A wavenumber-domain Kalman filtering approach to one-dimensional phase retrieval

摘要

The phase retrieval problem, i.e. computing a function known to have finite spatial support from knowledge of its Fourier magnitude, is considered. By writing the support constraint as a state equation in the Fourier domain (dual to the system used in state-space harmonic retrieval), an extended Kalman filter is used to compute the Fourier magnitudes as observations. The filter is initialized by solving a linear system of equations, followed by a nonlinear set of trigonometric equations.