Background: Residual image noise is substantial in positron emission tomography (PET) and one of the factors limiting lesion detection, quantification, and overall image quality. Thus, improving noise reduction remains of considerable interest. This is especially true for respiratory-gated PET investigations. The only broadly used approach for noise reduction in PET imaging has been the application of low-pass filters, usually Gaussians, which however leads to loss of spatial resolution and increased partial volume effects affecting detectability of small lesions and quantitative data evaluation. The bilateral filter (BF) — a locally adaptive image filter — allows to reduce image noise while preserving well defined object edges but manual optimization of the filter parameters for a given PET scan can be tedious and time-consuming, hampering its clinical use. In this work we have investigated to what extent a suitable deep learning based approach can resolve this issue by training a suitable network with the target of reproducing the results of manually adjusted case-specific bilateral filtering. Methods: Altogether, 69 respiratory-gated clinical PET/CT scans with three different tracers ([¹⁸F]FDG, [¹⁸F]L-DOPA, [⁶⁸Ga]DOTATATE) were used for the present investigation. Prior to data processing, the gated data sets were split, resulting in a total of 552 single-gate image volumes. For each of these image volumes, four 3D ROIs were delineated: one ROI for image noise assessment and three ROIs for focal uptake (e.g. tumor lesions) measurements at different target/background contrast levels. An automated procedure was used to perform a brute force search of the two-dimensional BF parameter space for each data set to identify the “optimal” filter parameters to generate user-approved ground truth input data consisting of pairs of original and optimally BF filtered images. For reproducing the optimal BF filtering, we employed a modified 3D U-Net CNN incorporating residual learning principle. The network training and evaluation was performed using a 5-fold cross-validation scheme. The influence of filtering on lesion SUV quantification and image noise level was assessed by calculating absolute and fractional differences between the CNN, manual BF, or original (STD) data sets in the previously defined ROIs. Results: The automated procedure used for filter parameter determination chose adequate filter parameters for the majority of the data sets with only 19 patient data sets requiring manual tuning. Evaluation of the focal uptake ROIs revealed that CNN as well as BF based filtering essentially maintain the focal SUV_max values of the unfiltered images with a low mean ± SD difference of δSUV_max^CNN,STD = (−3.9 ± 5.2)% and δSUV_max^BF,STD = (−4.4 ± 5.3)%. Regarding relative performance of CNN versus BF, both methods lead to very similar SUV_max values in the vast majority of cases with an overall average difference of δSUV_max^CNN,BF = (0.5 ± 4.8)%. Evaluation of the noise properties showed that CNN filtering mostly satisfactorily reproduces the noise level and characteristics of BF with δNoise^CNN,BF = (5.6 ± 10.5)%. No significant tracer dependent differences between CNN and BF were observed. Conclusions: Our results show that a neural network based denoising can reproduce the results of a case by case optimized BF in a fully automated way. Apart from rare cases it led to images of practically identical quality regarding noise level, edge preservation, and signal recovery. We believe such a network might proof especially useful in the context of improved motion correction of respiratory-gated PET studies but could also help to establish BF-equivalent edge-preserving CNN filtering in clinical PET since it obviates time consuming manual BF parameter tuning.