Hadamard Aperiodic Interval Codes for Parallel-Transmission 2D and 3D Synthetic Aperture Ultrasound Imaging
Bibliographic record
Abstract
We present a new set of near orthogonal codes which we call Hadamard Aperiodic Interval (HAPI) codes and demonstrate their utility for parallel multi-transmitter synthetic aperture imaging. The codes are tri-state and sparse. Locations of non-zero bits are based on marks in a sequence of aperiodic intervals, also known as a Golomb ruler. The values of non-zero bits are selected from Hadamard sequences that are mutually orthogonal. This ensures that cross-correlation sidelobe magnitudes between differing codes are bounded by unity while the autocorrelation approaches a delta function with mainlobe-to-sidelobe levels scaling with the number of non-zero bits. We use simulations to demonstrate the potential of the codes for synthetic aperture imaging. A multiplicity of transmitter elements is used to transmit codes simultaneously, with a different code for each element. Echo signals are received from a multiplicity of transducer elements in parallel. Channel data from each receiver element are cross-correlated with respective HAPI codes to estimate the transmit–receive signature associated with each transmitter–receiver pair while minimizing crosstalk. This estimate of the full transmit–receive synthetic aperture dataset is then used to form high-quality images demonstrating image quality and signal-to-noise ratio improvements over multiple flash angle imaging and synthetic aperture imaging methods for linear arrays. We also demonstrate simulated full volume synthetic aperture imaging with random sparse arrays, possible with one extended HAPI code-set transmit event.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
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".