An algebraic characterization of injectivity in phase retrieval

Aldo Conca, Dan Edidin, Milena Hering, Cynthia Vinzant

Research output: Contribution to journalArticlepeer-review

Abstract

A complex frame is a collection of vectors that span CM and define measurements, called intensity measurements, on vectors in CM. In purely mathematical terms, the problem of phase retrieval is to recover a complex vector from its intensity measurements, namely the modulus of its inner product with these frame vectors. We show that any vector is uniquely determined (up to a global phase factor) from
4M−4 generic measurements. To prove this, we identify the set of frames defining non-injective measurements with the projection of a real variety and bound its dimension.
Original languageEnglish
Pages (from-to)346-356
Number of pages11
JournalApplied and Computational Harmonic Analysis
Volume38
Early online date30 Jun 2014
DOIs
Publication statusPublished - Mar 2015

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