The development of fast and accurate image reconstruction algorithms is a central aspect of computed tomography. In this paper we investigate this issue for the sparse data problem of photoacoustic tomography (PAT). We develop direct and highly efficient reconstruction algorithms based on deep-learning. In this approach image reconstruction is performed with a deep convolutional neural network (CNN), whose weights are adjusted prior to the actual image reconstruction based on a set of training data. Our results demonstrate that the proposed deep learning approach reconstructs images with a quality komparable to state of the art iterative approaches from sparse data. At the same time, the numerically complexity of our approach is much smaller and the image reconstruction is performed in a fraction of the time required by iterative methods.