Before we continue with our inhomogeneity correction,

let's come back to the big picture and the storyline.

And in winter semester, the story is rather simple.

We talk about diagnostic medical image processing.

And what we do first, we learned a little bit

about different modalities.

That's basically an overview over different imaging

techniques that are used in medicine.

For instance, X-ray imaging, CT imaging, MR imaging,

endoscopy, and many more.

And based on these modalities, we have one chapter

that deals with acquisition,

sorry, acquisition, specific image enhancement,

where we look at the process, how images are generated,

what type of artifacts come in,

and how can these artifacts be corrected.

And we talked about X-ray so far.

And in X-ray, we have seen that there are two

detector technologies used today.

One is the more ancient technology that makes use

of image intensifiers like the older TV sets.

These things work with vacuum tubes and in electron optics.

And given the fact that we have electrons

in the earth magnetic field, these are deviated

by the magnetic field, and these deviations

cause distortions in the images.

And we talked about various ideas how these

distortions can be corrected.

And the problem per se is not so exciting,

but in this context, we have seen several concepts

that we will make use of in the future.

For instance, we have introduced

the singular value decomposition as one numerical tool

to deal with linear algebra.

What else did we introduce?

We introduced the least square estimation.

And I also pointed out in one of the Monday afternoon

sessions that the measurement matrix includes

also uncertainties and noise, and that is not basically

covered by the least square estimators.

And for that reason, we have introduced

the total least square estimator

that is taking care of them.

And in all the examples that we have considered,

we have seen that the least square estimation problem

and the total least square estimation problem

can be solved basically by using

singular value decomposition.

In case of the total least square,

we even have seen that there is not necessarily