Nonequispaced curvelet transform for seismic data reconstruction: A sparsity-promoting approach
Bibliographic record
Abstract
Abstract We extend our earlier work on the nonequispaced fast discrete curvelet transform (NFDCT) and introduce a second generation of the transform. This new generation differs from the previous one by the approach taken to compute accurate curvelet coefficients from irregularly sampled data. The first generation relies on accurate Fourier coefficients obtained by an l2-regularized inversion of the nonequispaced fast Fourier transform (FFT) whereas the second is based on a direct l1-regularized inversion of the operator that links curvelet coefficients to irregular data. Also, by construction the second generation NFDCT is lossless unlike the first generation NFDCT. This property is particularly attractive for processing irregularly sampled seismic data in the curvelet domain and bringing them back to their irregular recording locations with high fidelity. Secondly, we combine the second generation NFDCT with the standard fast discrete curvelet transform (FDCT) to form a new curvelet-based method, coined nonequispaced curvelet reconstruction with sparsity-promoting inversion (NCRSI) for the regularization and interpolation of irregularly sampled data. We demonstrate that for a pure regularization problem the reconstruction is very accurate. The signal-to-reconstruction error ratio in our example is above 40dB. We also conduct combined interpolation and regularization experiments. The reconstructions for synthetic data are accurate, particularly when the recording locations are optimally jittered. The reconstruction in our real data example shows amplitudes along the main wavefronts smoothly varying with limited acquisition imprint.
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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 | 0.003 |
| 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 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| 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".