We will start right away with the topic we stopped last lecture on computed tomography.

So the problem we are considering is the following.

We have a structure and we observe one dimensional projections of this two dimensional structure.

If I look at the one dimensional projections from various directions, I can take these

projections and consider these projections as columns in an image.

And this image is called sinogram.

That was the concept we have introduced right before Christmas.

So I walk around this simple pattern here where I just have the four dots.

I capture the projection images.

I take the one dimensional projections and put them column by column into the sinogram.

And it's clear that in the projection the points will move up and down.

There's just one point that will not move but that will be on a straight line.

Which one is it?

That's the point that's exactly in the rotation center.

The farther you are away, the higher are the ups and downs that we consider.

That's the idea.

And computed tomography is doing nothing else but computing the two dimensional structure

out of the one D projections that we observe.

That's what a computer tomography system does.

So if you look back to one of these images here, let me just briefly move back here.

This is what you should keep in mind.

You have here your patient.

You have here your x-ray tube with your collimator.

And then you send the x-rays through the object.

You measure the energy of the x-ray particles from different directions.

And then you build up your sinogram and you can do the reconstruction.

That means you can compute the distribution of the densities on this image slice through

the patient while looking through the patient from hundreds of different directions.

Just a few numbers that might be interesting for you.

Modern CT scanners rotate around about a patient three times a second.

So that's a huge speed.

It's immense what forces are on these parts here, mechanical parts.

Three rotations in a second.

The dose that is applied in computer tomography is around about 120 kilovolts, so also quite

a lot.

What else is interesting in terms of CT?

Rotation speed, the number of pixels that you can reconstruct slice by slice.

Today it's around about 512 by 512.

We also go up to 1024 to 1024.

So there is a huge amount of data that is acquired.

And the key concept that allows us to do the reconstruction is the so-called Fourier slice

theorem.

And what is this Fourier slice theorem telling us?

If I want to reconstruct a slice like this here with the two arms, I can say, okay, this

is my 2D slice.

And here I have a projection that tells me what are the attenuations here.

So I measure here the signal P theta T. Theta is the rotation angle.

P is the coordinate of the element on the detector.

And I know P theta T is what?

According to the X-ray attenuation law, that's I0 times E integral, the function I want to