Molière maximum likelihood proton path estimation approximated by cubic Bézier curve for scatter corrected proton CT reconstruction
Bibliographic record
Abstract
A maximum likelihood approach to the problem of calculating the proton paths inside the scanned object in proton computed tomography is presented. Molière theory is used for the first time to derive a physical model that describes proton multiple Coulomb scattering, avoiding the need for the Gaussian approximation currently used. To enable this, the proposed method approximates proton paths with cubic Bézier curves and subsequently maximizes the path likelihood through parametric optimization, based on the Molière model. Results from the Highland formula-based Gaussian approximation are also presented for comparison. The simplex method is utilized for optimisation. The scattering properties of the material(s) of the scanned object are taken into account by appropriately calculating the scattering parameters from the stopping power map that is calculated/updated at every iteration of the algebraic reconstruction process. Proton track length constraint imposed by the proton energy loss is accounted for. The method is also applied in the case that no exit angle data are measured. Geant4 Monte Carlo simulations were performed for model validation. Our results show that use of Molière probability density function for modelling the multiple Coulomb scattering presents a modest 2% accuracy improvement over the Gaussian approximation and most-likely-path method. Simulations of voxelized phantom showed no essential benefit from the inclusion of the material information into the optimization, while path optimization with energy constraint slightly increased path resolution in a bone/water interface phantom. Method error was found to depend on energy, proton track-length within the medium, and proportion of data filtering.
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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 | 0.002 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".