  This paper shows how data-driven deep generative models can be utilized to
solve challenging phase retrieval problems, in which one wants to reconstruct a
signal from only few intensity measurements. Classical iterative algorithms are
known to work well if initialized close to the optimum but otherwise suffer
from non-convexity and often get stuck in local minima. We therefore propose
DeepInit Phase Retrieval, which uses regularized gradient descent under a deep
generative data prior to compute a trained initialization for a fast classical
algorithm (e.g. the randomized Kaczmarz method). We empirically show that our
hybrid approach is able to deliver very high reconstruction results at low
sampling rates even when there is significant generator model error.
Conceptually, learned initializations may therefore help to overcome the
non-convexity of the problem by starting classical descent steps closer to the
global optimum. Also, our idea demonstrates superior runtime performance over
conventional gradient-based reconstruction methods. We evaluate our method for
generic measurements and show empirically that it is also applicable to
diffraction-type measurement models which are found in terahertz single-pixel
phase retrieval.
