The following content has been provided by the University of Erlangen-Nürnberg.

Good morning everybody. I'm Andreas Meyer and I'll be talking to you about image reconstruction.

Today we will have a look at basic principles of tomography

and I'll try to have a very gentle start into this topic.

Okay, so this message may pop up from now to then, so I have to click it away because it wants to do a reboot.

So let's start with this and let's look into the basic principles of tomography.

So we will first discuss what tomography is at all, then we'll look into important concepts of tomography.

First thing will be we need to know what a projection is and I will define it slightly different than you heard it before.

And then we need to know what we need to do to do image reconstruction.

And then I will introduce the concept of back projection.

In the end I will give a short, very short history, not maybe of CT or more of CT scanners and reconstruction geometry.

And at the end I will show a couple of state of the art developments.

So let's start with tomography.

So tomography comes from the Greek word thomas and this means slice.

And if you look to the right here you see a slice view of a simulated human body.

So you can see the spine here and here we are at the very bottom of the human body, of the torso actually.

And this corresponds to the view that we have over here.

So this is a simulated X-ray projection.

And you can see that on this X-ray projection you don't see as many details as you do on the tomography.

And I can click here, then I will see a short video scrolling through the body and you see we end at the head.

Let's do this again. This is kind of slow because I want to actually stop it.

But it stops much later than I want it to.

Okay.

Okay.

Or you can see a bit of the lungs here.

You can see the spine.

So these dark areas are filled with air.

So these are the lungs.

There is some body tissue around here.

You can see the rib cage.

And then we are almost at the top so you can already see the shoulder bones here.

Okay.

So this is kind of really interesting to look at these slices.

And they are really relevant for medical diagnosis.

And if you compare that to the normal X-ray projection you can say, oh, well, there is something there.

But you can't see as much detail as you can do in the reconstructed image.

And the idea to do that is, well, we have this great technology of X-rays and we can look through the human body.

And if I look at the human body from all sides, so I do a rotation around here,

then I can observe the complete body and I can reconstruct the actual slices.

Well, this is basically like a puzzle.

Your slice that we want to reconstruct here, this is like four variables, very simple example.

So what we actually observe is the ray sum through this slice.

So we observe X1 plus X2 on this ray and we observe X3 plus X4 on this ray.

And if we look from a different side, we observe the sums along these rays.

So we observe X1 plus X3 and we observe X2 plus X4.

And we can put that into some equations.

Now we have four equations and four unknowns.

So we basically can do the math and see what comes out of it.

So we can solve the system of equations and then you get your reconstructed slides.

So your X1 is this value and we can actually check it if this is right.