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Proceedings Paper

The Importance Of Being Positive
Author(s): B. Roy Frieden
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Paper Abstract

The most important advance in restoring images during the past decade probably was the realization that positive-enforced solutions are a real advance over unconstrained solutions. Surprisingly, the positive constraint both reduces spurious oscillation and enhances resolution simultaneously. This will be shown by a simple graphical argument. The earliest workers in this exotic field realized that by enforcing positivity they were inducing higher-frequency oscillation into their outputs than even is present in the image data. And more importantly, these were real and not artifacts. That is, super-resolution was being produced in real images for the first time. Some examples of these will be shown. The earliest methods for enforcing positivity were ad hoc, e.g., by arbitrarily representing the restoration as the square of a function. Later positivity was given a firm theoretical basis through the route of "maximum entropy," a concept which originated in the estimation of probability densities. A review of such methods will be given. Of late, positivity has also aided in producing real solutions to the "missing phase problem" of Labeyrie interferometry.

Paper Details

Date Published: 7 December 1981
PDF: 9 pages
Proc. SPIE 0292, Processing of Images and Data from Optical Sensors, (7 December 1981); doi: 10.1117/12.932827
Show Author Affiliations
B. Roy Frieden, University of Arizona (United States)

Published in SPIE Proceedings Vol. 0292:
Processing of Images and Data from Optical Sensors
William H. Carter, Editor(s)

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