Reconstruction of signal in plastic scintillator of PET using Tikhonov regularization

The new concept of Time of Flight Positron Emission Tomography (TOF-PET) detection system, which allows for single bed imaging of the whole human body, is currently under development at the Jagiellonian University. The Jagiellonian-PET (J-PET) detector improves the TOF resolution due to the use of fast plastic scintillators. Since registration of the waveform of signals with duration times of few nanoseconds is not feasible, a novel front-end electronics allowing for sampling in a voltage domain at four thresholds was developed. To take fully advantage of these fast signals a novel scheme of recovery of the waveform of the signal, based on idea from the Tikhonov regularization method, is presented. From the Bayes theory the properties of regularized solution, especially its covariance matrix, may be easily derived. This step is crucial to introduce and prove the formula for calculations of the signal recovery error. The method is tested using signals registered by means of the single detection module of the J-PET detector built out from the 30 cm long plastic scintillator strip. It is shown that using the recovered waveform of the signals, instead of samples at four voltage levels alone, improves the spatial resolution of the hit position reconstruction from 1.05 cm to 0.94 cm. Moreover, the obtained result is only slightly worse than the one evaluated using the original raw-signal. The spatial resolution calculated under these conditions is equal to 0.93 cm.