Functional ultrasound imaging is rapidly establishing itself as a state-of-the-art neuroimaging modality owing to its ability to image neural activation in awake and mobile small animals, its relatively low cost, and its unequaled portability. To achieve high blood flow sensitivity in the brain microvasculature, functional ultrasound relies on long sequences of ultrasound data acquired at high frame rates, which pose high demands on the hardware architecture and effectively limit the practical utility and clinical translation of this imaging modality. Here we propose Deep-fUS, a deep learning approach that aims to significantly reduce the amount of ultrasound data necessary, while retaining the imaging performance. We trained a neural network to learn the power Doppler reconstruction function from sparse sequences of compound ultrasound data, using ground truth images from high-quality in vivo acquisitions in rats, and with a custom loss function. The network produces highly accurate images with restored sensitivity in the smaller blood vessels even when using heavily under-sampled data. We tested the network performance in a task-evoked functional neuroimaging application, demonstrating that time series of power Doppler images can be reconstructed with adequate accuracy to compute functional activity maps. Notably, the network reduces the occurrence of motion artifacts in awake functional ultrasound imaging experiments. The proposed platform can facilitate the development of this neuroimaging modality in any setting where dedicated hardware is not available or even in clinical scanners, opening the way to new potential applications based on this technology. To our knowledge, this is the first attempt to implement a convolutional neural network approach for power Doppler reconstruction from sparse ultrasonic datasets.