An algebraic characterization of injectivity in phase retrieval

Abstract A complex frame is a collection of vectors that span C M and define measurements, called intensity measurements, on vectors in C M . 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 4 M − 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.

• Publication year

  2013

• Venue

  arXiv.org

• Publication date

  2013-11-30

• Fields of study

  Mathematics, Computer Science

• Identifiers
  DOI 10.1016/j.acha.2014.06.005arXiv 1312.0158
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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