We implemented a deep learning (DL) algorithm for the 3-dimensional segmentation of perivascular spaces (PVSs) in deep white matter (DWM) and basal ganglia (BG). This algorithm is based on an autoencoder and a U-shaped network (U-net), and was trained and tested using T1-weighted magnetic resonance imaging (MRI) data from a large database of 1,832 healthy young adults. An important feature of this approach is the ability to learn from relatively sparse data, which gives the present algorithm a major advantage over other DL algorithms. Here, we trained the algorithm with 40 T1-weighted MRI datasets in which all "visible" PVSs were manually annotated by an experienced operator. After learning, performance was assessed using another set of 10 MRI scans from the same database in which PVSs were also traced by the same operator and were checked by consensus with another experienced operator. The Sorensen-Dice coefficients for PVS voxel detection in DWM (resp. BG) were 0.51 (resp. 0.66), and 0.64 (resp. 0.71) for PVS cluster detection (volume threshold of 0.5 within a range of 0 to 1). Dice values above 0.90 could be reached for detecting PVSs larger than 10 mm(3) and 0.95 for PVSs larger than 15 mm(3). We then applied the trained algorithm to the rest of the database (1,782 individuals). The individual PVS load provided by the algorithm showed a high agreement with a semi-quantitative visual rating done by an independent expert rater, both for DWM and for BG. Finally, we applied the trained algorithm to an age-matched sample from another MRI database acquired using a different scanner. We obtained a very similar distribution of PVS load, demonstrating the interoperability of this algorithm.