Parametric Convolutional Dictionary Learning and its Applications to Seismic Data Processing
Bibliographic record
Abstract
Convolutional dictionary learning (CDL) can represent signals and images via the superposition of components given by the convolution of sparse coefficients (features) and the elements of a dictionary (filters). The filters represent universal signals that can model different images, whereas the coefficients are intrinsic to one particular image. Estimating the coefficients and the filters from a set of observed signals is similar to a blind deconvolution problem where we aim to simultaneously represent a signal via the convolution of two unknown signals. Classical CDL provides data-dependent filters that, in the seismic data processing case, might not have a solid resemblance to typical waveforms that one observes in seismic records. This limits the dictionary’s representation and discriminability, thus suffering from suboptimal denoising or reconstruction results. To address this challenge, we propose a new CDL algorithm. The proposed approach introduces a parametric constraint to enforce simplicity on the filters, guiding the learning process toward a more efficient and structured representation of the data. Specifically, we restrict each filter to include one single waveform parametrizable via a second-order traveltime curve and a seismic wavelet. The learned dictionary comprises linear and parabolic events that adapt adequately to observed seismic waveforms and resemble local Radon transform basis functions. The alternating direction method of multipliers (ADMMs) is adopted to solve the proposed parametric convolutional learning problem. The experimental results demonstrate that the proposed method achieves superior reconstruction results compared to the existing convolutional and patch-based dictionary learning methods.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 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 | 0.001 |
| 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".