Abstract

Obtaining resolution beyond the diffraction limit is desired in many image processing applications. The Gerchberg algorithm,¹ being an iterative technique, has the advantage over noniterative techniques of being less noise sensitive as well as being more robust since physical constraints may be imposed throughout the iteration process and which can be updated as more information about the object is recovered. Such constraints include positivity and space-limitedness properties of real objects. The well-known shortcoming of the algorithm—its slow convergence—is shown to be a direct result of overestimation of the boundary of the object. A technique is developed to detect the occurrence of stagnation in the algorithm where-upon a reduction of the boundary is carried out. A safeguard against overreduction is employed. Use of further a priori information, namely, the definite integral property of Fourier transform pairs is also investigated.

© 1988 Optical Society of America