Phase Retrieval: From Computational Imaging to Machine Learning
J. Dong, L. Valzania, A. Maillard, T.-a. Pham, S. Gigan, M. Unser
IEEE Signal Processing Magazine, vol. 40, no. 1, pp. 45-57, January 2023.
Phase 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.
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AUTHOR="Dong, J. and Valzania, L. and Maillard, A. and Pham, T.-a. and
Gigan, S. and Unser, M.",
TITLE="Phase Retrieval: {F}rom Computational Imaging to Machine
Learning",
JOURNAL="{IEEE} Signal Processing Magazine",
YEAR="2023",
volume="40",
number="1",
pages="45--57",
month="January",
note="")