Phase retrieval,i.e.the problem of recovering a function from the squared magnitude of its Fourier transform, arises in many applications, such as X-ray crystallography, diffraction imaging, optics, quantum mechanics and astronomy. This problem has confounded engineers, physicists, and mathematicians for many decades. Recently, phase retrieval has seen a resurgence in research activity, ignited by new imaging modalities and novel mathematical concepts. As our scientific experiments produce larger and larger datasets and we aim for faster and faster throughput, it is becoming increasingly important to study the involved numerical algorithms in a systematic and principled manner. Indeed, the past decade has witnessed a surge in the systematic study of computational algorithms for phase retrieval. In this paper we will review these recent advances from a numerical viewpoint.

中文翻译：

---

相位检索的数值

相位检索，IE从傅里叶变换的平方幅度恢复函数的问题出现在许多应用中，例如 X 射线晶体学、衍射成像、光学、量子力学和天文学。几十年来，这个问题一直困扰着工程师、物理学家和数学家。最近，在新的成像方式和新的数学概念的推动下，相位检索的研究活动重新抬头。随着我们的科学实验产生越来越大的数据集，并且我们的目标是越来越快的吞吐量，以系统和有原则的方式研究所涉及的数值算法变得越来越重要。事实上，过去十年见证了相位检索计算算法的系统研究激增。