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Xu, Y.* ; Tischenko, O. ; Hoeschen, C.

Approximation and Reconstruction from Attenuated Radon Projections.

SIAM J. Numer. Anal. 45, 108-132 (2007)
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Attenuated Radon projections with respect to the weight function $W_\mu(x,y) = (1-x^2-y^2)^{\mu-1/2}$ are shown to be closely related to the orthogonal expansion in two variables with respect to $W_\mu$. This leads to an algorithm for reconstructing two-dimensional functions (images) from attenuated Radon projections. Similar results are established for reconstructing functions on the sphere from projections described by integrals over circles on the sphere, and for reconstructing functions on the three-dimensional ball and cylinder domains.
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Publikationstyp Artikel: Journalartikel
Dokumenttyp Wissenschaftlicher Artikel
Schlagwörter approximation; reconstruction of images; Radon projections; polynomials of several variables; algorithms
ISSN (print) / ISBN 0036-1429
e-ISSN 1095-7170
Quellenangaben Band: 45, Heft: , Seiten: 108-132 Artikelnummer: , Supplement: ,
Verlag Society for Industrial and Applied Mathematics (SIAM)