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On phase retrieval via matrix completion and the estimation of low rank PSD matrices

Carlsson, Marcus LU and Gerosa, Daniele LU (2020) In Inverse Problems 36(1).
Abstract

Given underdetermined measurements of a positive semi-definite (PSD) matrix X of known low rank K, we present a new algorithm to estimate X based on recent advances in non-convex optimization schemes. We apply this in particular to the phase retrieval problem for Fourier data, which can be formulated as a rank 1 PSD matrix recovery problem. Moreover, we provide a theory for how oversampling affects the stability of the lifted inverse problem.

Please use this url to cite or link to this publication:
author
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organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Fourier phase retrieval, low rank matrices, non-convex optimization
in
Inverse Problems
volume
36
issue
1
article number
015006
publisher
IOP Publishing
external identifiers
  • scopus:85079780789
ISSN
0266-5611
DOI
10.1088/1361-6420/ab4e6d
language
English
LU publication?
yes
id
5ecaa8e0-8497-41a3-a628-9f8426ce361f
date added to LUP
2020-03-18 13:57:50
date last changed
2022-04-18 21:13:44
@article{5ecaa8e0-8497-41a3-a628-9f8426ce361f,
  abstract     = {{<p>Given underdetermined measurements of a positive semi-definite (PSD) matrix X of known low rank K, we present a new algorithm to estimate X based on recent advances in non-convex optimization schemes. We apply this in particular to the phase retrieval problem for Fourier data, which can be formulated as a rank 1 PSD matrix recovery problem. Moreover, we provide a theory for how oversampling affects the stability of the lifted inverse problem.</p>}},
  author       = {{Carlsson, Marcus and Gerosa, Daniele}},
  issn         = {{0266-5611}},
  keywords     = {{Fourier phase retrieval; low rank matrices; non-convex optimization}},
  language     = {{eng}},
  number       = {{1}},
  publisher    = {{IOP Publishing}},
  series       = {{Inverse Problems}},
  title        = {{On phase retrieval via matrix completion and the estimation of low rank PSD matrices}},
  url          = {{http://dx.doi.org/10.1088/1361-6420/ab4e6d}},
  doi          = {{10.1088/1361-6420/ab4e6d}},
  volume       = {{36}},
  year         = {{2020}},
}