The maximum entropy on the mean method for image deblurring: applying Fenchel-Rockafellar duality in finite and infinite dimensions
Bibliographic record
Abstract
Image deblurring is an inverse problem which has seen a surge of activity in recent years due to the advent of machine learning-based approaches. As such, traditional methods consisting of optimizing a fidelity term coupled with a regularizer over the set of all possible images have fallen in popularity. In the following, a novel approach to this problem is proposed, based upon the maximum entropy on the mean method. It consists of optimizing at the level of the set of probability distributions on the set of all images and employing an entropic regularization. The theory is first described in the context of barcode deblurring and, subsequently, for the deblurring of general images. The problem afforded by the principle of maximum entropy on the mean is intractable (it is finite-dimensional, but prohibitively large in the former case and infinite-dimensional in the latter). Nevertheless, a judicious application of the Fenchel-Rockafellar duality theorem affords a finite-dimensional dual problem which can be solved using standard optimization software, as well as a formula to recover a solution of the original problem from that of its dual counterpart. Numerical experiments are provided to demonstrate the strength of this method
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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 | 0.003 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".