'gamma-ray densitometry (also referred to as column scanning in industrial troubleshooting applications) is a non-invasive, simple, and relatively inexpensive technique for measuring time-averaged holdup profiles in multiphase flow systems. Most often, the projection data measured in densitometry is chordal, and not radial, owing to limitations of experimentation, particularly in challenging industrial environments. However, most of the theory of design and scale-up is based on radial profiles of phase holdups and velocity. The inter-conversion of chordal profiles to radial profiles is non-trivial and often prone to error propagation, particularly when the number of projection scans is small. In this work, we propose an algorithm for estimating radial gas holdup profiles, which is not subject to error propagation since we use only the direct (forward) Abel transformation process. Details of the algorithm are discussed. As a test case, -ray densitometry experiments performed on a bubble column are presented.