Recent Progress in Applied and Computational Harmonic Analysis
Bibliographic record
Abstract
Wavelet theory has been extensively developed in the function space L2 and discrete wavelet transform has successful applications in many areas. However, to understand better the performance of different discrete wavelet transforms, it is important to investigate their underlying discrete wavelet systems in l2. Though some preliminary results have been found recently, despite the fact that stability is a key issue in mathematical foundation of wavelet theory, results on stability of discrete wavelet systems in l2 have been barely developed so far. In the meantime, in recent years, to better handle edge singularities, it is realized that redundant wavelet transform is often preferred by providing better directionality and flexibility. Many different directional systems such as curvelets, framelets, and shearlets have been proposed in the literature. The hard/soft thresholding is theoretically optimal for discrete wavelet transform using orthogonal wavelet filter banks. Because the associated redundant transform is no longer orthonormal, it is not known so far what is the theoretically optimal thresholding strategies for redundant transforms, in particular, for the problem of image denoising. Research teams at University of Calgary and University of Alberta are currently collaborating together to investigate the discrete wavelet system associated with complex tight framelet filter banks and are exploring the thresholding strategies for such redundant transforms using Gaussian scale mixture, which has the capability to cope with correlated noise with superior performance. The idea of using patches
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 | 0.004 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.005 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.013 | 0.004 |
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".