TY  - JOUR
N2  - We study phase retrieval from magnitude measurements of an unknown signal as an algebraic estimation problem. Indeed, phase retrieval from rank-one and more general linear measurements can be treated in an algebraic way. It is verified that a certain number of generic rank-one or generic linear measurements are sufficient to enable signal reconstruction for generic signals, and slightly more generic measurements yield reconstructability for all signals. Our results solve a few open problems stated in the recent literature. Furthermore, we show how the algebraic estimation problem can be solved by a closed-form algebraic estimation technique, termed ideal regression, providing non-asymptotic success guarantees.
ID  - discovery1517413
UR  - https://arxiv.org/abs/1402.4053
JF  - arXiv.org
A1  - Király, FJ
A1  - Ehler, M
KW  - Functional Analysis; Computer Vision and Pattern Recognition; Information Theory; Algebraic Geometry; Machine Learning
TI  - The Algebraic Approach to Phase Retrieval and Explicit Inversion at the Identifiability Threshold
AV  - public
Y1  - 2014/02/14/
N1  - This version is the author accepted manuscript. For information on re-use, please refer to the publisher?s terms and conditions.
ER  -