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Purpose: Image artefacts continue to pose challenges in clinical molecular imaging, resulting in misdiagnoses, additional radiation doses to patients and financial costs. Mismatch and halo artefacts occur frequently in gallium-68 (68Ga)-labelled compounds whole-body PET/CT imaging. Correcting for these artefacts is not straightforward and requires algorithmic developments, given that conventional techniques have failed to address them adequately. In the current study, we employed differential privacy-preserving federated transfer learning (FTL) to manage clinical data sharing and tackle privacy issues for building centre-specific models that detect and correct artefacts present in PET images. Methods: Altogether, 1413 patients with 68Ga prostate-specific membrane antigen (PSMA)/DOTA-TATE (TOC) PET/CT scans from 3 countries, including 8 different centres, were enrolled in this study. CT-based attenuation and scatter correction (CT-ASC) was used in all centres for quantitative PET reconstruction. Prior to model training, an experienced nuclear medicine physician reviewed all images to ensure the use of high-quality, artefact-free PET images (421 patients' images). A deep neural network (modified U2Net) was trained on 80% of the artefact-free PET images to utilize centre-based (CeBa), centralized (CeZe) and the proposed differential privacy FTL frameworks. Quantitative analysis was performed in 20% of the clean data (with no artefacts) in each centre. A panel of two nuclear medicine physicians conducted qualitative assessment of image quality, diagnostic confidence and image artefacts in 128 patients with artefacts (256 images for CT-ASC and FTL-ASC). Results: The three approaches investigated in this study for 68Ga-PET imaging (CeBa, CeZe and FTL) resulted in a mean absolute error (MAE) of 0.42 ± 0.21 (CI 95%: 0.38 to 0.47), 0.32 ± 0.23 (CI 95%: 0.27 to 0.37) and 0.28 ± 0.15 (CI 95%: 0.25 to 0.31), respectively. Statistical analysis using the Wilcoxon test revealed significant differences between the three approaches, with FTL outperforming CeBa and CeZe (p-value < 0.05) in the clean test set. The qualitative assessment demonstrated that FTL-ASC significantly improved image quality and diagnostic confidence and decreased image artefacts, compared to CT-ASC in 68Ga-PET imaging. In addition, mismatch and halo artefacts were successfully detected and disentangled in the chest, abdomen and pelvic regions in 68Ga-PET imaging. Conclusion: The proposed approach benefits from using large datasets from multiple centres while preserving patient privacy. Qualitative assessment by nuclear medicine physicians showed that the proposed model correctly addressed two main challenging artefacts in 68Ga-PET imaging. This technique could be integrated in the clinic for 68Ga-PET imaging artefact detection and disentanglement using multicentric heterogeneous datasets. [ABSTRACT FROM AUTHOR]