Bounds on null functions of linear digital imaging systems

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7 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)1355-1360
Number of pages6
JournalJournal of the Optical Society of America A: Optics and Image Science, and Vision
Volume15
Issue number5
StatePublished - 1998

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Imaging systems
Noise

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Computer Vision and Pattern Recognition
  • Engineering(all)

Cite this

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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.",
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