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

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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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Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Mathematics

Keywords

  • Fourier phase retrieval, low rank matrices, non-convex optimization
Original languageEnglish
Article number015006
JournalInverse Problems
Volume36
Issue number1
Publication statusPublished - 2020
Publication categoryResearch
Peer-reviewedYes