Preconditioning for Edge-Preserving Image Super Resolution
Bibliographic record
Abstract
We propose a simple preconditioning method for accelerating the solution of edge-preserving image super-resolution (SR) problems in which a linear shift-invariant point spread function is employed. Our technique involves reordering the high-resolution (HR) pixels in a similar manner to what is done in preconditioning methods for quadratic SR formulations. However, due to the edge preserving requirements, the Hessian matrix of the cost function varies during the minimization process. We develop an efficient update scheme for the preconditioner in order to cope with this situation. Unlike some other acceleration strategies that round the displacement values between the low-resolution (LR) images on the HR grid, the proposed method does not sacrifice the optimality of the observation model. In addition, we describe a technique for preconditioning SR problems involving rational magnification factors. The use of such factors is motivated in part by the fact that, under certain circumstances, optimal SR zooms are nonintegers. We show that, by reordering the pixels of the LR images, the structure of the problem to solve is modified in such a way that preconditioners based on circulant operators can be used.
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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 | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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".