ABSTRACT Compton-scattering tomography is an imaging technique that exploits the energy dependence of Compton-scattered radiation. This image reconstruction problem is characterized by measurements of path integrals over circular arcs. In the conventional x-ray transmission computed tomography (CT) problem, the path integrals are along straight lines. We show that, with a simple transformation of variables, the circular-arc problem can be expressed as the filtered-backprojection solution identical to that of the straight-line CT problem.