Okay, awesome. Welcome back, everybody, to our next week of computational MRI. And today

what we're going to do is we, this is going to be the theme of the next week's is just

to increase the complexity and generalization of the concepts that we have talked about

so far. So in particular, so far in everything that you have been doing, both in the exercise

and what we've covered in the lecture is we have assumed that our frequency sample points,

our case base, that they lie on an equally distant Cartesian grid. And that is the prerequisite

for using an FFT. So you took this matrix that we call case base, applied an IFP and

this gave you the image, right? This is what you have been doing in the exercises. But

as you know, from the very first lecture and the first exercise, we actually have complete

control how we sample our data, just by the way we play our gradients. And they can be

on any sampling trajectory. Just because so far we have assumed that we do this step by

step sampling, sample on a Cartesian grid, it doesn't have to be this way. And today

we're going to cover a technique so that we can generalize this and deal with data that

comes from every type of sampling trajectory. Before we get started with this, I have one

administrative reminder. I already mentioned it last week. It is the exam. So I have seen

that some of you have already registered on Campo for individual exam slots. So that is

obviously showing me that this registration on Campo is working and you found the correct

one, at least some of you did. If anybody has any questions or maybe just give it a

try and see if it works for you. And if not, maybe you can ask around there. It seems to

work. Some people have registered for the slots, but just a reminder. Yes.

I have one question. So there's this exercise for tutorial achievement. Yes. So I registered

also for this. Sign up for it. It doesn't hurt. You will not get a separate grade for

the exercise. It is just for the bonus points. Honestly, I still don't know how Campo really

works and how it deals with this and when I will be able to enter a grade. To be sure,

enter a register for the exercise as well. But there is no participant restriction. So

just register for it. The important one is that you register for these because these

are for the time slots in this room and we only have capacity for 20 people at a time.

So make sure that if you have a preferred time slot that you register for this one.

For the exercise, just sign up. But I don't know what it will do. Any other questions

about the exam? Assume there will be more questions about the exam in January. But.

All right. Okay. So let's get started. This is the premise. We have our Fourier data.

We're doing inverse Fourier transform and we go to the image. And if this is a teaching

equally distance in sample, so instead of just a matrix, then you can use NumPy, I have

the people this in a single step and you get the image. And. This is how we create this

case space. I'm showing this over and over again. So whether time of the end of this

lecture, you probably be bored by it, but it's just worth repeating it just that you

internalize these elements. We are navigating each of these points in case space by these

phase offsets that we create with our gradients and frequency encoding, phase encoding. And

that means that we can just by choosing how we play these gradient pulses, we can separate

this in any particular way. And I mean, this was one of your tasks in the first lab report

on how you need to set the gradient so that you can do the division sampling or radial

sampling or spirals. These are three popular choices. There are many more people are very,

very creative when it comes to trajectories. And in particular, for some specialized application

or even kind of say for every specialist application, there is a trajectory that will be optimal

for it. And this is an entire field of research. It really, really depends on what you want

to do. Even though in clinical practice, I would say the bread and butter, probably 80%

of the exams are done with this Cartesian acquisition. It's just very robust. It's

simple. The simplicity of being able to use an FSD is just a very, very strong selling

point. But in research, and especially if you want to do more specialized things, opening

up this freedom that you can sample in any particular ways is very, very powerful. And