Reconstructing images from magnitude measurements is an important and difficult problem arising in many research areas, such as X-ray crystallography, astronomical imaging and more. While optimization-based approaches often struggle with the non-convexity and non- linearity of the problem, learning-based approaches are able to produce reconstructions of high quality for data similar to a given training dataset. In this work, we analyze a class of methods based on conditional generative adversarial networks (CGAN). We show how the benefits of optimization-based and learning-based methods can be combined to improve reconstruction quality. Furthermore, we show that these combined methods are able to generalize to out-of-distribution data and analyze their robustness to measurement noise. In addition to that, we compare how the methods are impacted by missing measurements. Extensive ablation studies demonstrate that all components of our approach are essential and justify the choice of network architecture.

In this paper, we propose the application of conditional generative adversarial networks to solve various phase retrieval problems. We show that including knowledge of the measurement process at training time leads to an optimization at test time that is more robust to initialization than existing approaches involving generative models. In addition, conditioning the generator network on the measurements enables us to achieve much more detailed results. We empirically demonstrate that these advantages provide meaningful solutions to the Fourier and the compressive phase retrieval problem and that our method outperforms well-established projection-based methods as well as existing methods that are based on neural networks. Like other deep learning methods, our approach is robust to noise and can therefore be useful for real-world applications.