Expanding the domain of contraction mapping in the inverse problem of imaging with incoherently scattered radiation
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Bibliographic record
Abstract
A mathematical formulation that provides a converging solution for the successive approximation solution of the inverse problem of imaging with incoherently scattered radiation is introduced. The nonlinear nature of this problem can cause its solution to oscillate between two physically acceptable domains. By nonlinear scaling of the forward problem, it is shown that the range of one of the two domains can be made to expand at the expense of the other. This enables contraction mapping of the iterative solution of the inverse problem over an extended domain. The mathematical features of this scaling approach are analytically demonstrated for a one-pixel inverse problem, to elucidate its features and limitations. Reconstruction for many-pixel tomographic images is then presented for ideal (error free) and noisy simulated measurements, demonstrating the ability of the presented scheme to solve the inverse problem for radiation scatter imaging over a wide range of physically acceptable attributes.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it