DeepInit Phase Retrieval

TL;DR

This paper introduces DeepInit Phase Retrieval, a hybrid approach combining deep generative models and classical algorithms to improve signal reconstruction from limited measurements, especially in challenging non-convex scenarios.

Contribution

It proposes a novel hybrid method that uses learned initializations from deep generative models to enhance classical phase retrieval algorithms.

Findings

Achieves high-quality reconstructions at low sampling rates.

Performs well even with significant generator model errors.

Offers faster runtime compared to traditional gradient-based methods.

Abstract

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.