动态Gabor矩阵测量的相位恢复

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动态Gabor矩阵测量的相位恢复李蕊, 刘蓓, 张庆月天津理工大学理学院天津 300384 Phase Retrieval from Matrix Measurements of Dynamical Gabor Systems Rui LI, Bei LIU, Qing Yue ZHANGCollege of Science, Tianjin University of Technology, Tianjin 300384, P. R. China

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摘要相位恢复是一类由无相位采样值恢复待估信号的问题.本文讨论的采样是由动态Gabor系统得到的.我们证明了关于动态Gabor测量矩阵可相位恢复的充分条件，并给出了C²和R³中的例子.

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收稿日期: 2020-02-10

MR (2010):

O174.2

基金资助:国家自然科学基金资助项目（11601383，11671214，11971348，12071230）；天津市自然科学基金资助项目（18JCYBJC16200）和天津市教委科研计划项目（2018KJ148）

通讯作者:刘蓓,E-mail:liubei1@mail.nankai.edu.cnE-mail: liubei1@mail.nankai.edu.cn

作者简介: 李蕊,E-mail:lrsx@163.com;张庆月,E-mail:jczhangqingyue@163.com

引用本文:

李蕊, 刘蓓, 张庆月. 动态Gabor矩阵测量的相位恢复[J]. 数学学报, 2021, 64(5): 801-810. Rui LI, Bei LIU, Qing Yue ZHANG. Phase Retrieval from Matrix Measurements of Dynamical Gabor Systems. Acta Mathematica Sinica, Chinese Series, 2021, 64(5): 801-810.

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[1] Aceska R., Aldroubi A., Davis J., et al., Dynamical sampling in shift-invariant spaces, In:Mayeli A., Iosevich A., Jorgensen P. E. T., Ólafsson G. (eds.) Commutative and Noncommutative Harmonic Analysis and Applications, Vol. 603 of Contemporary Mathematics, American Mathematical Society, Providence, 2013, 139-148.
[2] Aldroubi A., Cabrelli C., Molter U., et al., Dynamical sampling, Appl. Comput. Harmon. Anal., 2017, 42:378-401.
[3] Aldroubi A., Davis J., Krishtal I., Dynamical sampling:Time space trade-off, Appl. Comput. Harmon. Anal., 2013, 34:495-503.
[4] Aldroubi A., Davis J., Krishtal I., Exact reconstruction of signals in evolutionary systems via spatiotemporal trade-off, J. Fourier Anal. Appl., 2015, 21:11-31.
[5] Aldroubi A., Krishtal I., Tang S., Phaseless reconstruction from space-time samples, Appl. Comput. Harmon. Anal., 2020, 48:395-414.
[6] Balan R., Bodmann B. G., Casazza P. G., et al., Painless reconstruction from magnitudes of frame coefficients, J. Fourier Anal. Appl., 2009, 15:488-501.
[7] Balan R., Casazza P., Edidin D., On signal reconstruction without phase, Appl. Comput. Harmon. Anal., 2006, 20:345-356.
[8] Bandeira A. S., Cahill J., Mixon D. G., et al., Saving phase:injectivity and stability for phase retrieval, Appl. Comput. Harmon. Anal., 2014, 37(1):106-125.
[9] Bauschke H. H., Combettes P. L., Luke D. R., Phase retrieval, error reduction algorithm, and Fienup variants:a view from convex optimization, J. Opt. Soc. Am. A, 2002, 19:1334-1345.
[10] Bojarovska I., Flinth A., Phase retrieval from Gabor measurements, J. Four. Anal. Appl., 2016, 22:542-567.
[11] Candès E. J., Strohmer T., Voroninski V., PhaseLift:Exact and stable signal recovery from magnitude measurements via convex programming, Comm. Pure and Appl. Math., 2013, 66:1241-1274.
[12] Feichtinger H. G., Gröchenig K., Gabor frames and time-frequency analysis of distributions, J. Funct. Anal., 1997, 146(2):464-495.
[13] Gerchberg R., Saxton W., A practical algorithm for the determination of the phase from image and diffraction plane pictures, Optik, 1972, 35:237-246.
[14] Griffin D., Lim J. S., Signal estimation from modified short-time Fourier trans-form, IEEE Trans. Acoust. Speech Signal Proces., 1984, 32:236-243.
[15] Gröchenig K., Foundations of Time-Frequency Analysis, Birkhäuser Boston Inc., Boston, 2001.
[16] Jaganathan K., Eldar Y. C., Hassibi B., STFT phase retrieval:uniqueness guarantees and recovery algorithms, IEEE J. Sel. Topics Signal Process., 2016, 10:770-781.
[17] Millane R., Phase retrieval in crystallography and optics, J. Opt. Soc. Amer. A, 1990, 7(3):394-411.
[18] Nawab S. H., Quatieri T. F., Lim J. S., Signal reconstruction from short-time Fourier transform magnitude, IEEE Trans. Acoust. Speech Signal Process., 1983, 31:986-998.
[19] Pfander G. E., Gabor Frames in Finite Dimensions, Finite Frames, Springer, Berlin, 2013, 193-239.
[20] Zhang Q. Y., Liu B., Li R., Dynamical sampling in multiply generated shift-invariant spaces, Appl. Anal., 2017, 96(5):760-770.
[21] Zheng G. A., Horstmeyer R., Yang C. H., Wide-field, High-resolution Fourier ptychographic microscopy, Nature Photonics, 2013, 7(9):739-745.

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