Awesome.

Alright, so welcome back, everybody, to the third lecture of computational MRI.

And this week is where we leave behind the basics, you know, right, so the last of the first two lectures where introductory material about sorry about sequences.

Okay. Okay. And about free imaging and about case space, and starting from today, we really going to talk about computational and algorithmic methods. So this is usually when this lecture starts to get interesting, even more interesting, hopefully, to the students

in the lecture, and also in the exercise, because this week, you actually going to implement a real algorithm that does something interesting with our data instead of just looking at the data and manipulating it.

Before we get started with this, I have two administrative announcements. The first one is about the lab reports. So we created the first set of lab reports and I'm very, very happy with them because they were really, really excellent.

So all of you have been doing a really, really good job. I think that most people are, I think everybody has something between 1.0 and 2.0 on these, on these lab reports so you're doing really well so keep up with that so that's, that's a very good sign.

The second administrative item that I have is the exam. So now the campus system allowed me to open up and create exams for the winter semester meaning for this particular course.

And I have chosen all the ones that I was able to get where this was this week, so you know that the exams need to be in this week after the end of the semester.

So the week of February 14th and 16th, 14th and 16th, these are exactly the dates of the lecture, the 14th, and the exercise, the 16th and these are the times so we're going to have three slots for exams, each to 20 people, there's just not more space in this particular room.

And maybe you can already try if you want to that if you if you can sign up to those, and then next week, let me know or maybe the, I still, I mean nobody has experience with this couple of things yet so hopefully that the registration works for you if not,

let me know then they can ask what we can do.

Okay.

So, the thing is, I'm process, it's an oral exam, I don't know why I cannot change it. It's going to be a written exam, and you're going to get five to 10 points about the topics that we discuss about one topic, each or a selection of one question per topic so for example today,

we're talking about partial free imaging so something from partial free imaging could be an exam topic, and actually give you an example.

And as a reminder, you can bring your written lab reports printed out or on an iPad or how you want them and use them as lookup sheets in the exam.

Okay.

All right, if that's not the case, then any other administrative questions, since we're at the topic of that.

No, okay great everything to you.

So then, let's get started. And as I said earlier, we're going to look at our first computational algorithm for MRI today, and it's going to be the partial Fourier method and it has a nice passion for us one name half for a is another name, and then the

particular algorithms we're going to look at unknown under the name homodyne demagotion method based constraint reconstruction projection of convex sets so all of these terms mean the same thing and this is what we're going to cover today.

So what's the idea.

Everybody see well contrast wise or should I know what the clients a little bit more.

Everybody sees fine.

If you remember from the previous lectures and from the exercises.

We're starting always with this setup that we have our measured free or case based coefficients, and then we will invest for a transform and we get our image and this is exactly what you have been doing last week in the exercises and manipulating this

space and observing the properties on the image so just as a recap question, what happens if I roll out the outer three coefficients everything except as more

window in the center.

We get a blurry image here, we're throwing out our high frequency components so we get a blurred image.

So, ideally we always want highest and our high resolution and shorts can time. I mean that is the holy trying in a way in our imaging or imaging in general that that's what we want in practice we can never have this, so we have to make a compromise.

Unless we use clever computational methods, then we actually make it away with getting the best out of both worlds.

And if you remember particularly on the issue of skin.

What we need to do with our pulse sequence is we really need to scan our free space you know we turn on our gradients, we measure one line we turn on our gradients again, make sure the next time we wait to TR.

And then, as soon as we have all our three signals separate, then, then we are done.

So let's just assume for the sake of this particular example that this measurement of this for your space takes me 10 minutes, just random. It's pretty easy to scan.

So, it's a nice high resolution image.

So there's one really really trivial thing, of course, that I can do. Let's say if I want to.

I only have five minutes. What can I do.

Sample now, just sample half of it. That's, I mean, that is that the trivial solution.

And now I have a couple of strategies what what can I do. The first thing, which is really the trivial thing to do is instead of using a simple sample.

And I can do this instead of let's say this is a 256 matrix with a certain defined field of view. Remember that the field of view that I want to measure is defined by the distance between the sampling points and the resolution find by the K max and K min.

So we're going to do another test from our basic bullet quantities.

So I can one thing that I can do is I can skip every other line that will give me a reason, because I am violating the sampling theory. So that's where the G is out.

The other strategy that I can do is, well, just sample half of it by sampling the inner half of the case space.

But then I lose resolution. So I cannot have phone, right.

Everybody.

We can do one other thing. We, when we say, let's have the measurement, let's not measure this half of case space.

But let's measure this part of case space.

So I can do this right now we can stop me from just acquiring these case space coefficients.

The problem that I now that this is so it's a nice because now I suddenly have measured frequencies and high frequencies. So I actually have a lot of the original high frequency information in there.