A general framework for the design of stack filters using the L/sub p/ norm objective function
Bibliographic record
Abstract
It has been thought for some time now that the design of stack filters using the L/sub p/ norm is mathematically intractable. This paper, for the first time, addresses the problem of designing optimal stack filters by employing an L/sub p/ norm of the error between the desired signal and the estimated one. It is shown that the L/sub p/ norm can be expressed as a linear function of the decision errors at the binary levels of the filter. Thus, an L/sub p/-optimal stack filter can be obtained as a solution of a linear program. The conventional design of using the mean absolute error (MAE), therefore, becomes a special case of the general, L/sub p/ norm based design, developed here. The conventional MAE design of an important subclass of stack filters, the weighted order statistic filters, is also extended to the L/sub p/ norm-based design. By considering a typical application of restoring images corrupted with impulsive noise, several design examples are presented, to illustrate that the L/sub p/-optimal stack filters with p/spl ges/2 can provide a far superior performance in terms of their capability of removing impulsive noise, compared to that achieved by using the conventional minimum MAE stack filters.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.002 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| 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".