Phase retrieval

Phase retrieval is the process of algorithmically finding solutions to the phase problem. Given a complex signal $F(k)$ , of amplitude $|F (k)|$ , and phase $\psi(k)$ :

where x is an M-dimensional spatial coordinate and k is an M-dimensional spatial frequency coordinate, phase retrieval consists in finding the phase that for a measured amplitude satisfies a set of constraints. Important applications of phase retrieval include X-ray crystallography, transmission electron microscopy and coherent diffractive imaging, for which $M = 2$ . (Fienup 1982:2759) Uniqueness theorems for both 1-D and 2-D cases of the phase retrieval problem, including the phaseless 1-D inverse scattering problem, were proved by Klibanov and his collaborators (see References).

单词	Phase retrieval
释义	Phase retrieval 英语百科 Phase retrieval Phase retrieval is the process of algorithmically finding solutions to the phase problem. Given a complex signal $F(k)$ , of amplitude $\|F (k)\|$ , and phase $\psi(k)$ : where x is an M-dimensional spatial coordinate and k is an M-dimensional spatial frequency coordinate, phase retrieval consists in finding the phase that for a measured amplitude satisfies a set of constraints. Important applications of phase retrieval include X-ray crystallography, transmission electron microscopy and coherent diffractive imaging, for which $M = 2$ . (Fienup 1982:2759) Uniqueness theorems for both 1-D and 2-D cases of the phase retrieval problem, including the phaseless 1-D inverse scattering problem, were proved by Klibanov and his collaborators (see References).
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