A simplified expression for the Radon transform of Bessel basis functions in tomography
- 1 March 1991
- journal article
- Published by AIP Publishing in Review of Scientific Instruments
- Vol. 62 (3) , 842-843
- https://doi.org/10.1063/1.1142047
Abstract
A simplified formula for the Radon transformation of Bessel basis functions in the method of series expansion in 2-D tomography has been derived. The result is p1 Jm (xmlr) Tm(p/r)r dr√r2−p2<frx =−J′m(xml) 0 cos−1 p dθ cos(mθ) sin[xml( cos θ−p)]. A numerical comparison demonstrates at least an order of magnitude CPU time reduction using the simplified version because the integrand is written in terms of simple sinusoidal functions with no singularities.Keywords
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