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

Okay, so welcome back everybody. Happy New Year 2012.

Let's continue with talking about diagnostic medical image processing.

Today we'll talk about reconstruction on different imaging modalities.

I will just recapture the idea of image reconstruction.

Basically we want to solve the puzzle that we have a couple of observations from the outside of our object

that image through the object and we can see it from different sides.

And looking at the object from different sides, we can set up a system of basically linear equations.

And we want to solve this kind of puzzle and look into the object and see which point of the object absorbs more energy

or has a certain amount of absorption or a certain distribution of a certain marker that we want to image.

And we want to reconstruct the distribution of these values inside our object.

We have seen that we can set this up as a system of linear equations and we have also seen that if we try to solve this with a matrix inverse

we either have to have a really small problem, then we can do that, or if we have a really normal problem

we see that this inversion problem gets really huge so we cannot easily solve that with a matrix inverse.

Today we will look into different modalities. So far we have been concerned with X-ray computed tomography.

We will shortly think about what actually happens with X-ray computed tomography and what actually happens if we send X-rays through an object.

And then we will think about different modalities which will be positron emission tomography PET and single photon emission computed tomography SPECT

as well as magnetic resonance imaging and how the physics behind these modalities are different and why we need slightly different reconstruction algorithms for that.

With X-ray computed tomography we know that these X-rays penetrate the object of interest and what we basically visualize is the amount of absorption of the X-rays.

So what happens inside the object that either the X-rays are completely, the quanta of the X-rays are either absorbed

meaning that the photoelectric effect causes an incident photon to knock out an electron and this electron is later absorbed by the body.

So what actually happens is that this energy is being absorbed in the body and there are later X-ray quanta missing

and we can see that the amount of X-ray missing quanta is the information very based on the reconstruction of the object.

Another effect that also is of relevance is that the photon is not completely absorbed but it's scattered into a different direction with lower energy.

But in either case there is energy deposited in the object so we have ionizing radiation there and this may be a cause of changes inside the object

and we know that if we have excess radiation there are certain effects that happen to living beings.

For example if you really have high radiation you can see certain that the skin is burned or that you really have deterministic damage to the tissue

but we also know if there is not deterministic damage that even small amounts of radiation can make changes to the tissue and also to the DNA in the cells

and this can cause mutations which really alters the image tissue and there is also a risk of cancer.

We've seen that we can do parallel beam geometry and this is one of the earliest acquisition schemes.

We've had a single point source and a small detector and we were shifting the source and the detector and by this we could achieve a parallel beam geometry

so we just had single rays in parallel manner passing through the object and every time we have casted such a ray and detected it

we had to shift our detector and the source and after we have acquired a complete projections we needed to rotate and this was one of the earliest schemes of acquisition

and of course this one is also the slowest one.

We've seen that we can also derive reconstruction algorithms for fan beam geometry and with the fan beam we can cover the complete object

and detect all the rays at the same time but we don't have a parallel imaging geometry anymore but we have a divergent beam geometry

but we can use certain techniques to reformulate our problem into a parallel geometry

and in this scheme we can still reconstruct by using a parallel beam reconstruction algorithm and resorting of the rays into a parallel beam geometry.

The nice thing with this geometry is that we can now do a continuous rotation so we don't have to shift and rotate

but we can acquire one rotation at a time and we can acquire data much faster doing this.

The next imaging geometry that we were looking at was comb beam geometry and in comb beam geometry the idea was not just to look at a single plane

but we look at a complete volume at the same time so we don't only cast a single fan but we open the second angle as well, the cone angle

and then we can image on a complete cone that passes through the object and image this hole at the same time.

We've seen that we can acquire data much faster with this but we also have to be careful with data completeness.

If we do such an acquisition only on a circular scan basis we suffer from incomplete data

so we do not see all rays that would be required to reconstruct the complete volume and we get comb beam artifact if we use such a geometry.

Depending on the purpose it may be that we can live with such a comb beam artifact or we shift to another scan trajectory which was the helical scan

and we remember that if we rotate continuously and shift the patient at the same time we can get a kind of helix

and acquiring on this helix allows a fully 3D acquisition with complete data and we can reconstruct without artifact

and we can get a complete reconstruction that is exact.