Practical phase retrieval using double deep image priors

Phase retrieval (PR) consists of recovering complex-valued objects from their oversampled Fourier magnitudes and takes a central place in scientific imaging. A critical issue around PR is the typical nonconvexity in natural formulations and the associated bad local minimizers. The issue is exacerbated when the support of the object is not precisely known and hence must be overspecified in practice. Practical methods for PR hence involve convolved algorithms, e.g., multiple cycles of hybrid input-output (HIO) + error reduction (ER), to avoid the bad local minimizers and attain reasonable speed, and heuristics to refine the support of the object, e.g., the famous shrinkwrap trick. Overall, the convolved algorithms and the support-refinement heuristics induce multiple algorithm hyperparameters, to which the recovery quality is often sensitive. In this work, we propose a novel PR method by parameterizing the object as the output of a learnable neural network, i.e., deep image prior (DIP). For complex-valued objects in PR, we can flexibly parametrize the magnitude and phase, or the real and imaginary parts separately by two DIPs. We show that this simple idea, free from multi-hyperparameter tuning and support-refinement heuristics, can obtain superior performance than gold-standard PR methods. For the session: Computational Imaging using Fourier Ptychography and Phase Retrieval.