Király, FJ;
Ehler, M;
(2014)
The Algebraic Approach to Phase Retrieval and Explicit Inversion at the Identifiability Threshold.
arXiv.org
, Article arXiv:1402.4053 [math.FA].
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Abstract
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.
| Type: | Article |
|---|---|
| Title: | The Algebraic Approach to Phase Retrieval and Explicit Inversion at the Identifiability Threshold |
| Open access status: | An open access version is available from UCL Discovery |
| Publisher version: | https://arxiv.org/abs/1402.4053 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Functional Analysis; Computer Vision and Pattern Recognition; Information Theory; Algebraic Geometry; Machine Learning |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1517413 |
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