  Phase retrieval is the problem of reconstructing images from magnitude-only
measurements. In many real-world applications the problem is underdetermined.
When training data is available, generative models allow optimization in a
lower-dimensional latent space, hereby constraining the solution set to those
images that can be synthesized by the generative model. However, not all
possible solutions are within the range of the generator. Instead, they are
represented with some error. To reduce this representation error in the context
of phase retrieval, we first leverage a novel variation of intermediate layer
optimization (ILO) to extend the range of the generator while still producing
images consistent with the training data. Second, we introduce new
initialization schemes that further improve the quality of the reconstruction.
With extensive experiments on the Fourier phase retrieval problem and thorough
ablation studies, we can show the benefits of our modified ILO and the new
initialization schemes. Additionally, we analyze the performance of our
approach on the Gaussian phase retrieval problem.
