  The ClearMind project aims to develop the TOF-PET position sensitive
detection module optimized for the time resolution, spatial resolution, and
detection efficiency. For this, the ClearMind project uses a large (59 $\times$
59 mm$^2$) monolithic PbWO$_4$ (PWO) scintillating crystal with a bialkali
photo-electric layer deposited directly on the crystal. Scintillation and
Cherenkov photons result together from the 511 keV gamma-ray interation into
the PWO crystal. A micro-channel plate photomultiplier tube (MCP-PMT)
encapsulating the PWO crystal amplifies photoelectrons generated at the
photocathode, and the corresponding anode signals are collected through the
transmission lines read out at both ends and digitized by a SAMPIC module. In
this work, we present a realistic Geant4 simulation of the ClearMind prototype
detector, including the propagation of the visible photons in the crystal, the
modelling of a realistic response of the photocathode and of the PMT, and the
propagation of the electrical signals over the transmission lines. The
reconstruction of the gamma conversion in the detector volume is performed from
the signals registered at both ends of the transmission lines. We compare the
reconstruction precision of a statistical algorithm against machine learning
algorithms developed using the TMVA package. We expect to reach a spatial
resolution down to a few mm$^3$ (FWHM). Finally, we will discuss prospects for
the ClearMind detector.
