Signal Processing Using Dictionaries, Atoms, and Deep Learning: A Common Analysis-Synthesis Framework
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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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.003 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| 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".