[Castor-users] Scatter rate estimation for LM-TOF-MLEM

[jbaran]

Dear CASToR Users and Developers,

me and my colleagues found an issue with scatter correction implemented 
in CASToR (based on simulated data). I will start from the beginning.

We performed a simulation with GATE (NEMA IEC phantom) for the long 
axial FOV PET scanner and tried to reconstruct the results (true+scatter 
events) with scatter correction information incorporated. We estimated 
the scatter rate for each TOF bin independently (it is about 1-2 per TOF 
bin). We also specify the size of the TOF bin in the header. For the 
comparison, as the reference, we also reconstructed 2 other cases:
- only true coincidences
- true+scatter coincidences without any correction
For all three cases we use the same TOF resolution. All the images are 
done with LM-MLEM and raytracing projector. All the reconstructed images 
are attenuation corrected. You can find in the attached plot the 
reconstructed images from 20th iteration (NEMA_IEC_factor1.png):
TOP LEFT: true + scatter coincidences scatter corrected
TOP RIGHT: true + scatter coincidences
BOTTOM LEFT: true coincidences
BOTTOM RIGHT: profiles along the orange line from previous plots

Unfortunately, the images reconstructed with true+scatter coincidences 
with scatter correction do not look like those reconstructed only with 
true. They are more like the one reconstructed with true+scatter events. 
Even the values are at the same level as for the images reconstructed 
with true+scatter events. Moreover, we also dig a little bit in the 
CASToR source code and dump forward projection values and it seems that 
the factor of the image estimation is three levels of magnitude greater 
than the additive correction factor. It suggests that probably our 
scatter correction does not work correctly.

So we started to play around with scatter correction rates. We did some 
other exercises and multiplied our scatter rate by several factors 
ranging from 1 to 10E6. I attached the results for the multiplicative 
factor equal to 20000 (NEMA_IEC_factor20000.png). The legend is as for 
the previous image. The results with the scatter correction applied 
start to look like images reconstructed with true coincidences. However 
the scatter effect (increased signal in the middle of NEMA IEC) inside 
the phantom is visible. Image quality (factor_20000 images) at the 
boundaries of the scanner is better. Additionally, the overall voxel 
units are still at the level of the voxels of images reconstructed with 
true+scatter coincidences. Study with other factors also does not affect 
image in the expected way. So, we think that at some point our scatter 
correction method might not work properly but we are also wondering if 
the scatter correction in CASToR is also implemented correctly.

To check it we performed one more study - simulation of the cuboid 
phantom with very high statistics. We performed the reconstruction 
without TOF resolution for such cases:
- true coincidences
- true + scatter coincidences
- true + scatter coincidences with scatter correction performed by 
CASToR internally.
The resulted reconstructed images are shown in cuboid.png:
TOP LEFT: true coincidences
TOP RIGHT: true + scatter coincidences
BOTTOM LEFT: true + scatter coincidences with scatter correction 
performed by CASToR internally
BOTTOM RIGHT: profiles along the orange line from previous plots
The number of scatter coincidences registered per LOR is around 10-30 
coincidences.
What we found is that the images reconstructed with true+scatter and 
true+scatter with incorporated scatter correction look almost the same 
in terms of image quality and voxel activity units, which is surprising.

In conclusion, we are wondering if you have ever found similar things 
and could help us understand why the scatter correction does not work 
(especially for the last case). The second thing is that maybe there is 
a feature of the CASToR which we do not consider.

We will appreciate your help.

All the best,
Jakub
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