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The exponential Radon transform, which arises in single photon emission computed tomography, is defined by ℛ ƒ(μ:ω,s) = ∫Rƒ(sω + tomega;⟂) eμt dtƒ. Here ƒ is a compactly supported distribution in the plane which represents the location and intensity of a radio‐pharmaceutical in a body of constant, but unknown, attenuation μ, and ω is a direction. The identification problem is to determine the attenuation μ from the data ℛƒ with ƒ unknown. We will show that μ can be determined from the data if and only if ƒ is not a radial distribution and give formulae for computing μ when ƒ is not radial.

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.