论文标题
阶段检索的数字
The Numerics of Phase Retrieval
论文作者
论文摘要
相位检索，即，从其傅立叶变换的平方幅度中恢复函数的问题是在许多应用中出现的，例如X射线晶体学，衍射成像，光学，光学，量子力学和天文学。这个问题使工程师，物理学家和数学家混淆了数十年。最近，阶段检索已经在研究活动中复兴，并被新的成像方式和新型数学概念所点燃。随着我们的科学实验产生越来越大的数据集，我们的目标是越来越快地吞吐量，以系统和原则的方式研究所涉及的数值算法变得越来越重要。的确，过去十年中，对相位检索的计算算法进行系统的研究激增。在本文中，我们将从数值观点回顾这些最新进展。
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 becomes increasingly important to study the involved numerical algorithms in a systematic and principled manner. Indeed, the last 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.
