Technical note: Comparison of arithmetic mean and energy‐weighted mean flood histogram generation methods for dual‐ended readout positron emission tomography detectors
Authors: Cong Longhan , Kuang Zhonghua , Sang Ziru , Wang Xiaohui , Niu Ming , Yang Yongfeng 
Published: May 2022

Purpose

Dual‐ended readout pixelated scintillator array detectors can provide a suitable crystal resolvability and satisfactory depth of interaction (DOI), energy, and timing resolutions. Usually, the flood histogram measured by one‐sided readout is depth dependent, and the flood histogram quality degrades as the distance between the interaction site and photodetector increases. Information measured by two photodetectors must be combined to obtain an improved flood histogram yielding a better PET scanner spatial resolution.

Methods

Two flood histogram generation algorithms for dual‐ended readout of pixelated scintillator array detectors were compared by theoretical calculations and experimental measurements. The first algorithm is the arithmetic mean (AM) algorithm, which assigns the same weight to the flood histograms measured by photodetectors 1 and 2. The second algorithm is the energy‐weighted mean (EWM) algorithm, which assigns each flood histogram a certain weight proportional to the energy measured by the photodetector. Theoretical equations were derived to determine the quality of the flood histograms obtained with these two algorithms. Experimental measurements were performed with an 18 × 18 lutetium–yttrium oxyorthosilicate (LYSO) array with a crystal size of 0.62 × 0.62 × 20 mm3 read out by two multi‐anode photomultiplier tubes at both ends. Flood histograms of the whole array and five specific depths were compared between the above two algorithms.

Results

The theoretical results indicated that the flood histograms obtained with the EWM method matched those obtained with the AM method at the middle detector depth and were better at other detector depths when the distance (S) between the locations of the same crystal in the flood histograms measured by photodetectors 1 and 2 reached 0. The advantage of the EWM method decreased with increasing S value since the crystal position in the flood histogram obtained with the EWM method varies with the depth when S does not equal 0. The advantage of the EWM method decreased with increasing S value. The experimental results generally agreed with the theoretical predictions. Compared to the AM method, the EWM method provided a similar flood histogram at a depth of 10 mm but generated a better flood histogram at depths of 2 and 18 mm. Although an inverse correlation between Q (a quality factor representing the advantage of the EWM method) and S was observed, the variation in Q given the same S value was high. The average Q value at the same S still agreed with the theoretical predictions.

Conclusions

Theoretical equations were derived, and experimental measurements were performed to compare two flood histogram generation algorithms for dual‐ended readout PET detectors. The results indicated that the EWM method based on inverse variance weighting theory could provide better flood histograms than those provided by the AM method.