Frequency Encoding in Both Directions
INCORRECT. All magnetic field gradients used in MRI are ostensibly the same; they simply change the magnetic field linearly in one direction and cause a range of Larmor frequencies to exist (according to the Larmor equation). There is nothing stopping us frequency encoding in two directions within an imaging slice. But actually, if we did, it wouldn't work.
Example nine-pixel image slice. Frequency encoding in two directions within an image slice does not produce unique Larmor frequencies related to position. It becomes impossible to deduce unique signal intensity values for image pixels.
CORRECT. It has been shown that frequency encoding allows us to localise the signal from within an imaging slice into columns. The next step is to encode the columns (into rows) so that we can "plot" unique signal values into an array of pixels to get an image of the slice. One might think that we can simply apply a third magnetic field in a direction perpendicular to the frequency encoding gradient within the imaging slice. That is to say, why not just frequency-encode in the other direction too? Unfortunately, that doesn't work. If frequency encoding is performed in two directions, it becomes impossible to deduce signal intensity values for unique image pixels. This is because the Fourier transform can tell us the total amplitude of the signal at a particular frequency, but when that amplitude is the sum of multiple voxels in the image slice, we don't have enough information to plot signal intensity values in unique pixels in an image.
INCORRECT. There's plenty of time; we'd simply apply two orthogonal frequency encoding gradients as we record the MRI signal. But if we did, we wouldn't be able to create a good image.
Further reading on this topic:
Books: Q&A in MRI p87