A Closed-form Expression for the Point Spread Function in Synthetic Transmit Aperture Ultrasound Imaging
Bibliographic record
Abstract
The Point Spread Function (PSF) is an essential tool used to characterize the resolution and response of an imaging system. This paper presents, for the first time, closed-form expressions for the PSF in Synthetic Transmit Aperture (STA) ultrasound imaging. The expressions were first derived under the assumption that the imaging depth is much larger than the aperture size and the PSF size, and then improved for the large-aperture configuration. The proposed PSF formulas include the position of the point object explicitly, and therefore are spatially varying. They can be applied to both off-axis locations and near-field regions. Field II simulations validated the PSF expressions. In addition to visual inspections, we used two quantitative metrics — the correlation coefficient and the central frequency of the PSF — to evaluate the agreement between the proposed method and Field II. We also studied the PSF behavior for a large-aperture configuration, where the small-aperture assumption used in the derivation doesn't hold. We found that rescaling the spectrum improved the performance of the proposed method for the large-aperture case. The proposed method can be applied to various applications, such as deconvolution of ultrasound images and quantitative ultrasound imaging.
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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 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.003 |
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".