So let's start the lecture for today. So as some people may have noticed, I'm not Professor

Honegger. So unfortunately he had to be in Aachen today and we got a short notice yesterday

that we had to jump in for him. But anyway, so I will do the lecture today. My name is

Martin Berger and the main focus of the lecture will be on truncation. So last time I think

you did fan beam reconstruction and also talked a little bit about the implications of fan

beam and what's different to parallel and very briefly at the end about parka waiting.

And this time we talk about truncation. So the title slide is actually a bit misleading

because what's happening is that truncation can be in fan beam and in parallel beam. So

the things we discussed today are valid for parallel beam and fan beam as well. So and

the title slide suggests that it's only valid for fan beam but it's actually for both. Okay,

so let's start. So maybe I go a short, yeah. Better? Good. So maybe I go shortly about,

maybe we have a short look on the topics of today. I will start with a short recap of

what's actually parallel and fan beam. So this will be very easy to understand. Then

I will define what is truncation and then we talk about what can we do against truncation

and what can we do against the artifacts and how can we correct for that. And at the end

we will also have a look at phantoms. So unfortunately I got forwarded only slides for a 45 minutes

lecture so I had to come up with some new plans. So we will see how it works out with

the timing and everything. And I have an additional talk prepared that is actually a final talk

from a bachelor's thesis in our lab and that's also related to truncation. Okay, so let's

start with the short recap. So here you can see a parallel beam geometry. Let me just

get my old school laser pointer. So clearly we have multiple sources along a line here

and also multiple detector cells here on this side. And then we basically compute the line

integrals through the object from a certain angle and that's then our projection on this

side. Okay, and then we rotate either the object or the scanning system and we do the

same thing again. So you might wonder if that was ever implemented in a real system because

typically X-ray source can produce like a parallel beam ray. But yes it was and they

did that with a little trick and the trick was to use this translate and rotate principle.

So the very first CT in the beginning, like I think 71, that's on the next slide actually,

the very first CT used a translate and rotate principle and what they did is they just had

a detector with one detector cell. So you don't even get an image or a line, you just

get one value for one exposure. And what you then do is you move the detector cell and

also your source, you translate it along the line. So basically you do it step by step.

So you sample this one, the next one, the next one, so this is the translation part.

Then you rotate the system and then you sample again with the translations. So you can imagine

that this took quite a while. So this is actually the first scanner that did it this way. And

you can also see that there is not like a specific patient table here, it's just probably

a conventional patient table from the interventional suite here. And in this scanner exactly this

happened. So you translate your single pixel and the source to get a projection and then

you rotate it and then you do the same thing again. That obviously took quite some time,

so an acquisition took about five minutes. And the reconstruction, the reconstruction

I think was even done iterative, so no filter back projection here. So they used this algebraic

reconstruction technique. I don't know if that's been already discussed. So yeah, just

wait for it and you will know how the first scanner worked. And the slice resolution was

about 80 to 80 pixels. So you can imagine if you ever saw an image with 80 to 80 pixels,

so that's probably not very nice. On the other hand, you can't really tell anything about

a system's resolution by simply giving 80 by 80 pixels. So that just tells you that

you did your reconstruction with 80 by 80 pixels. But it doesn't really tell you if

the resolution of the system is good or bad, but it was pretty bad. Okay, so what happened

in the years after, so people switched to fan beam geometry. And that's simply because

you can save these translations then, which took quite some time. So in fan beam geometry,