Projects
Miscellaneous Projects:
We can edit k-space to remove low spatial frequency signals by implementing sharp high-pass filters. Here, I set all spatial frequencies lower than a certain ‘radius’ value (in cm-1), to 0. This mimics an ideal filter. In the picture above, all frequencies lower than 4 cm-1 are cut out. By only allowing high-frequency components to pass, the resulting image after inverse FT results in high visibility of high spatial frequency areas (places that had sharp edges, high contrast, and finer details). For example, the ridges (sulci) and the edge of the brain both have high spatial frequencies.
If we set every other row in k-space equal to zero, we are effectively using a lower sampling rate by sampling half as many spatial frequencies, still keeping a constant period just twice as long.
Aliasing, caused by having too low a sampling density, may result in this phenomenon. The true signal could be of a higher frequency than assigned, resulting in the repeating pattern. According to the Nyquist thm, we should sample with at least twice the maximum frequency of the sample itself to prevent this effect.