3D-Localization of Single Point-Like Gamma Sources with a Coded Aperture Camera

3D-localization of gamma sources has the potential to improve the outcome of radio-guided surgery. The goal of this paper is to analyze the localization accuracy for point-like sources with a single coded aperture camera. We both simulated and measured a point-like $^{241}$Am source at $17$ positions distributed within the field of view of an experimental gamma camera. The setup includes a 0.11mm thick tungsten sheet with a MURA mask of rank $31$ and pinholes of $0.08$mm in diameter and a detector based on the photon counting readout circuit Timepix3. Two methods, namely an iterative search (ISL) including either a symmetric Gaussian fitting or an exponentially modified Gaussian fitting (EMG) and a center of mass method were compared to estimate the 3D source position. Considering the decreasing axial resolution with source-to-mask distance, the EMG improved the results by a factor of $4$ compared to the Gaussian fitting based on the simulated data. Overall, we obtained a mean localization error of $0.77$mm on the simulated and $2.64$mm on the experimental data in the imaging range of $20$mm to $100$ mm. This paper shows that despite the low axial resolution, point-like sources in the nearfield can be localized as well as with more sophisticated imaging devices such as stereo cameras. The influence of the source size and the photon count on the imaging and localization accuracy remains an important issue for further research. The acquired datasets and the localization methods of this research are publicly available on GitHub at "https://zenodo.org/records/11449544".