Abstract
The ill-posed problem of restoring object information from finitely many measurements of its spectrum can be solved by using the best approximation in Hilbert spaces appropriately designed to include a priori information about object extent and shape and noise statistics. The procedures that are derived are noniterative, the linear ones extending the minimum-energy band-limited extrapolation methods (and thus related to Gerchberg–Papoulis iteration) and the nonlinear ones generalizing Burg’s maximum-entropy reconstruction of nonnegative objects.
© 1983 Optical Society of America
Full Article | PDF ArticleMore Like This
Hsin M. Shieh, Charles L. Byrne, and Michael A. Fiddy
J. Opt. Soc. Am. A 23(2) 258-266 (2006)
Jorge L. C. Sanz and Thomas S. Huang
J. Opt. Soc. Am. 73(11) 1455-1465 (1983)
J. B. Abbiss, M. Defrise, C. De Mol, and H. S. Dhadwal
J. Opt. Soc. Am. 73(11) 1470-1475 (1983)