, bottom row) corresponding to Simulated Datasets A, B, and C left to right as labeled. The appearance of induced lateral conductive artifacts in $ \sigma $ is not sufficiently improved by the addition of priors in $ \sigma' $. The reconstructions $ \tilde \sigma' $ exhibit visually reduced artifact appearance by comparison

Figure 8.  Results from simulated data. NRMSE values (top row) and SSIM values (bottom row) for Simulated Datasets A, B, and C as labeled, comparing normalized reconstructions $ \sigma' $ (with priors but no artifact filtering, solid blue bars) and $ \tilde \sigma' $ (with artifact filtering, striped bars), computed for both the entire domain (left column) and the true lung region (right column) in each reconstruction. We take the normalized conductivity phantom without artifacts to be ground truth. Note that smaller NRMSE values and larger SSIM values are desirable

Figure 9.  Results from simulated data. Level set segmentation of lung boundaries for reconstructions (blue) against the true lung region used in the conductivity phantom (gray), for $ \sigma' $ (with priors but no artifact filtering, top row), and $ \tilde\sigma' $ (with artifact filtering, bottom row), corresponding to Simulated Datasets A, B, and C left to right as labeled. Lungs regions corresponding to filtered reconstructions $ \tilde\sigma' $ exhibit greater visual fidelity to the ground truth lung shape as compared to those corresponding to reconstructions $ \sigma' $

Figure 10.  Results from simulated data. NRMSE values for the segmented lung regions for Simulated Datasets A, B, and C as labeled, comparing binary images of lung regions segmented from $ \sigma' $ (with priors but no artifact filtering, solid green bars) and $ \tilde \sigma' $ (with artifact filtering, striped bars), computed over the entire domain for each reconstruction. We take the binary lung region used in the conductivity phantom without artifacts to be ground truth. Note that smaller NRMSE values are desirable

Figure 11.  Archival CT scans corresponding to Human Datasets 1 (left) and 2 (right), collected upon inspiration in the plane of the electrodes immediately following the EIT scans. We take these scans to be ground truth, and they were used to extract the a priori boundaries for each dataset. Images are displayed in DICOM orientation

Figure 12.  Results from human data. Sequence of representative difference images corresponding to one full breathing cycle from Human Datasets 1 (top) and 2 (bottom). For each dataset, the top row gives the standard regularized D-bar reconstructions $ \sigma' $ with a priori sharpening methods applied. Note the appearance of lateral conductive artifacts in the reconstructions $ \sigma' $, which have not been removed by inclusion of a priori data. The bottom row for each dataset gives reconstructions after artifact filtering, showing significant reduction of artifacts and improvement of lung boundary shapes

Figure 13.  Results from human data. Plots of the segmented lung regions for the representative reconstructions $ \sigma' $ and $ \tilde\sigma' $ for Human Datasets 1 (top) and 2 (bottom). In each image, the segmented lung region (blue) is plotted over the lung region extracted from the CT scan (gray). Lungs regions corresponding to filtered reconstructions $ \tilde\sigma' $ exhibit greater visual fidelity to the ground truth lung shape as compared to those corresponding to reconstructions $ \sigma' $

Figure 14.  Results from human data. NRMSE values for the binary images of segmented lung regions corresponding to the representative reconstructions $ \sigma' $ (with priors, no artifact filtering, solid green), and $ \tilde\sigma' $ (with artifact filtering, striped) for Human Datasets 1 (top) and 2 (bottom) as compared to the lung region extracted from the CT scans for each patient, which we take to be ground truth. Smaller NRMSE values are desirable. This metric provides evidence that the reconstructions with artifact filtering exhibit greater fidelity to the ground truth lung shape