## Automatic multidimensional deconvolution

JOSA A, Vol. 4, Issue 1, pp. 180-188 (1987)

http://dx.doi.org/10.1364/JOSAA.4.000180

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### Abstract

A multiple convolution (e.g., an image formed by convolving several individual components) is automatically deconvolvable, provided that its dimension (i.e., the number of variables of which it is a function) is greater than unity. This follows because the Fourier transform of a *K*-dimensional function (having compact support) is zero on continuous surfaces (here called zero sheets) of dimension (2*K* − 2) in a space that effectively has 2*K* dimensions. A number of important practical applications are transfigured by the concept of the zero sheet. Image restoration can be effected without prior knowledge of the point-spread function, i.e., blind deconvolution is possible even when only a single blurred image is given. It is in principle possible to remove some of the additive noise when the form of the point-spread function is known. Fourier phase can be retrieved directly, and, unlike for readily implementable iterative techniques, complex images can be handled as straightforwardly as real images.

© 1987 Optical Society of America

**History**

Original Manuscript: May 1, 1986

Manuscript Accepted: August 20, 1986

Published: January 1, 1987

**Citation**

R. G. Lane and R. H. T. Bates, "Automatic multidimensional deconvolution," J. Opt. Soc. Am. A **4**, 180-188 (1987)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-4-1-180

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### References

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