On use of inhomogeneous media for elimination of ill-posedness in the inverse problem
Bibliographic record
Abstract
This thesis outlines a novel approach to make ill-posed inverse source problem well-posed exploiting inhomogeneous media. More precisely, we use Maxwell fish-eye lens to make scattered field emanating from distinct regions of an object of interest more directive and concentrated onto distinct regions of observation. The object of interest in this thesis is a thin slab placed conformally to the Maxwell fish-eye lens. Focused Green’s function of the background medium results in diagonal dominance of the matrix to be inverted for inverse problem solution. Hence, the problem becomes well-posed. We have studied one-dimensional variation of a very thin dielectric slab of interest having conformal shape to the lens. This method has been tested solving the forward problem using both Mie series and using COMSOL. Most common techniques for solving inverse problem are full non-linear inversion techniques, such as: distorted Born iterative method (DBIM) and contrast source inversion (CSI). DBIM needs to be regularized at every iteration. In some cases, it converges to a solution, and, in some cases, it does not. Diffraction tomography does not utilize regularization. It is a technique under Born approximation. It eliminates ill-posedness, but it works only for small contrast. Our proposed method works for high contrast and also provides well-posedness. In this thesis, our objective is to demonstrate inverse source problem and inverse scattering problem are not inherently ill-posed. They are ill-posed because conventional techniques usually use homogeneous or non-focusing background medium. These mediums do not support separation of scattered field. Utilization of background medium for scattered field separation casts the inverse problem in well-posed form.
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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) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 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".