SIAM Review, Volume 62, Issue 2, Page 301-350, January 2020.
The problem of phase retrieval, i.e., the problem of recovering a function from the magnitudes of its Fourier transform, naturally arises in various fields of physics, such as astronomy, radar, speech recognition, quantum mechanics, and, perhaps most prominently, diffraction imaging. The mathematical study of phase retrieval problems possesses a long history with a number of beautiful and deep results drawing from different mathematical fields, such as harmonic analysis, complex analysis, and Riemannian geometry. The present paper aims to present a summary of some of these results with an emphasis on recent activities. In particular we aim to summarize our current understanding of uniqueness and stability properties of phase retrieval problems.

中文翻译：

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相位检索：唯一性和稳定性

SIAM评论，第62卷，第2期，第301-350页，2020年1月
。相变的问题，即从傅立叶变换的幅值恢复函数的问题自然会出现在物理学的各个领域，例如天文学，雷达，语音识别，量子力学以及（也许最突出的）衍射成像。相检索问题的数学研究源远流长，其谐波分析，复数分析和黎曼几何等不同数学领域的大量优美而深刻的结果。本文旨在对其中一些结果进行总结，重点是最近的活动。特别是，我们旨在总结我们目前对相恢复问题的唯一性和稳定性的理解。