Direct EIT Jacobian calculations for conductivity change and electrode movement
Bibliographic record
Abstract
Electrical impedance tomography (EIT) is very sensitive to deformations of the medium boundary shape. For lung imaging, breathing and changes in posture move the electrodes and change the chest shape, resulting in image artefacts. Several approaches have been proposed to improve the reconstructed images; most methods reconstruct both the boundary deformation and conductivity change from the measured data. These techniques require the calculation of the 'movement Jacobian', reflecting measurement changes due to the boundary deformation. Previous papers have calculated this Jacobian using perturbation techniques, which are slow (requiring multiple solutions of the forward problem) and become inaccurate with increasing finite element model size. This effect has limited reconstruction algorithms for deformable media to mostly 2D. To address this problem, we propose a direct method to calculate the Jacobian, based on a formulation of the derivatives of the finite element system matrix with respect to geometry changes. An illustrative example of these calculations is given, as well as a comparison between the proposed method and a perturbation method. Results show this method is approximately 300 times faster; and for larger model sizes, the perturbation method begins to diverge from those from the direct method proposed.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.008 | 0.002 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".