7 December 1981 The Importance Of Being Positive
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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.
© (1981) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
B. Roy Frieden, B. Roy Frieden, "The Importance Of Being Positive", Proc. SPIE 0292, Processing of Images and Data from Optical Sensors, (7 December 1981); doi: 10.1117/12.932827; https://doi.org/10.1117/12.932827

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