A novel multi-frequency regularization method for the 2D inverse scattering problem under the born iterative method
Bibliographic record
Abstract
In this paper, we consider the scalar transverse magnetic (TM), two-dimensional, time-harmonic, lossless inverse scattering problem. The goal of this problem is to determine an unknown permittivity contrast within some domain from field measurements taken outside that domain. It is well known that this problem is both non-linear and ill-posed in the classical sense, i.e., the solution is non-unique and small changes in the measured field data may cause arbitrarily large changes in the solution [1]. At a single frequency, the illposedness of the problem remains even under linearizing assumptions e.g., the Born approximation [2]. Under such an approximation, one obtains a Fredholm integral equation of the first kind and a discretization of the monochromatic integral equation yields an ill-conditioned system as a result of the illposedness of the underlying continuous problem [1]. The result of this ill-conditioning is that one must utilize some form of regularization, i.e., a method which selects a particular solution from within a class of possible solutions by imposing additional constraints.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 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 | 0.001 |
| 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".