Stability of unique Fourier-transform phase reconstruction
暂无分享,去创建一个
The problem of Fourier-transform phase reconstruction from the Fourier-transform magnitude of multidimensional discrete signals is considered. It is well known that, if a discrete finite-extent n-dimensional signal (n ≥ 2) has an irreducible z transform, then the signal is uniquely determined from the magnitude of its Fourier transform. It is also known that this irreducibility condition holds for all multidimensional signals except for a set of signals that has measure zero. We show that this uniqueness condition is stable in the sense that it is not sensitive to noise. Specifically, it is proved that the set of signals whose z transform is reducible is contained in the zero set of a certain multidimensional polynomial. Several important conclusions can be drawn from this characterization, and, in particular, the zero-measure property is obtained as a simple byproduct.
[1] M. Hayes. The reconstruction of a multidimensional sequence from the phase or magnitude of its Fourier transform , 1982 .
[2] M. Hayes,et al. Reducible polynomials in more than one variable , 1982, Proceedings of the IEEE.
[3] A. Walther. The Question of Phase Retrieval in Optics , 1963 .
[4] J. Fienup. Fine Resolution Imaging of Space Objects. , 1981 .