Advanced

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
and
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
2020-12-29 03:59:21
@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},
  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},
}