The Algebraic Approach to Phase Retrieval and Explicit Inversion at the Identifiability Threshold
The Algebraic Approach to Phase Retrieval and Explicit Inversion at the Identifiability Threshold
复制标题
可识别性阈值处的相位检索和显式反演的代数方法
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
M. Ehler
中科院分区：
文献类型：
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作者：
F. Király;M. Ehler
我们研究相位恢复从一个未知信号的幅度测量作为一个代数估计问题。实际上，从秩一和更一般的线性测量的相位恢复可以以代数方式处理。验证了一定数量的通用秩一或通用线性测量足以实现通用信号的信号重构，并且稍微更通用的测量产生所有信号的可重构性。我们的研究结果解决了一些开放的问题，在最近的文献中。此外，我们展示了如何代数估计问题可以解决的封闭形式的代数估计技术，称为理想回归，提供非渐近的成功保证。
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.