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Uniqueness and sampling conditions for image reconstruction from the Hartley-transform intensity

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Abstract

Using a constructive proof, I show that a real two-dimensional image is uniquely determined by the intensity of its Hartley transform if the latter is sampled on a particular set of points whose density is approximately half the Nyquist density for the intensity. This result indicates that image reconstruction from the Hartley-transform intensity is in general overdetermined and has implications in situations where the intensity is sub-Nyquist sampled.

© 1994 Optical Society of America

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