Compressed sensing using neural networks

Methods, systems, and apparatus, including computer programs encoded on computer storage media, for compressed sensing using neural networks. One of the methods includes receiving an input measurement of an input data item; for each of one or more optimization steps: processing a latent representation using a generator neural network to generate a candidate reconstructed data item, processing the candidate reconstructed data item using a measurement neural network to generate a measurement of the candidate reconstructed data item, and updating the latent representation to reduce an error between the measurement and the input measurement; and processing the latent representation after the one or more optimization steps using the generator neural network to generate a reconstruction of the input data item.