Application of the hybrid stochastic-deterministic minimization method to a surface data inverse scattering problem
Bibliographic record
Abstract
Abstract. A method for the identification of small inhomogeneitiesfrom a surface data is presented in the framework of an inverse scat-tering problem for the Helmholtz equation. Using the assumptions ofsmallness of the scatterers one reduces this inverse problem to an iden-tification of the positions of the small scatterers. These positions arefound by a global minimization search. Such a search is implementedby a novel Hybrid Stochastic-Deterministic Minimization method. Themethod combines random tries and a deterministic minimization. Theeffectiveness of this approach is illustrated by numerical experiments.In the modeling part our method is valid when the Born approximationfails. In the numerical part, an algorithm for the estimate of the numberof the small scatterers is proposed. 1 IntroductionIn many applications it is essential to find small inhomogeneities from surfacedata. For example, such a problem arises in ultrasound mammography, where smallinhomogeneities are cancer cells. Current X-ray mammography will be replaced bythe ultrasound one because X-ray mammography has a high probability of creatingnew cancer cells in a woman’s breast in the course of taking the mammography test.Other examples include the problem of finding small holes and cracks in metals andother materials, or the mine detection. The scattering theory for small scatterersoriginated in the classical works of Lord Rayleigh. It was developed in [15] and [16],where analyticalformulas forthe scattering matrix werederived for the acoustic and
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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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".