Efficient least‐squares imaging with sparsity promotion and compressive sensing
Bibliographic record
Abstract
ABSTRACT Seismic imaging is a linearized inversion problem relying on the minimization of a least‐squares misfit functional as a function of the medium perturbation. The success of this procedure hinges on our ability to handle large systems of equations – whose size grows exponentially with the demand for higher resolution images in more and more complicated areas – and our ability to invert these systems given a limited amount of computational resources. To overcome this ‘curse of dimensionality’ in problem size and computational complexity, we propose a combination of randomized dimensionality‐reduction and divide‐and‐conquer techniques. This approach allows us to take advantage of sophisticated sparsity‐promoting solvers that work on a series of smaller subproblems each involving a small randomized subset of data. These subsets correspond to artificial simultaneous‐source experiments made of random superpositions of sequential‐source experiments. By changing these subsets after each subproblem is solved, we are able to attain an inversion quality that is competitive while requiring fewer computational and possibly, fewer acquisition resources. Application of this concept to a controlled series of experiments shows the validity of our approach and the relationship between its efficiency – by reducing the number of sources and hence the number of wave‐equation solves – and the image quality. Application of our dimensionality‐reduction methodology with sparsity promotion to a complicated synthetic with a well‐log constrained structure also yields excellent results underlining the importance of sparsity promotion.
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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) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 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".