Monday, August 5, 2013
PFUFA Part Fourteen introduced the idea of acquiring partial k-space and explained how the method, hereafter referred to as partial Fourier (pF), is typically used for EPI acquisitions. At this point it is useful to look at some example data and to begin to assess the options for using pF-EPI for experiments.
The first consequence of using pF is image smoothing. It arises because we've acquired all of the low spatial frequency information twice - on both halves of k-space - but only half of some of the high spatial frequency information. We've then zero-filled that part of k-space that was omitted. This has the immediate effect of degrading the signal-to-noise ratio (SNR) for the high spatial frequencies that reside in the omitted portion of k-space. (PFUFA Part Eleven dealt with where different spatial frequencies are to be found in k-space.) Thus, the final image has less detail and is smoother than it would have been had we acquired the full k-space matrix, and because of the smoothing the final image SNR tends to be higher for pF-EPI than for the full k-space variant.
It was surprising to me that pF-EPI has higher SNR - due to smoothing - than full Fourier EPI in spite of the reduced data sampling in the acquisition. Conventional wisdom, which is technically correct, states that acquiring less data will degrade SNR. To understand this conundrum, we can think of pF as being like a square filter applied asymmetrically to the phase encoding dimension of an EPI obtained from a complete k-space acquisition. Indeed, as we start to evaluate the costs and benefits of pF for EPI we should probably be thinking about a minimum of a three-way comparison. Firstly, we obviously want to compare our pF-EPI to the full k-space alternative having the same nominal resolution. But we should also consider whether there is any advantage over a lower resolution EPI with full k-space coverage, too. Why? Because this lower resolution version is, in effect, what you get when partial Fourier is applied symmetrically, i.e. when the high spatial frequencies are omitted from both halves of the phase encoding dimension!
Let's do our first assessment of pF on a phantom. There are four images of interest: the full k-space image, two versions of pF - omitting the early or the late echoes from the echo train - and, for the sake of quantifying the amount of smoothing, a lower resolution full k-space image which is tantamount to omitting both the early and late echoes. (See Note 1.) From this point on I'm going to refer to omission of the early and late echo variants as pF(early)-EPI and pF(late)-EPI, respectively.