Estimation of Time-Scaling Factor for Ultrasound Medical Images Using the Hilbert Transform
Bibliographic record
Abstract
A new formulation for the estimation of the time-scaling factor between two ultrasound signals is presented. The estimator is derived under the assumptions of a small time-scaling factor and signals with constant spectrum over its bandwidth. Under these conditions, we show that the proposed approach leads to a simple analytic formulation of the time-scaling factor estimator. The influences of an increase of the time-scaling factor and of signal-to-noise ratio (SNR) are studied. The mathematical developments of the expected mean and bias of the estimator are presented. An iterative version is also proposed to reduce the bias. The variance is calculated and compared to the Cramer-Rao lower bound (CRLB). The estimator characteristics are measured on flat-spectra simulated signals and experimental ultrasound scanner signals and are compared to the theoretical mean and variance. Results show that the estimator is unbiased and that variance tends towards the CRLB for SNR higher than 20 dB. This is in agreement with typical ultrasound signals used in the medical field, as shown on typical examples. Effects of the signal spectrum shape and of the bandwidth size are evaluated. Finally, the iterative version of the estimator improves the quality of the estimation for SNR between 0 and 20 dB as well as the time-scaling factor estimation validity range (up to ).
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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 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".