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Inversion of the exponential X-ray transform. II: Numerics

✍ Scribed by Irene A. Hazou; Donald C. Solmon

Publisher
John Wiley and Sons
Year
1990
Tongue
English
Weight
633 KB
Volume
13
Category
Article
ISSN
0170-4214

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✦ Synopsis

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 corresponding to a general point spread function E that can be used to invert the exponential X‐ray transform via a filtered backprojection algorithm. Here, we use those formulae to derive expressions suitable for numerical computation of the filters corresponding to a specific family of bandlimited point spread functions and give the results of reconstructions of a mathematical phantom using these filters. Also included is an analogue of the Shepp–Logan ellipse theorem, [IEEE Trans. Nucl. Sci. (21), 21–43, 1974], for the exponential X‐ray transform.

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