Efficient Algorithm for Nonconvex Minimization and Its Application to PM Regularization
Bibliographic record
Abstract
In image processing, nonconvex regularization has the ability to smooth homogeneous regions and sharpen edges but leads to challenging computation. We propose some iterative schemes to minimize the energy function with nonconvex edge-preserving potential. The schemes are derived from the duality-based algorithm proposed by Bermúdez and Moreno and the fixed point iteration. The convergence is proved for the convex energy function with nonconvex potential and the linear convergence rate is given. Applying the proposed schemes to Perona and Malik's nonconvex regularization, we present some efficient algorithms based on our schemes, and show the approximate convergence behavior for nonconvex energy function. Experimental results are presented, which show the efficiency of our algorithms, including better denoised performance of nonconvex regularization, faster convergence speed, higher calculation precision, lower calculation cost under the same number of iterations, and less implementation time under the same peak signal noise ratio level.
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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 | 0.003 |
| 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 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".