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 by using the method of generalized projections. The method of generalized projections is an extension of the method of convex projections and can be used when constraint sets are nonconvex, as is the case here. While a structurally similar algorithm exists for retrieval from a signed magnitude, the advantage of generalized projections is that a certain type of error-reduction property is ensured. To the best of our knowledge this claim is not made for the other algorithm. Computer simulations of restorations in one and two dimensions are furnished. The recovered images are of good quality and do not exhibit the severe stagnation that is sometimes seen in magnitude-only restorations. In addition to nonconvex sets, signed-magnitude recovery involves nonclosed sets as well. We discuss this theoretical problem in some detail.

© 1987 Optical Society of America

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