A current problem Diffusion MRI (dMRI) based microscopy faces under the narrow pulse approximation is how to best exploit the 4D (q-space + diffusion time) nature of the signal. Assaf et al. showed that exploring the dMRI attenuation at different diffusion times provides information on the apparent distribution of axonal diameters within a voxel in their seminal work: AxCaliber1. However, AxCaliber requires knowing beforehand the predominant orientation of the axons within the analyzed volume to adjust the q-space sampling accordingly. In this work, we show that our novel sparse representation of the 3D+t dMRI signal2 enables the recovery of axonal diameter distribution parameters with two main advantages. First, it doesn't require knowledge of the predominant axonal direction at acquisition time. Second, using the hypothesised dMRI signal symmetry, it allows computing the average attenuation on the plane perpendicular to the predominant axonal direction analytically. Hence, it takes advantage of the full 3D+t signal information to fit the AxCaliber model.