线性正则变换相位恢复的稳定性研究

王 文馨, 王 渺, 曾 国庆
天津理工大学理学院

摘要

相位恢复的稳定性主要研究的是当无相位采样发生微小扰动时,原信号是否也只发生微小扰
动的问题。本文主要研究了线性正则变换的相位恢复稳定性问题。通过讨论线性正则变换和Fourier变
换之间的关系,在已有的Fourier变换相位恢复稳定性的结果基础上,给出了线性正则变换相位恢复稳
定性的结论,即当函数和满足一定的条件时,f-g的二范数是可被控制的,即线性正则变换能被其相
位绝对值所控制。

关键词

线性正则变换;相位恢复;Fourier变换;稳定性

参考

[1] R. Balan, P.G. Casazza and D. Edidin, On signal

reconstruction without noisy phase, Appl. and Compt. Harmon.

Anal., 20(3),2006,345-356.

[2] S. Steinerbergeron， The stability of fourier phase

retrieval, https://arxiv.org/pdf/2004.06671.pdf.

[3]P. Grohs, S. Koppensteiner, M. Rathmair. Phase

Retrieval: Uniqueness and Stability, https://arxiv.org/

pdf/1901.07911.pdf.

[4] E. J. Akutowicz. On the determination of the phase of

a Fourier integral, I. Trans. Am. Math. Soc.,179–192, 1956.

[5] E. J. Akutowicz. On the determination of the phase of a

Fourier integral. II. Proc. Amer. Math. Soc. 8,234–238, 1957.

[6] E. Hofstetter. Construction of time-limited functions

with specified autocorrelation functions. IEEE Trans. Inf.

Theory, 10,1964,119–126.

[7] A. Walther. The question of phase retrieval in optics. J

Mod Opt, 10(1),1963,41–49.

[8] P. Grohs, S.Koppensteiner and M. Rathmair. Phase

Retrieval: Uniqueness and Stability[J]. SIAM Review, 62(2),

2020,301-350.