Phase retrieval

Phase retrieval concerns the solution to the phase problem. Given a complex signal $F(k)$, of amplitude $|F(k)|$, and phase $phi(k)$:::$F(k)=|F(k)|e^\{i\; phi(k)\}$,

phase retrieval consists in finding the phase that for a measured amplitude satisfies a set of constraints. For example if $F(k)$ is the Fourier transform of $f(x)$, a typical constraint would be that $f(x)$ is a bounded real and positive function.

The most important application of phase retrieval is X-ray crystallography, awarded of several Nobel prizes.

ee also

* Phase problem
* Crystallography
* X-ray crystallography