ogy.

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Ok, so, welcome everybody.

Let's continue the topic of reconstruction.

Last time we did some theory and...

Something important going on over there?

Okay, so let's continue.

So for today I decided to look at a few practical aspects of parallel beam reconstruction.

And, hey, welcome.

So let's go through the tomographic reconstruction once again, just to remember what we did last week.

And I can continue on that with a couple of examples.

So, hey, welcome!

We started free right?

You know.

The bus was late.

Public transport. Okay, so

Let's remember what we did last week. So last week we decided to look at reconstruction and we came up that

Tomographic reconstruction is basically that we want to reconstruct the slice and here we parameterize the slice with only

four values so

the slice we want to reconstruct is basically a

lot of unknowns and we want to compute their values and what we know about it is that we can

See the sums of the rays passing through that tissue or through that slice

So in this case, whoa

Welcome

Okay

So we've seen that the x-rays we basically can observe the sum of the absorption

coefficients along that ray and

Here we could see that if we cast for rays through this slice

We can observe the sums of the respective unknowns here

We had the simple system of equations that this value basically

corresponds to this ray sum and

and the other values here correspond to different sums

and we can actually solve that and get a solution

what we have in the slice.

So then we thought, well, maybe we can just solve it

with a system of linear equations

and we put that together in matrix notation

and we just solve for our unknown for X

and we can do that by computing the matrix inverse

of A and then we can see that this basically

use a solution but our problem size was kind of big

so we usually have 512 to the power of three voxels

and the volume then projections usually are of the size

512 to the power of two sometimes bigger

but we are about in this ballpark

and we have something like 512 projections.

And if we do the math, we ended up to see

that we get something like 65,000 terabytes

and we decided that we don't want to do it this way.

Right?