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 ℝ n 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.
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 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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".