Abstract

It is known that the Gerchberg method for iteratively extrapolating the spectrum of an object of finite support has a different limit when the infinite frequency band used in the iterations is replaced by a finite one. It is shown that, for both continuous and discrete data, this limit involves an optimal extrapolation within the finite band to minimize the component of the limit that lies beyond the object support.

© 1983 Optical Society of America

Unified Hilbert space approach to iterative least-squares linear signal restoration

Jorge L. C. Sanz and Thomas S. Huang
J. Opt. Soc. Am. 73(11) 1455-1465 (1983)

Image restoration and resolution enhancement

Charles L. Byrne, Raymond M. Fitzgerald, Michael A. Fiddy, Trevor J. Hall, and Angela M. Darling
J. Opt. Soc. Am. 73(11) 1481-1487 (1983)

Stability of an algorithm to restore continuously sampled band-limited images from aliased data

Robert J. Marks and Dmitry Kaplan
J. Opt. Soc. Am. 73(11) 1518-1522 (1983)

Spectral extrapolation of constrained signals

R. J. Mammone
J. Opt. Soc. Am. 73(11) 1476-1480 (1983)

Coherent optical extrapolation of 2-D band-limited signals: processor theory

Robert J. Marks
Appl. Opt. 19(10) 1670-1672 (1980)