Question about the list-mode ToF algorithm


There are two algorithms described in the CASToR Time-of-Flight PET documentation: one for binned data and one for list-mode. I had never thought that the list-mode version could be implemented with continuous TOF information. I would like to see the details behind the development of the update formula, equation (18) in the document, however the papers I have found seems to use TOF bins with list-mode data.
  Could you refer me to an article/document that gives more details on how this formula is obtained?

Have a nice day,
Maxime Toussaint

Hi Maxime,

Thanks for the question, we have also had some troubles finding articles or documents dealing in depth with implementation details for TOF list mode reconstruction. To be honest, we haven't really found much information.

For the equation 18, we started from the usual MLEM list-mode equation without TOF, and modified all the relevant terms to be a continuous function of time-of-flight. The main difficulty was actually to obtain the random and scatter estimation for this setting, based on usual estimations provided by scanners (we proposed approximative solutions as explained in the document).

The TOF information provided by scanners for list-mode data is probably always quantized or discretized, but we considered that these discretization steps were much smaller than the size of sinogram TOF bins or the TOF resolution. If a scanner provides TOF information for list-mode with large quantization steps, I guess some problems may occurs with our reconstruction.

Implementing TOF list-mode reconstruction in CASToR using tiny TOF bins was a bit burdensome, the continuous solution was more straightforward and computation efficient.

Do you find this explanation sufficient?


Marina Filipovic

Yup, it was! Thank you for the explanation.

Have a nice day,
Maxime Toussaint