Unrolling Deep Learning End-to-End Method for Phase Retrieval

In real-world applications such as optics, signal processing, and computational imaging, complex-valued waves, signals, or images are often encountered, yet only their intensity (magnitude) information is measurable or accessible. However, the phase carries crucial information about their structure and properties. Phase retrieval poses a challenging problem of recovering the phase information from the measured intensity (magnitude), making it a valuable tool for analyzing and reconstructing wavefields. In this chapter, we propose an unrolling-based deep learning framework for phase retrieval. Our approach utilizes both local and nonlocal adaptive regularization, leveraging convolutional neural networks (CNN) for local features and graph neural networks (GNN) for nonlocal features. This deep learning framework has built-in mathematical interpretability as it is inspired by an iterative algorithm. We also propose an unrolling-based enhancement method to improve results from classical phase retrieval algorithms. We evaluate our methodology using Fourier measurements of masked images. Numerical experiments comparing it with classical non-learning and learning-based approaches demonstrate better performance in cases of noisy measurements. Furthermore, our methodology can be readily adapted to accommodate other types of phaseless measurements.