A simplified expression for the Radon transform of Bessel basis functions in tomography

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.