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The interest of the automotive industry has progressively focused on subjects related to driver assistance systems as well as autonomous cars. Cars combine a variety of sensors to perceive their surroundings robustly. Among them, radar sensors are indispensable because of their independence of lighting conditions and the possibility to directly measure velocity. However, radar interference is an issue that becomes prevalent with the increasing amount of radar systems in automotive scenarios. In this paper, we address this issue for frequency modulated continuous wave (FMCW) radars with fully convolutional neural networks (FCNs), a state-of-the-art deep learning technique. We propose two FCNs that take spectrograms of the beat signals as input, and provide the corresponding clean range profiles as output. We propose two architectures for interference mitigation which outperform the classical zeroing technique. Moreover, considering the lack of databases for this task, we release as open source a large scale data set that closely replicates real world automotive scenarios for single-interference cases, allowing others to objectively compare their future work in this domain. The data set is available for download at: http://github.com/ristea/arim.