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首页> 外文期刊>IEEE Signal Processing Magazine >Recent Advances in Phase Retrieval [Lecture Notes]
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Recent Advances in Phase Retrieval [Lecture Notes]

机译：相位检索的最新进展[讲义]

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摘要

In many applications in science and engineering, one is given the modulus squared of the Fourier transform of an unknown signal and then tasked with solving the corresponding inverse problem, known as phase retrieval. Solutions to this problem have led to some noteworthy accomplishments, such as identifying the double helix structure of DNA from diffraction patterns, as well as characterizing aberrations in the Hubble Space Telescope from point spread functions. Recently, phase retrieval has found interesting connections with algebraic geometry, low-rank matrix recovery, and compressed sensing. These connections, together with various new imaging techniques developed in optics, have spurred a surge of research into the theory, algorithms, and applications of phase retrieval. In this lecture note, we outline these recent connections and highlight some of the main results in contemporary phase retrieval.
机译：在科学和工程学的许多应用中，给定未知信号的傅立叶变换的模平方，然后负责解决相应的逆问题，即相位检索。解决该问题的方法已取得了一些值得注意的成就，例如从衍射图谱识别DNA的双螺旋结构，以及从点扩散函数表征哈勃太空望远镜的像差。最近，相位检索发现了与代数几何，低秩矩阵恢复和压缩感测之间的有趣联系。这些联系，以及在光学领域开发的各种新的成像技术，激起了对相位检索的理论，算法和应用的研究热潮。在本讲义中，我们概述了这些最近的联系，并重点介绍了现代相位检索中的一些主要结果。

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