Year: 2022
Author: Jian-Feng Cai, Meng Huang, Dong Li, Yang Wang
Annals of Applied Mathematics, Vol. 38 (2022), Iss. 1 : pp. 62–114
Abstract
A fundamental problem in phase retrieval is to reconstruct an unknown signal from a set of magnitude-only measurements. In this work we introduce three novel quotient intensity models (QIMs) based on a deep modification of the traditional intensity-based models. A remarkable feature of the new loss functions is that the corresponding geometric landscape is benign under the optimal sampling complexity. When the measurements ai∈Rn are Gaussian random vectors and the number of measurements m≥Cn, the QIMs admit no spurious local minimizers with high probability, i.e., the target solution x is the unique local minimizer (up to a global phase) and the loss function has a negative directional curvature around each saddle point. Such benign geometric landscape allows the gradient descent methods to find the global solution x (up to a global phase) without spectral initialization.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aam.OA-2021-0010
Annals of Applied Mathematics, Vol. 38 (2022), Iss. 1 : pp. 62–114
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 53
Keywords: Phase retrieval landscape analysis non-convex optimization.
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