INVERSION OF THE EXPONENTIAL X-RAY TRANSFORM .2. NUMERICS

The exponential X‐ray transform arises in single photon emission computed tomography and is defined on functions on the plane by 𝒫μf(φ,x) = ∫ − ∞∞f (x + tφ)eμt where μ 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. Copyright © 1990 John Wiley & Sons, Ltd