Monolithic crystals are considered as an alternative for complex segmented scintillator arrays in positron emission tomography systems. Monoliths provide high sensitivity, good timing, and energy resolution while being cheaper than highly segmented arrays. Furthermore, monoliths enable intrinsic depth of interaction capabilities and good spatial resolutions (SRs) mostly based on statistical calibrations. To widely translate monoliths into clinical applications, a time-efficient calibration method and a positioning algorithm implementable in system architecture such as field-programmable gate arrays (FPGAs) are required. We present a novel positioning algorithm based on gradient tree boosting (GTB) and a fast fan beam calibration requiring less than 1 h per detector block. GTB is a supervised machine learning technique building a set of sequential binary decisions (decision trees). The algorithm handles different sets of input features, their combinations and partially missing data. GTB models are strongly adaptable influencing both the positioning performance and the memory requirement of trained positioning models. For an FPGA-implementation, the memory requirement is the limiting aspect. We demonstrate a general optimization and propose two different optimization scenarios: one without compromising on positioning performance and one optimizing the positioning performance for a given memory restriction. For a 12 mm high LYSO-block, we achieve an SR better than 1.4 mm FWHM.

Monolithic crystals are examined as an alternative to segmented scintillator arrays in positron emission tomography (PET). Monoliths provide good energy, timing and spatial resolution including intrinsic depth of interaction (DOI) encoding. DOI allows reducing parallax errors (radial astigmatism) at off-center positions within a PET ring. We present a novel DOI-estimation approach based on the supervised machine learning algorithm gradient tree boosting (GTB). GTB builds predictive regression models based on sequential binary comparisons (decision trees). GTB models have been shown to be implementable in FPGA if the memory requirement fits the available resources. We propose two optimization scenarios for the best possible positioning performance: One restricting the available memory to enable a future FPGA implementation and one without any restrictions. The positioning performance of the GTB models is compared with a DOI estimation method based on a single DOI observable (SO) comparable to other methods presented in literature. For a 12 mm high monolith, we achieve an averaged spatial resolution of 2.15 mm and 2.12 mm FWHM for SO and GTB models, respectively. In contrast to SO models, GTB models show a nearly uniform positioning performance over the whole crystal depth.

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