Foveated image reconstruction recovers full image from a sparse set of samples distributed according to the human visual system's retinal sensitivity that rapidly drops with eccentricity. Recently, the use of Generative Adversarial Networks was shown to be a promising solution for such a task as they can successfully hallucinate missing image information. Like for other supervised learning approaches, also for this one, the definition of the loss function and training strategy heavily influences the output quality. In this work, we pose the question of how to efficiently guide the training of foveated reconstruction techniques such that they are fully aware of the human visual system's capabilities and limitations, and therefore, reconstruct visually important image features. Due to the nature of GAN-based solutions, we concentrate on the human's sensitivity to hallucination for different input sample densities. We present new psychophysical experiments, a dataset, and a procedure for training foveated image reconstruction. The strategy provides flexibility to the generator network by penalizing only perceptually important deviations in the output. As a result, the method aims to preserve perceived image statistics rather than natural image statistics. We evaluate our strategy and compare it to alternative solutions using a newly trained objective metric and user experiments
