Fourier Inversion Of Deficient Data

Ronald N. Bracewell

doi:10.1117/12.934552

27 February 1984 Fourier Inversion Of Deficient Data

Ronald N. Bracewell

Proceedings Volume 0373, Transformations in Optical Signal Processing; (1984) https://doi.org/10.1117/12.934552
Event: Transformations in Optical Signal Processing, 1981, Seattle, United States

Abstract

Abstract. Image construction by Fourier inversion may be hindered by various deficiencies in the data. Examples of defects include data presented on a nonrectangular array of points and missing data values. Among special cases that are commonly encountered are measurements made in polar coordinates and the existence of sectors where data may be entirely missing. An exact method of interpolation analogous to sincfunction interpolation in the rectangular situation is described. However, inverting such data involves not merely a problem of mathematical interpolation, but also account must be taken of the character of the object, the kind of information desired, and the penalties to be associated with errors, considerations that go beyond what is involved under conditions where the one-to-one correspondence between function and transform may be invoked and the Fourier inversion formula is applicable.

Citation Download Citation

Ronald N. Bracewell "Fourier Inversion Of Deficient Data", Proc. SPIE 0373, Transformations in Optical Signal Processing, (27 February 1984); https://doi.org/10.1117/12.934552

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