So, I have one announcement about next week. We will have to skip next week's Tuesday lecture

because I have to go on to a business trip. So next week we will only have the lecture

on Thursday, only disappointment. Hopefully not disappointment. Good. So, welcome back

to Interventional Medical Image Processing. And what I would like to do today is discuss

a bit scatter, scatter correction, scatter estimation and later on a very fast algorithm

for scatter correction in image processing. And what I essentially want to show today

is that you can simplify a model if you have certain assumptions that you place into that

model and by simplification you can reduce the amount of complexity in the correction

and the necessary corrections that's considerably. But of course the accuracy of your correction

or of your estimation may be reduced. But if you are working towards a particular task,

it may be valid to do these assumptions and to sacrifice accuracy in order to get an improved

image quality. And so I like this example because it shows on the one hand that when

you're working with an imaging device or if you work with an image, the image processing

most of the time, so you solve your image processing problems with image processing

methods. But of course all the image processing that you do is also related to the imaging

modality itself. And if you want to process an image, it's good to have a feeling of the

underlying physics. So we will have some physical equations in this class today, but I don't

want to emphasize too much on the physics. And also concerning this point, this is more

about that it's good to have an understanding of the physics, but this is not a physics

class and none of you is required to have deep in-depth knowledge about physics. But

if you have a feeling what's happening, then you can design much better algorithms and

get a feeling for much more efficient algorithms. And we will do that by looking at a couple

of examples and the example that I'm putting in here is scatter correction. So what I want

to convey in the class today is that if you have a feeling how stuff works, then you can

adopt your image processing methods in a way that you can actually use them more efficiently.

There's guys out there who don't care about the actual formation of the image. They just

apply image processing and they say an image is an image is an image. So it's always the

same thing, but if you understand how your imaging modality works, it's always a pro.

But of course, this is not a physics class. Okay, so let's talk a bit about the effect

of scatter. And in principle, when you're talking, when we're talking about scatter,

we are often, so this example is related to X-ray imaging. And when you do X-ray imaging,

you typically have the constellation that you have some kind of X-ray tube that is positioned

here and then you have your patient. So this is the general setup. If you attended diagnostic

medical image processing, you already know this graph. And then you have an X-ray detector

here. So this is generally how it works. And what you do is you shoot an X-ray through

your patient, through your object. Often we call this patient an f of x, y. So this is

generally the name of our patients. They're called f of x, y. And then we measure the

intensity here at our detector. And generally what you measure here is photons. And when

you measure here, you measure some intensity i. And this i in a physical model that also

incorporates scatter is composed of two sources. So on the one hand, it's the primary photons,

it's iP, because these are the photons that arrive here directly. And then it's composed

of a secondary intensity. And this is called iS. And iS is the scattered intensity. And

this is caused by some different X-ray that is maybe shot here. And then there is some

scattering event. And it arrives at the very same detector cell. So this guy here is then

the scattered intensity. And this guy here is the primary intensity. And what you measure

at the detector is generally the sum of both. And your detector pixel can't differentiate

between the scattered intensity and the primary intensity. Because there's countermeasures

to reduce the scatter. We will look at a couple of them also today. But generally what you

measure is the sum of the primaries. This is actually what you want to measure. You

want to measure the primary signal. And also if you go into reconstruction data, you want