The density reconstruction of a cylindrically symmetric object from a single radiographic view is a classic and important tomography problem. The primary tool is Abel inversion, as the attenuation of radiation through such an object is governed by the Abel transform. However, simply inverting the Abel transform has the effect of amplifying noise in the radiograph. We apply total-variation regularization to this problem. This has the result of suppressing noise, while avoiding the loss of edge information that result from other forms of regularization.