Gabor Phase Retrieval in the Generalized Paley–wiener Space
Gabor Phase Retrieval in the Generalized Paley–wiener Space
复制标题
DOI：
10.1007/s00034-023-02485-1
复制
发表时间：
2023-08
期刊：
影响因子：
--
通讯作者：
Qingyue Zhang;Liping Wu;Zhen Guo;Bei Liu
中科院分区：
文献类型：
--
作者：
Qingyue Zhang;Liping Wu;Zhen Guo;Bei Liu
Gabor相位恢复是指从Gabor变换的绝对值中恢复信号的问题，目前已成为一个非常活跃的研究领域。本文利用特殊仿射傅里叶变换定义了广义Paley-Wiener空间，并给出了广义Paley-Wiener空间中Gabor相位反演的唯一性。当窗口函数是的逆仿射傅里叶变换时，我们证明了广义Paley-Wiener空间中的每个信号都可以从其在矩形晶格上采样的Gabor测量值的幅度唯一地恢复到一个全局符号。近年来，Grohs， Liehr和Wellershoff研究了传统Paley-Wiener空间中的Gabor相位恢复问题。本文将其结果推广到广义Paley-Wiener空间。由于广义Paley-Wiener空间包含更广泛的信号类别，我们的结果扩展了Gabor相位检索的应用范围。
Gabor phase retrieval is the problem of recovering a signal from the absolute values of Gabor transform, which has turned into a very active research area. In the paper, we define a generalized Paley–Wiener space, which is obtained by applying the special affine Fourier transform toand provide the uniqueness of the Gabor phase retrieval in the generalized Paley–Wiener space. When the window functionis the inverse special affine Fourier transform of, we show that every signal in the generalized Paley–Wiener space can be uniquely recovered, up to a global sign, from its the magnitudes of Gabor measurement sampled on a rectangular lattice. Recently, Grohs, Liehr and Wellershoff studied the Gabor phase retrieval problems in the conventional Paley–Wiener space. The paper extends their results to the generalized Paley–Wiener space. Since the generalized Paley–Wiener space includes a broader class of signals, our results expand the applied range of the Gabor phase retrieval.