Fundamental Limits of Weak Recovery with Applications to Phase Retrieval

In phase retrieval, we want to recover an unknown signal x ∈ C d from n quadratic measurements of the form y i = | ⟨ a i , x ⟩ | 2 + w i , where a i ∈ C d are known sensing vectors and w i is measurement noise. We ask the following weak recovery question: What is the minimum number of measurements n...

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Bibliographic Details
Published in:	Foundations of computational mathematics Vol. 19; no. 3; pp. 703 - 773
Main Authors:	Mondelli, Marco, Montanari, Andrea
Format:	Journal Article
Language:	English
Published:	New York Springer US 01.06.2019 Springer Nature B.V
Subjects:	Algorithms Applications of Mathematics Computational geometry Computer Science Computer simulation Convexity Correlation Covariance matrix Economics Eigenvectors Empirical analysis Generalized linear models Information theory Linear and Multilinear Algebras Lower bounds Math Applications in Computer Science Mathematics Mathematics and Statistics Matrix Theory Message passing Noise measurement Numerical Analysis Optimization Phase retrieval Phase transitions Recovery Spectra Spectral methods Statistical models Upper bounds Spectral initialization Second-moment method 91E40 68T05 Phase retrieval 68Q32 Mutual information Phase transition
ISSN:	1615-3375, 1615-3383
Online Access:	Get full text
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