Low patch-rank image decomposition using alternating minimization algorithms
Bibliographic record
Abstract
Cartoon-texture image decomposition, which refers to the problem of decomposing an image into a cartoon part and a texture component, is one of the most fundamental problems in image processing. In this paper, we are concerned with the low patch-rank enhanced image decomposition model, which is a convex but nonsmooth optimization problem that could not be solved directly by traditional gradient-based optimization algorithms. Accordingly, we introduce two unconstrained reformulations to the underlying low patch-rank optimization model. Furthermore, by exploiting favorable structures of the resulting reformations, we propose two easily implementable alternating minimization algorithms, whose subproblems have closed-form solutions. Compared to the state-of-the-art multi-block alternating direction method of multipliers and its variants, our proposed algorithms enjoy simpler iterative schemes and lower memory requirements for saving computing time. A series of numerical experiments further support the promising performance of the proposed approaches.
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How this classification was reachedexpand
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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".