Phase Retrieval: From Computational Imaging to Machine Learning: A tutorial

Abstract

hase retrieval consists in the recovery of a complex-valued signal from intensity-only measurements. As it pervades a broad variety of applications, many researchers have striven to develop phase-retrieval algorithms. Classical approaches involve techniques as varied as generic gradient descent routines or specialized spectral methods, to name a few. However, the phase-recovery problem remains a challenge to this day. Recently, however, advances in machine learning have revitalized the study of phase retrieval in two ways: 1) significant theoretical advances have emerged from the analogy between phase retrieval and single-layer neural networks, and 2) practical breakthroughs have been obtained thanks to deep learning regularization. In this tutorial, we review phase retrieval under a unifying framework that encompasses classical and machine learning methods. We focus on three key elements: applications, an overview of recent reconstruction algorithms, and the latest theoretical results.

Experimentally realized physical-model-based frugal wave control in metasurface-programmable complex media

“…The achieved around exceeds what the benchmark models achieve with complex-valued calibration data. Retrieving phase information from phaseless data is an established discipline within signal processing with applications across the EM spectrum because it removes the costly need for coherent detection 42 – 44 . However, conventional phase-retrieval deals with static rather than programmable systems and uses elaborate algorithms to retrieve either the system’s transfer function or the input wavefront.…”

Single particle imaging of biological specimens

“…Generally based on both forward and inverse Fourier transforms and iterated in both directions, these algorithms could converge to a reliable solution to the phase problem. To bypassing the questions of robustness and efficiency well known in iterative algorithms, deep-learning phase retrieval algorithms [25][26][27][28][29][30][31][32][33][34] are demonstrating the potential for real-time and automated phase retrieval.…”

“…With the tremendous data follows a challenge for efficiently handling with the big data 24 . Fortunately, recent researches are demonstrating that machine learning and deep learning may provide powerful tools for better data processing and reconstructions, such as automated image selection, classification and phase retrieval [25][26][27][28][29][30][31][32][33][34] .…”

On the use of deep learning for phase recovery

“…Zhou et al 65 and Wang et al 66 reviewed and compared different usage strategies of AI in phase unwrapping. Dong et al 67 introduced a unifying framework for various algorithms and applications from the perspective of phase retrieval and presented its advances in machine learning. Park et al 68 discussed AI-QPI-based analysis methodologies in the context of life sciences.…”