Stochastic image reconstruction is a key part of modern digital rock physics and material analysis that aims to create representative samples of microstructures for upsampling, upscaling and uncertainty quantification. We present new results of a method of three-dimensional stochastic image reconstruction based on generative adversarial neural networks (GANs). GANs are a family of unsupervised learning methods that require no a priori inference of the probability distribution associated with the training data. Thanks to the use of two convolutional neural networks, the discriminator and the generator, in the training phase, and only the generator in the simulation phase, GANs allow the sampling of large and realistic volumetric images. We apply a GAN-based workflow of training and image generation to an oolitic Ketton limestone micro-CT unsegmented gray-level dataset. Minkowski functionals calculated as a function of the segmentation threshold are compared between simulated and acquired images. Flow simulations are run on the segmented images, and effective permeability and velocity distributions of simulated flow are also compared. Results show that GANs allow a fast and accurate reconstruction of the evaluated image dataset. We discuss the performance of GANs in relation to other simulation techniques and stress the benefits resulting from the use of convolutional neural networks . We address a number of challenges involved in GANs, in particular the representation of the probability distribution associated with the training data.