Convex Optimization of Coincidence Time Resolution for a High-Resolution PET System

Abstract

We are developing a dual panel breast-dedicated positron emission tomography (PET) system using LSO scintillators coupled to position sensitive avalanche photodiodes (PSAPD). The charge output is amplified and read using NOVA RENA-3 ASICs. This paper shows that the coincidence timing resolution of the RENA-3 ASIC can be improved using certain list-mode calibrations. We treat the calibration problem as a convex optimization problem and use the RENA-3’s analog-based timing system to correct the measured data for time dispersion effects from correlated noise, PSAPD signal delays and varying signal amplitudes. The direct solution to the optimization problem involves a matrix inversion that grows order (n3) with the number of parameters. An iterative method using single-coordinate descent to approximate the inversion grows order (n). The inversion does not need to run to convergence, since any gains at high iteration number will be low compared to noise amplification. The system calibration method is demonstrated with measured pulser data as well as with two LSO-PSAPD detectors in electronic coincidence. After applying the algorithm, the 511 keV photopeak paired coincidence time resolution from the LSO-PSAPD detectors under study improved by 57%, from the raw value of 16.3 ± 0.07 ns full-width at half-maximum (FWHM) to 6.92 ± 0.02 ns FWHM (11.52 ± 0.05 ns to 4.89 ± 0.02 ns for unpaired photons).

A Study of Position-Sensitive Solid-State Photomultiplier Signal Properties

“…As described in the beginning of Section A, and also in [15], the data acquisition system is based on digitizing the peak amplitude after shaping. Because of the PS-SSPM's anode signal position dependent shape we observed changes in flood histogram dynamic range and energy estimation by varying the delay between the CF generated time stamp and acquisition trigger time (which we refer to as the DAQ trigger delay).…”

“…Much of this work follows, and in some cases builds upon, our knowledge of position-sensitive avalanche photodiode (PS-APD) signal properties [14], [15]. As we will show, PS-SSPMs share the cathode signal position dependent timing shift found in PS-APD designs but with the addition of a significant position-dependent rise time shift in the four corner anode signals following a charge sensitive preamplifier.…”

Optical delay encoding for fast timing and detector signal multiplexing in PET

“…Since these delays are known for each channel and do not change, they can be subtracted from the timestamp during processing, or compensated for with a convex optimization method. 20 Delay optimization will not prevent pulse overlap in all cases, however, so more advanced logic must be implemented to successfully decode and avoid the need to discard these events.…”

Development of a data acquisition architecture with distributed synchronization for a Positron Emission Tomography system with integrated front-end.

“…This corresponds to merging the calibration run with the actual measurement run. For instance, the method presented in [113] for the correction of coincidence detection in PET belongs to this class, as it relies on data from valid captured events for the estimation of calibration parameters. Another example is the timing distribution for the Belle II experiment [114].…”

“…The situation is analogous to the cases of energy and position estimation in that the processes behind time assignment in a PET detector contain random components and the detection of different annihilation photons originating at the same point and traveling with the same direction may result in different time estimates that can be described with a probability distribution. Systematic errors in the mean of the distribution may be compensated against by way of different, more or less time consuming alignment methods [113,260], but variance cannot be calibrated away and determines the time resolution in the system.…”