The velocity and remaining ablator mass of an imploding capsule are critical metrics for assessing the progress towards ignition of an inertially confined fusion experiment. These and other convergent ablator performance parameters have been measured using a single streaked x-ray radiograph. Traditional Abel inversion of such a radiograph is ill-posed since backlighter intensity profiles and x-ray attenuation by the ablated plasma are unknown. To address this we have developed a regularization technique which allows the ablator density profile, ρ(r) and effective backlighter profile, I 0 (y), at each time step to be uniquely determined subject to the constraints that ρ(r) is localized in radius space and I 0 (y) is delocalized in object space. Moments of ρ(r) then provide the time-resolved areal density, mass, and average radius (and thus velocity) of the remaining ablator material. These results are combined in the spherical rocket model to determine the ablation pressure and mass ablation rate during the implosion. The technique has been validated on simulated radiographs of implosions at the National Ignition Facility [G. H. Miller et al., Nucl. Fusion 44, 228 (2004)] and implemented on experiments at the OMEGA laser facility [T. R. Boehly et al., Opt. Comm., 133, 495 (1997)].