Functional ultrasound (fUS) is a rapidly emerging modality that enables whole-brain imaging of neural activity in awake and mobile rodents. To achieve sufficient blood flow sensitivity in the brain microvasculature, fUS relies on long ultrasound data acquisitions at high frame rates, posing high demands on the sampling and processing hardware. Here we develop an image reconstruction method based on deep learning that significantly reduces the amount of data necessary while retaining imaging performance. We trained convolutional neural networks to learn the power Doppler reconstruction function from sparse sequences of ultrasound data with compression factors of up to 95%. High-quality images from in vivo acquisitions in rats were used for training and performance evaluation. We demonstrate that time series of power Doppler images can be reconstructed with sufficient accuracy to detect the small changes in cerebral blood volume (~10%) characteristic of task-evoked cortical activation, even though the network was not formally trained to reconstruct such image series. The proposed platform may facilitate the development of this neuroimaging modality in any setting where dedicated hardware is not available or in clinical scanners.