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An explicit closed‐form solution to the limited‐angle discrete tomography problem for finite‐support objects
Author(s) -
Yagle Andrew E.
Publication year - 1998
Publication title -
international journal of imaging systems and technology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.359
H-Index - 47
eISSN - 1098-1098
pISSN - 0899-9457
DOI - 10.1002/(sici)1098-1098(1998)9:2/3<174::aid-ima14>3.0.co;2-x
Subject(s) - mathematics , integer (computer science) , range (aeronautics) , finite set , measure (data warehouse) , sample (material) , algorithm , fourier transform , mathematical analysis , mathematical optimization , computer science , physics , materials science , database , composite material , thermodynamics , programming language
An explicit formula is presented for reconstructing a finite‐support object defined on a lattice of points and taking on integer values from a finite number of its discrete projections over a limited range of angles. Extensive use is made of the discrete Fourier transform in doing so. The approach in this article computes the object sample values directly as a linear combination of the projections sample values. The well‐known ill‐posedness of the limited angle tomography problem manifests itself in some very large coefficients in these linear combinations; these coefficients (which are computed off‐line) provide a direct sensitivity measure of the reconstruction samples to the projections samples. The discrete nature of the problem implies that the projections must also take on integer values; this means noise can be rejected. This makes the formula practical. © 1998 John Wiley & Sons, Inc. Int J Imaging Syst Technol, 9, 174–180, 1998