A Well-Conditioned Non-Iterative Approach to Solution of the Inverse Problem
Bibliographic record
Abstract
A novel methodology leading to well-conditioned formulation of the inverse scattering problem is proposed. The solution of the inverse scattering problem is made possible through elimination of the inherent ill-posedness of the inverse source problem. The latter is achieved by staging of the imaging experiment in a medium with the Green's function exhibiting focusing properties. The method is shown to cast the inverse source problem into a well-conditioned matrix equation without addition of the non-physical regularization term to the pertinent integral equation. This is contrary to the conventional iterative optimization-like methods applied to regularized integral equation with non-directional Green's function. The method is shown to be applicable in both traditional diffraction limited imaging where the evanescent waves do not participate in the information transfer from the object to the observation region as well as in the metamaterial media where focusing goes beyond the diffraction limit with the aid of the evanescent wave propagation. The diffraction limited imaging prototype is implemented using a parabolic reflector providing desired focusing properties of the Green's function. The Raleigh criteria for diffraction limited resolution is revisited to demonstrate that upon availability of the medium providing sufficient focusing properties the resolution in the conventional diffraction limited microwave tomography can go up to half-wavelength. The implementation of algorithm in medium supporting evanescent wave propagation is demonstrated using the focusing Green's function of the Veselago lens.
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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 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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".