MixTURE: L1-Norm-Based Mixed Second-Order Continuity in Strain Tensor Ultrasound Elastography
Bibliographic record
Abstract
Energy-based displacement tracking of ultrasound images can be implemented by optimizing a cost function consisting of a data term, a mechanical congruency term, and first- and second-order continuity terms. This approach recently provided a promising solution to 2-D axial and lateral displacement tracking in ultrasound strain elastography. However, the associated second-order regularizer only considers the unmixed second derivatives and disregards the mixed derivatives, thereby providing suboptimal noise suppression and limiting possibilities for total strain tensor imaging. We propose to improve axial, lateral, axial shear, and lateral shear strain estimation quality by formulating and optimizing a novel -norm-based second-order regularizer that penalizes both mixed and unmixed displacement derivatives. We name the proposed technique -MixTURE, which stands for -norm Mixed derivative for Total UltRasound Elastography. When compared with simulated ground-truth results, the mean structural similarity (MSSIM) obtained with -MixTURE ranged 0.53-0.86 and the mean absolute error (MAE) ranged 0.00053-0.005. In addition, the mean elastographic signal-to-noise ratio (SNR) achieved with simulated, experimental phantom, and in vivo breast datasets ranged 1.87-52.98, and the mean elastographic contrast-to-noise ratio (CNR) ranged 7.40-24.53. When compared with a closely related existing technique that does not consider the mixed derivatives, -MixTURE generally outperformed the MSSIM, MAE, SNR, and CNR by up to 37.96%, 67.82%, and 25.53% in the simulated, experimental phantom, and in vivo datasets, respectively. These results collectively highlight the ability of -MixTURE to deliver highly accurate axial, lateral, axial shear, and lateral shear strain estimates and advance the state-of-the-art in elastography-guided diagnostic and interventional decisions.
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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 | 0.004 |
| 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 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".