The identification problem for the exponential Radon transform

摘要

AbstractThe exponential Radon transform, which arises in single photon emission computed tomography, is defined by ℛ ƒ(μ:ω,s) = ∫Rƒ(sω +tomega;⟂) eμtdtƒ. 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 computin