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The spherical X-ray transform

✍ Scribed by P. Cerejeiras; H. Schaeben; F. Sommen

Publisher
John Wiley and Sons
Year
2002
Tongue
English
Weight
134 KB
Volume
25
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

The general objective of this communication is to present the basics of mathematical texture analysis as part of integral geometry involving spherical analogues of the X‐ray and Radon transform, and in particular to clarify its relationship with mathematical tomography. Copyright Β© 2002 John Wiley & Sons, Ltd.

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## Abstract The exponential X‐ray transform arises in single photon emission computed tomography and is defined on functions on the plane by 𝒫~ΞΌ~__f__(Ο†,__x__) = ∫__f__ (__x__ + __t__Ο†)__e__^ΞΌt^ where ΞΌ is a constant. In [MMAS(10), 561–574, 1988], we derived analytical formulae for filters __K__ co