On phase retrieval via matrix completion and the estimation of low rank PSD matrices
(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.
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https://lup.lub.lu.se/record/5ecaa8e0-8497-41a3-a628-9f8426ce361f
- author
- Carlsson, Marcus LU and Gerosa, Daniele LU
- organization
- publishing date
- 2020
- 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}}, }