Article ID Journal Published Year Pages File Type
6416922 Applied and Computational Harmonic Analysis 2015 11 Pages PDF
Abstract

•We describe polynomial equations that characterize injective intensity measurements.•We prove that 4M−4 generic intensity measurements suffice for phase retrieval in CM.•When M=2k+1, 4M−4 measurements are necessary for phase retrieval.

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.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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