Signal Processing Using Dictionaries, Atoms, and Deep Learning: A Common Analysis-Synthesis Framework
Why this work is in the frame
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Bibliographic record
Abstract
Signal decomposition (analysis) and reconstruction (synthesis) are cornerstones in signal processing and feature recognition tasks. Signal decomposition is traditionally achieved by projecting data onto predefined basis functions, often known as atoms. Coefficient manipulation (e.g., thresholding) combined with signal reconstruction then either provides signals with enhanced quality or permits extraction of desired features only. More recently dictionary learning and deep learning have also been actively used for similar tasks. The purpose of dictionary learning is to derive the most appropriate basis functions directly from the observed data. In deep learning, neural networks or other transfer functions are taught to perform either feature classification or data enhancement directly, provided solely some training data. This review shows first how popular signal processing methods, such as basis pursuit and sparse coding, are related to analysis and synthesis. We then explain how dictionary learning and deep learning using neural networks can also be interpreted as generalized analysis and synthesis methods. We introduce the underlying principles of all techniques and then show their inherent strengths and weaknesses using various examples, including two toy examples, a moonscape image, a magnetic resonance image, and geophysical data.
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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 | 0.000 |
| 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