Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6416922 | Applied and Computational Harmonic Analysis | 2015 | 11 Pages |
â¢We describe polynomial equations that characterize injective intensity measurements.â¢We prove that 4Mâ4 generic intensity measurements suffice for phase retrieval in CM.â¢When M=2k+1, 4Mâ4 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 4Mâ4 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.