Abstract

We consider the problem of restoring an image from the phase-sign function (the so-called one-bit of phase) and the Fourier magnitude using the method of generalized projections. A formal obstacle to implementing projection methods to obtain a solution is that the set of functions with a prescribed phase-sign function, while convex, is not closed. To close the set we add an appropriate set of limit functions and then show that the algorithm does not converge to one of the added limit functions (a good feature of the algorithm). While other algorithms exist for retrieval from signed magnitude, the advantage of generalized projections is that a certain type of error reduction property is assured—provided that the algorithm does not stagnate in a trap (a local minimum) or a tunnel (a region where sets are nearly parallel). To the best of our knowledge this claim is not made by competing algorithms.

© 1986 Optical Society of America