We introduce a list-mode time-of-flight maximum likelihood expectation maximisation (TOF MLEM) image reconstruction algorithm for the total-body Jagiellonian PET (J-PET) scanner, using an analytical model for the system response matrix (SRM), estimated as a log-polynomial fit of the Monte Carlo simulated emissions of back-to-back -photons for each bin. Using the GATE software, the updated method is tested on the simulated NEMA IEC phantom, scanned over a short 35-second time by the 140-cm long 24-module J-PET. By comparison to the reference TOF MLEM without the resolution modelling for the detectors from the CASToR framework, a significant improve-ment in image quality was observed. The inclusion of the penalisation into the reconstruction algorithm may achieve outcomes comparable to 500-second scans, with the best results obtained for the anisotropic median-diffusion with a finite-impulse-response median hybrid filter. The proposed TOF MLEM can also be extended to account for the non-collinearity, positron range and other factors.

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