Partial Fourier EPI
(The full contents for the PFUFA series of posts is here.)
In PFUFA Part Twelve you saw how 2D k-space for EPI is achieved in a single shot, i.e. using a repetitive gradient echo series following a single excitation RF pulse. The back and forth gradient echo trajectory permits the acquisition of a 2D plane of k-space in tens of milliseconds. That's fast to be sure, but when one wants to achieve a lot of three-dimensional brain coverage then every millisecond counts.
In the EPI method as presented in PFUFA Part Twelve it was (apparently) necessary to cover - that is, to sample - the entire k-space plane in order to then perform a 2D Fourier transform (FT) and recover the desired image. Indeed, this "complete" sampling requirement was developed earlier, in PFUFA Part Nine, when we looked at 2D k-space and its relationship to image space.
One aspect of the FT that I glossed over in previous posts has to do with symmetry. Perhaps the eagle-eyed among you spotted the symmetry in the 2D k-space of the first couple of pictures in PFUFA Part Nine. If you didn't, don't worry about it because I'm about to show it to you in detail. It turns out that there's actually no need to acquire the entire 2D k-space plane; it suffices to acquire some of it - at least half - and then use post-processing methods to fill in the missing part. At that point one can apply the 2D FT and recover the desired image.
Now, as you would expect, there's no free lunch on offer. There are practical consequences from not acquiring the full k-space plane. In this post we will look briefly at the physical principles of
partial Fourier EPI, then in the next post we'll take a look at some
example data that will provide a basis for evaluating partial versus full k-space coverage for fMRI.