The apex method in image sharpening and the use of low exponent levy stable laws
Bibliographic record
Abstract
The APEX method is an F FT-based direct blind deconvolution technique that can process complex high resolution imagery in a few minutes of cpu time on current desktop platforms.The method is predicated on a restricted class of shift-invariant blurs that can be expressed as finite convolution products of two-dimensional radially symmetric Levy stable probability density functions.This class generalizes Gaussian and Lorentzian densities but excludes defocus and motion blurs.Not all images can be enhanced with the APEX method.However, it is shown that the method can be usefully applied to a wide variety of real blurred linages, including astronomical, Landsat and aerial images, MRI and PET brain scans, and scanning electron microscope images.APEX processing of these images enhances contrast and sharpens structural detail, leading to very noticeable improvements in visual quality.The discussion includes a documented example of non uniqueness where distinct point spread functions produce high-quality restorations of the same blurred image.Significantly, low exponent Levy point spread functions were detected and used in all the above examples.Such low exponents are exceptional in physical applications where symmetric stable laws appear.In the present case, the physical meaning of t hese Levy exponents is uncertain.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| 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".