Now this is really almost hard to believe because basically when we have

k-space here, what I'm saying here is that the k-space measurements that we see

to the left here are simply weights of these different waves, and we

take the linear combination based on these waves and we get the image to the right.

And so it's hard to believe that this image is just made up of different waves,

but we can show that this is true if we take a single k-space point and

just manipulate it by doubling it.

So let's say that we take this case spaced point, which is sort of to the Northeast

of the center, and I double its value, and now I reconstruct the image again.

Basically what you see is, you see that the way of going in that direction

becomes overvalued, and now we get this kind of grid like artifact over the brain.

So, now we're just overvaluing the wave going in a certain direction,

and this is giving rise to this artifact.

So this sort of illustrates that this image is

a finely kind of balanced combination of these waves, and

if we overvalue one of them, it kind of ruins the whole image.

If we go in the opposite direction, we ge the same type of grid

like pattern, but moving now in the Northwest direction.

So in this case, so the k-space contains information about the entire brain in this

case but now if we're interested in the relative contribution of the high

versus the low frequency parts of k-space, we can do the following example.

Let's split k-space up into nine equally sized boxes, and we take the center box,

and we reconstruct the image using that data, and then we take the outer

eight boxes, just removing the center, and we reconstruct the data using this.

Because the Fourier transform is a linear operation,

the sum of those two should add up to the original image.

So now by doing this little thought experiment, we can see what the relative

contribution of the center of k-space is, versus the outskirts of k-space.

So if we reconstruct the image using the center of k-space,

we get something that looks like this.

It looks very much like the original image, but a little bit blurrier and

you'll see that the detail is not as fine as it was in the original image,

but we've retained most of the information of the brain.

And that's just using one-ninth of the k-space measurement, so

about 11% of the data.

So if we look at what information is conveyed by the additional 88%,

or 89%, we can make that reconstruction.

Here you'll see that we're only getting detail, we're seeing the boundary between

the ventricles in the brain and between the skull and the brain.

So basically, these high frequency parts are the ones