A pixel is an artifact: On the necessity of zero‐filling in fourier imaging
Bibliographic record
Abstract
Abstract MR imaging data is sometimes presented in a “patchwork quilt” format with individual pixels visible as squares of uniform intensity. This phenomenon often arises by default from an image space convolution (performed implicitly by the graphics system) used to convert the sparse point sampling of the spatial domain offered by the discrete Fourier transform (DFT) into a sufficiently dense sampling to allow assignment of an intensity value to each addressable point on the display device. Typical examples are fMRI maps, spectroscopic images and zoomed‐in views. These square patches are image structure not present in the object, i.e., artifacts. This form of image display is studied by both an image analysis method and by Fourier analysis. Image formation by display of the 2D DFT of an acquired k‐space matrix as a 2D pixel array is a poor reconstruction because it does not ensure a faithful representation of the spatial frequency content actually present in the data. By analysis of the visual appearance of 2D pixel arrays we show that there are two principal effects: (a) attenuation of higher spatial frequencies (i.e., low‐pass filtering); (b) introduction of artifactual high frequency image structure. These effects can lead to very poor performance with an artifact/signal ratio of over 200% in the corners of 2D k‐space. Generated k‐space maps demonstrate that both detrimental effects increase radially in k‐space. The simple remedy is to zero‐fill (resulting in image interpolation) until individual pixels become invisible in the displayed image. Alternatively, data modeling may be used. © 2013 Wiley Periodicals, Inc. Concepts Magn Reson Part 42A: 32–44, 2013.
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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 | 0.004 | 0.023 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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".