Algorithm for constructing symmetric dual framelet filter banks
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Dual wavelet frames and their associated dual framelet filter banks are often constructed using the oblique extension principle. In comparison with the construction of tight wavelet frames and tight framelet filter banks, it is indeed quite easy to obtain some particular examples of dual framelet filter banks with or without symmetry from any given pair of low-pass filters. However, such constructed dual framelet filter banks are often too particular to have some desirable properties such as balanced filter supports between primal and dual filters. From the point of view of both theory and application, it is important and interesting to have an algorithm which is capable of finding <italic>all</italic> possible dual framelet filter banks with symmetry and with the shortest possible filter supports from any given pair of low-pass filters with symmetry. However, to our best knowledge, this issue has not been resolved yet in the literature and one often has to solve systems of nonlinear equations to obtain nontrivial dual framelet filter banks. Given the fact that the construction of dual framelet filter banks is widely believed to be very flexible, the lack of a systematic algorithm for constructing all dual framelet filter banks in the literature is a little bit surprising to us. In this paper, by solving only small systems of linear equations, we shall completely settle this problem by introducing a step-by-step efficient algorithm to construct all possible dual framelet filter banks with or without symmetry and with the shortest possible filter supports. As a byproduct, our algorithm leads to a simple algorithm for constructing all symmetric tight framelet filter banks with two high-pass filters from a given low-pass filter with symmetry. Examples will be provided to illustrate our algorithm. To explain and to understand better our algorithm and dual framelet filter banks, we shall also discuss some properties of our algorithms and dual framelet filter banks in this paper.
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.
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 | 0.002 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| 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 it