phase retrieval
Phase retrieval
Phase retrieval is the process of algorithmically finding solutions to the phase problem. Given a complex signal
$${\displaystyle F(k)}$$
, of amplitude
$${\displaystyle |F(k)|}$$
, and phase
$${\displaystyle \psi (k)}$$
$${\displaystyle F(k)=|F(k)|e^{i\psi (k)}=\int _{-\infty }^{\infty }f(x)\ e^{-2\pi ik\cdot x}\,dx}$$
where x is an M-dimensional spatial coordinate and k is an M-dimensional spatial frequency coordinate. Phase retrieval consists of finding the phase that satisfies a set of constraints for a measured amplitude. Important applications of phase retrieval include X-ray crystallography, transmission electron microscopy and coherent diffractive imaging, for which
$${\displaystyle M=2}$$
. Uniqueness theorems for both 1-D and 2-D cases of the phase retrieval problem, including the phaseless 1-D inverse scattering problem, were proven by Klibanov and his collaborators (see References).
Wikipedia contributors. "Phase retrieval." Wikipedia, The Free Encyclopedia. Wikipedia, The Free Encyclopedia, Feb. 19, 2024.
