2013/11/30 by Aldo Conca, Dan Edidin, Milena Hering +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · Materials Science · Mathematics · Physics and Astronomy · #Advanced Electron Microscopy Techniques and Applications #Advanced X-ray Imaging Techniques #Algebra over a field #Algebraic number #Characterization (materials science) #Electron and X-Ray Spectroscopy Techniques #Fourier transform #Mathematical analysis #Mathematics #Phase (matter) #Phase retrieval #Pure mathematics #cs.IT #math.AG #math.FA #math.IT
paper · pdf · doi:10.1016/j.acha.2014.06.005
published as Applied and Computational Harmonic Analysis 38:2 (2015) pp. 346-356 · 11 pages
arxiv created 2013/11/30 · openalex publication_date 2014/07/01 · arxiv updated 2015/02/17 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/06
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.