J Austral Math Soc Ser B 37 pp26--44, 1995.

On Gerchberg's method for the Fourier inverse problem

T. J. Connolly, K. A. Landman and L. R. White

Abstract

If a finite segment of a spectrum is known, the determination of the finite object function in image space (or the full spectrum in frequency space) is a fundamental problem in image analysis. Gerchberg's method, which solves this problem, can be formulated as a fixed point iteration. This and other related algorithms are shown to be equivalent to a steepest descent method applied to the minimization of an appropriate functional for the Fourier Inversion Problem. Optimal steepest descent and conjugate gradient methods are derived. Numerical results from the application of these techniques are presented. The regularization of the problem and control of noise growth in the iteration are also discussed.

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Authors

T. J. Connolly

K. A. Landman

L. R. White

Department of Mathematics, University of Melbourne, Parkville Victoria 3052, Australia.