The relationship between the Nyquist criterion and the point spread function
Bibliographic record
Abstract
Abstract It is well known that to avoid aliasing in the reconstruction of functions on ℝn that have support on a compact set B (having n‐volume |B|), it is necessary to sample k‐space with a density equal to or higher than one sample per 1/|B| n‐volume of k‐space. It is also well known that undersampling any particular region of k‐space will lead to an aliasing, or “folding in” of image information containing the spatial frequency information of the undersampled region. Here a simple description of what it means to fold in specific spatial frequency information is given in terms of the structure of the point spread function. The description should be useful for designers of k‐space sampling schemes that deliberately incorporate undersampled regions. © 2003 Wiley Periodicals, Inc. Concepts Magn Reson Part B (Magn Reson Engineering) 17B: 17–24, 2003.
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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 | 0.009 | 0.081 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.003 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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".