The reconstruction of a multidimensional sequence from the phase or magnitude of its Fourier transform
The reconstruction of a multidimensional sequence from the phase or magnitude of its Fourier transform
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DOI：
10.1109/tassp.1982.1163863
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发表时间：
1982-04
期刊：
影响因子：
--
通讯作者：
M. Hayes
中科院分区：
文献类型：
--
作者：
M. Hayes
本文讨论了两个基本问题，涉及重建的多维序列的相位或幅度的傅立叶变换。第一个问题涉及多维序列在其相位或幅度方面的唯一性。虽然单独的相位或幅度信息是不够的，在一般情况下，唯一地指定一个序列，一个大类的序列被证明是可恢复的，从他们的相位或幅度。第二个问题，这是在本文中涉及的实际重建的多维序列从其相位或幅度。对于那些由其相位唯一指定的序列，描述了几种实用的算法，这些算法可用于从其相位重建序列。还提出了几个例子的相位只有重建。然而，不幸的是，即使对于那些由其幅度唯一定义的序列，似乎还没有开发出一种实用的算法来仅从其幅度重建序列。尽管如此，一个迭代的程序，已被提出简要讨论和评价。
This paper addresses two fundamental issues involved in the reconstruction of a multidimensional sequence from either the phase or magnitude of its Fourier transform. The first issue relates to the uniqueness of a multidimensional sequence in terms of its phase or magnitude. Although phase or magnitude information alone is not sufficient, in general, to uniquely specify a sequence, a large class of sequences are shown to be recoverable from their phase or magnitude. The second issue which is addressed in this paper concerns the actual reconstruction of a multidimensional sequence from its phase or magnitude. For those sequences which are uniquely specified by their phase, several practical algorithms are described which may be used to reconstruct a sequence from its phase. Several examples of phase-only reconstruction are also presented. Unfortunately, however, even for those sequences which are uniquely defined by their magnitude, it appears that a practical algorithm is yet to be developed for reconstructing a sequence from only its magnitude. Nevertheless, an iterative procedure which has been proposed is briefly discussed and evaluated.