The exponential X‐ray transform arises in single photon emission computed tomography and is defined on functions on ℝn by , where μ is a constant. Approximate inversion, and inversion formulae of filtered back‐projection type are derived for this operator in all dimensions. In particular, explicit formulae are given for convolution kernels (filters) K corresponding to a general point spread function E that can be used to invert the exponential X‐ray transform via a filtered back‐projection algorithm. The results extend and refine work of Tretiak and Metz17.

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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.

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