Polar Fourier transform in practice: its efficiency and characteristics in reconstructing radially acquired MRI images
Bibliographic record
Abstract
OBJECTIVE: The Polar Fourier Transform (PFT) has been proposed as a direct alternative to gridding for reconstructing radially acquired MRI data. This study evaluates the feasibility of inline PFT implementation on a clinical MRI scanner and assesses its computational performance and image quality under acceleration. MATERIALS AND METHODS: PFT was implemented as modular components within the Siemens Image Calculation Environment, using a recursive numerical Hankel transform. Phantom and in vivo brain datasets acquired with 2D radial trajectories were reconstructed using both PFT and vendor-supplied gridding. Reconstruction time, SNR, artifact behavior, and spatial resolution were assessed across multiple undersampling levels (up to 8 ×), using simulations and repeated scans. RESULTS: PFT was successfully integrated with a runtime of ~ 6-9 × acquisition time. It exhibited spatially variant behavior, concentrating resolution in central region while shifting undersampling-induced blurring outward. Compared to gridding, PFT reduced structured streaks and better preserved image quality under acceleration. Gradient delay artifacts were reduced by alternating spoke polarity. Notably, the pituitary gland and basilar artery remained visible at high acceleration, highlighting preserved central fidelity. DISCUSSION: PFT enables effective inline reconstruction for radial MRI and preserves image quality in small central regions of interest under aggressive undersampling-supporting dynamic and ROI-focused applications.
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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 | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| 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) | 0.003 | 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".