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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 15, Iss. 5 — May. 1, 1998
  • pp: 1355–1360

Bounds on null functions of linear digital imaging systems

Eric Clarkson and Harrison Barrett  »View Author Affiliations


JOSA A, Vol. 15, Issue 5, pp. 1355-1360 (1998)
http://dx.doi.org/10.1364/JOSAA.15.001355


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Abstract

Any linear digital imaging system produces a finite amount of data from a continuous object. This means that there are always null functions, so a reconstruction of the object, even without noise in the system, will differ from the actual object. With positivity constraints, the size of a null function is limited, provided that size is measured by the integral of the absolute value of the null function. When smoothing is used in reconstruction, then smoothed null functions become relevant. There are bounds on various measures of the size of smoothed null functions, and these bounds can be quite small. Smoothing will decrease the effects of null functions in object reconstructions, and this effect is greater if the smoothing operator is well matched to the system operator.

© 1998 Optical Society of America

OCIS Codes
(100.2000) Image processing : Digital image processing
(110.0110) Imaging systems : Imaging systems

History
Original Manuscript: August 7, 1997
Revised Manuscript: December 24, 1997
Manuscript Accepted: December 11, 1997
Published: May 1, 1998

Citation
Eric Clarkson and Harrison Barrett, "Bounds on null functions of linear digital imaging systems," J. Opt. Soc. Am. A 15, 1355-1360 (1998)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-15-5-1355


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