CT corrupted by Poisson noise, weighted least squares, how to calculate in detail
The first paper is more clear than the second.

&quot;Let $\mu$ represent the distribution of linear attenuation coefficient of an object and $[A \mu]_m$ represents their line integral. &quot;

The signal obtained from Computed Tomography (CT) depends on how much was the X-Ray beam attenuated as it travels through the human body (there are other modalities such as the Positron Emission Tomography (PET) where the signal depends on how much emission you measure. Same reconstruction technique, different signal model).
You don't really know what is inside some $A$. It represents the body. What you do know is that it comes in the form of a matrix of sites which is called $A$. Now that you have the $A$, then you consider the total attenuation along the path of a ray through this $A$. That is the &quot;line integral&quot; $[A \mu]_m$ .

The $m^{th}$ CT measurement, $y_m$ is a Poisson random variable with parameters
$ p_m \sim Poisson( b_m e^{-[A \mu]_m} +r_m)$
$ y_m = -log(\frac{p_m}{b_m})$
where $b_m$ is the blank scan factor and $r_m$ is the readout noise.&quot;

This $[A \mu]_m$ is inaccessible to you. What is accessible to you is $y_m$, which is what you measure, it contains noise and is expressed here as the ratio of a measurement through the body divided by a measurement in air (&quot;blank scan factor&quot;).
Notice here, $y_m$ is the line integral. One number. One ray through $A$. That is, one pixel from one line of your Radon transform. One measurement. NOT the whole line of the Radon transform. To look along the line of the Radon you need to do it in an iteration (i.e, expressions where $\sum_{m=1}^M y_m \times ...$).
Hope this helps.
EDIT:

I still don't really know how to calcalute $p_m$.

$p_m$'s expression is given in the paper as coming from a Poisson distribution. It does not look very much Poisson because it is missing the rate ($k$) and so it ends up being closer to an exponentially decaying distribution. The effect this is trying to simulate is the variation of the detector's sensitivity with attenuation (or radiation energy).

Would it be possible to get $p_m$ from $y_m=−log(\frac{p_m}{b_m})$, that means $p_m=b_m e^{−y_m}$?

That means $p_m \sim Poisson( b_m e^{-[A \mu]_m} + r_m)$. $r_m$ is the readout noise.

But how exactly would I determine $y_m$;
[...]
And what should I choose for the blank scan factor?

I don't know what should you choose for $b_m, r_m$, it depends on what you are modeling (detector voltage? Hounsfield scale?). Usually, $A$ is supposed to contain Hounsfield scale values directly, in which case your blank scan factor should be that for air. But this means that the rest of your image values are adjusted according to what sort of tissue they depict. The point of this is to take into account the Poisson noise because it modulates the readings. So, perhaps you can lump things together into reasonable values obtained by measurements over phantoms.

let's say my image $x$ is from $\mathbb{R}^{512×512}$ and performing a radon tranformation gives me a sinogram $Hx \in \mathbb{R}^{512×32}$.

Just a note here, if you keep your &quot;detector width&quot; at 512 measurements, you will be sampling a disc inscribed within the $512 \times 512$ square. When the detector is looking at a $512 \times 512$ image at a $ \frac{\pi}{4}$ bearing, its diagonal is $\approx 724$ pixels. What I like to do is to center the square image in a black frame that is $diagonal \times diagonal$ in dimensions and use that for reconstruction. It is also easier to keep the detector geometry fixed and rotate the image. For a parallel ray detector, the line integrals are simply the sums of the columns of the image. For a fan beam, each ray deviates but you don't have to re-calculate this for every projection.

Then $W \in \mathbb{R}^{512×512}$ and there are $512$ values of $p_m$. How would I go on from there?

As far as I can tell, this $W$ term is $w_m = \frac{(p_m - r_m)^2}{p_m}$ (equation 29).
But, the part of the discussion on page 1451 that involves $W$ is to explain how to calculate your $E$ that drives the optimisation detailed in equation 33. between what you &quot;guess&quot; $Hx$ (see &quot;data fidelity term&quot; pages 1440-1441 around equations 1 and 2) and what you measure $ym$.
So how image is affected by Poisson noise is one thing and calculating that error term during optimisation is another.
Hope this helps.