Random noise attenuation via the randomized canonical polyadic decomposition
Bibliographic record
Abstract
ABSTRACT Tensor algebra provides a robust framework for multi‐dimensional seismic data processing. A low‐rank tensor can represent a noise‐free seismic data volume. Additive random noise will increase the rank of the tensor. Hence, tensor rank‐reduction techniques can be used to filter random noise. Our filtering method adopts the Candecomp/Parafac decomposition to approximates a N‐dimensional seismic data volume via the superposition of rank‐one tensors. Similar to the singular value decomposition for matrices, a low‐rank Candecomp/Parafac decomposition can capture the signal and exclude random noise in situations where a low‐rank tensor can represent the ideal noise‐free seismic volume. The alternating least squares method is adopted to compute the Candecomp/Parafac decomposition with a provided target rank. This method involves solving a series of highly over‐determined linear least‐squares subproblems. To improve the efficiency of the alternating least squares algorithm, we uniformly randomly sample equations of the linear least‐squares subproblems to reduce the size of the problem significantly. The computational overhead is further reduced by avoiding unfolding and folding large dense tensors. We investigate the applicability of the randomized Candecomp/Parafac decomposition for incoherent noise attenuation via experiments conducted on a synthetic dataset and field data seismic volumes. We also compare the proposed algorithm (randomized Candecomp/Parafac decomposition) against multi‐dimensional singular spectrum analysis and classical prediction filtering. We conclude the proposed approach can achieve slightly better denoising performance in terms of signal‐to‐noise ratio enhancement than traditional methods, but with a less computational cost.
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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 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 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) | 0.002 | 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".