Axon Diameter Distributions (ADDs) change during brain development and are altered in several brain pathologies. Mapping ADDs non-invasively using dMRI could provide a useful biomarker, but existing methods are either parametric, orientation dependent, surmmarize the whole ADD as a single measure or use non-standard protocols. We propose to estimate the ADD from an orientation-invariant PGSE protocol optimized for axon diameter sensitivity, using a discrete linear model with smoothness and sparsity regularization. To our knowledge, we are the first to report orientationally invarant ADD estimates from dMRI data.