The speed of super-resolution microscopy methods based on single-molecule localization, for example, PALM and STORM, is limited by the need to record many thousands of frames with a small number of observed molecules in each. Here, we present ANNA-PALM, a computational strategy that uses artificial neural networks to reconstruct super-resolution views from sparse, rapidly acquired localization images and/or widefield images. Simulations and experimental imaging of microtubules, nuclear pores, and mitochondria show that high-quality, super-resolution images can be reconstructed from up to two orders of magnitude fewer frames than usually needed, without compromising spatial resolution. Super-resolution reconstructions are even possible from widefield images alone, though adding localization data improves image quality. We demonstrate super-resolution imaging of >1,000 fields of view containing >1,000 cells in ∼3 h, yielding an image spanning spatial scales from ∼20 nm to ∼2 mm. The drastic reduction in acquisition time and sample irradiation afforded by ANNA-PALM enables faster and gentler high-throughput and live-cell super-resolution imaging.