Beyond mechanics: Maximum-likelihood-driven PET detector alignment calibration

Accurate quantification is a cornerstone of positron-emission tomography (PET), yet mechanical inaccuracies during detector assembly continue to undermine this goal. Deviations from intended design geometries arise due to factors such as manufacturing tolerances, mechanical stress, and cumulative errors during module installation and operation. High-resolution PET systems, in particular, are highly susceptible to even minor misalignments, such as translational offsets of $0.5mm$ and angular deviations of $0.5{}^{\circ }$ , leading to distorted lines of response, a reduction in signal-to-noise ratio, and compromised quantitative reliability.

To address the limitations imposed by mechanical misalignments in PET systems, particularly in high-resolution applications, we propose a calibration strategy that eliminates reliance on precise physical assembly or movable calibration setups. The goal is to develop a data-driven framework for estimating detector alignment parameters directly from PET measurements, allowing for robust recalibration across a broad range of scanner geometries and detector designs.

We present a statistical optimization framework that estimates detector alignment parameters directly from time-of-flight list-mode coincidence data using gradient-based optimization. By casting the problem as a maximum likelihood estimation conditioned on a known 3D tracer distribution, the optimization targets to maximize the Poisson likelihood of the measured coincidence data under the parametrized alignment model. This formulation eliminates the need for any movable parts, including motion stages, rotating sources, or manual calibration efforts. The approach supports complex extended tracer distributions and generic scanner geometries, enabling a flexible, regular, software-based recalibration from static acquisitions.

The method was validated on both simulated and real PET systems, including measurements with point sources and a tracer-filled tube phantom. In the simulation study, deviations from a cylindrical configuration were introduced prior to data generation, while the cylindrical geometry was used as initialization for the optimization. For the point source setup, alignment parameters were recovered with an accuracy of approximately $50\mu m$ and $0.15{}^{\circ }$ , and for the simulated tube phantom, with approximately $120\mu m$ and $0.2{}^{\circ }$ . On two real scanners with differing crystal topologies and arbitrarily induced misalignments to the blueprint initialization, the recovered configurations yielded image resolutions in the range of $1.0mm\mathrm{to}1.2mm$ , matching the performance of a precisely known design specification. For both real systems, the optimizations relied on approximately five million coincidences, demonstrating that accurate alignment can be achieved with modest amounts of measurement data. Notably, for the second scanner, a single gamma positioning model was shared across all detectors, indicating the method's robustness towards model-sharing constraints.

This framework bridges hardware imperfections and quantitative fidelity by enabling robust recalibration in mechanically unstable or mobile settings. It is compatible with diverse phantom types and scanner topologies, and operates effectively even in the absence of precise scanner-phantom alignment. By reducing dependency on strict manufacturing tolerances while preserving an accurate line of response positioning, our approach offers a practical and scalable solution for modern PET calibration, where quantitative accuracy is paramount.