I need to perform tomographic reconstruction of a gas jet. The jet assumed to have a circular symmetry so only a single projection (in one angle) of the jet was taken for each height along the jet. When I made the reconstruction using the filtered back-projection algorithm I got heavily noised reconstruction (to the point that even negative values were gotten). I found out that when there is a radial symmetry the Radon transform reduces to the Abel transform and the reconstruction should implement the Abel inversion, which is very much susceptible to noise in the projections. There are indeed multitude articles regarding methods trying to tackle the numeric difficulties that exist in the implementation of Abel inversion. The most cited ones were designed for inversion of 2D images obtained in ion/photoelectron imaging experiments and use specific properties of these type of imaging, and I'm not expert enough to know how to modify them to suite my reconstruction task (if it's  possible at all). Some of the methods use filtering and other use regularization, which is also some type of filtering. We want to avoid filtering as much as possible in order to avoid losing information.     

I therefore am looking for a robust implementation (preferably in Matlab) or a detailed algorithm (that elaborates also on issues of implementation) for Abel inversion  which minimizes noise and artifacts induced by the inversion operation and avoids filtering (as much as possible).