What can go wrong if the samples are too course?
The contribution from the higher frequencies of the right-hand FT show up at lower frequencies in the main F.T. (centered on zero frequency).
This misplacement of high frequencies to lower frequencies is referred to as the
JA Parker presents good examples of aliasing artifacts in two-dimensional nuclear medicine images due to undersampling on pages 338-339 of his book, Image Processing in Radiology. In these examples, note banding and striping at lower frequencies and in directions not found in the actual image.
So the sampling of our image data has made us go from a single FT function to a periodic, repeating FT function.
This is where the challenge comes in image acquisition:
If we do not sample fine enough, that if our samples are too course, we introduce artifacts. However, if our samples are too fine, we consume excessive computer memory space and reconstructions take much time. We must always find the optimum sampling rate - the compromise between aliasing and computer resource utilization.
In practice, sampling rate is determined by the combination of matrix size (e.g., 128x128) and zoom factor (1.0 - whole crystal, 2.0 - 1/4 of the crystal, etc.):
| ZOOM | ||
|---|---|---|
| 1.0 | 2.0 | |
| 128x128 | coursest samples | medium samples (small view) |
| 256x256 | medium samples (large view) | finest samples |
Douglas J. Wagenaar, Ph.D., wagenaar@nucmed.bih.harvard.edu