So, all interesting things to do.

So far we have considered one dimensional signals like ECG or EEG or EMG and the ECG

signal tells you or provides information about the cardiac motion, so the state of the heart

and you have seen in Norbert Strobel's lecture on x-ray imaging that the ECG data is important

to do a 3D computed tomography image of the beating heart because the ECG tells you in

which state of the heart the x-ray image was acquired.

So ECG data for instance is also important for imaging and imaging is the second large

block or the important block that we are considering right now, medical imaging.

And what we do within these chapters, we discussed endoscopy.

Now we have seen a demo of endoscopes.

Then we were thinking about what are the research topics in endoscopy.

So we talked about the time of light principle and the usage of a time of light camera in

combination with an endoscope.

We talked about stereo endoscopy.

We also talked about using a microscope in combination with an endoscope.

Then we introduced optical coherence tomography that is mostly used in ophthalmology.

The three guys, did they get already their OCT or is it this week?

Where are the guys who get an OCT?

Oh, maybe they did not survive.

Okay.

Yeah, well, this is research, yeah.

Animal experiments.

We talked about OCT and then Norbert Strobel from Siemens, he was talking about x-ray imaging.

So we learned about the x-ray attenuation law.

We learned about things like those problems, the general setup of an x-ray system was explained

and also various applications like angiography, how you can use image processing methods to

visualize the blood vessels and things like that.

And then last week we started out to discuss computed tomography.

That's an imaging area where engineering is very, very important.

It's not just physics because computed tomography does nothing else but using the x-ray attenuation

law and x-ray images and then we develop algorithms to do a 3D reconstruction of the object using

the 2D projection.

And that's something where Benny was explaining to you an algorithm on Monday.

And I will briefly summarize the method to make sure that you get it.

So we have the x-ray attenuation law.

That's all on the slide so you don't need to copy it, listen to me, yeah, try to get

the idea.

The x-ray attenuation law is telling us that the observed intensity is the intensity if

no object is in between the source and the detector times e to the power of minus f of

xt, yxt or we call it L because it's a line, dl, integrated along a line.

So we integrate along the projection.

And now we did a reformulation of this.

I'm learning.

And reconstruction basically means compute this function where I only measure line integrals

of this function, compute this function out of line integrals.

So I have multiple observations, multiple lines, let's say n lines, and the question

is how can I compute out of these observations and these line integrals the original function.

So we have to solve an integral equation.

We get a set of equations and we solve an integral equation.

So that's the problem.