Dong, JonathanValzania, LorenzoMaillard, AntoinePham, Thanh-anGigan, SylvainUnser, Michaël2023-02-142023-02-142023-02-142023-01-0110.1109/MSP.2022.3219240https://infoscience.epfl.ch/handle/20.500.14299/194871Phase 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.text::journal::journal article::research article