Abstract Learning meaningful representations is at the heart of many tasks in the field of modern machine learning. Recently, a lot of methods were introduced that allow learning of image representations without supervision. These representations can then be used in downstream tasks like classification or object detection. The quality of these representations is close to supervised learning, while no labeled images are needed. This survey paper provides a comprehensive review of these methods in a unified notation, points out similarities and differences of these methods, and proposes a taxonomy which sets these methods in relation to each other. Furthermore, our survey summarizes the most recent experimental results reported in the literature in form of a meta-study. Our survey is intended as a starting point for researchers and practitioners who want to dive into the field of representation learning.

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.