  We consider the deconvolution problem for densities supported on a
$(d-1)$-dimensional sphere with unknown center and unknown radius, in the
situation where the distribution of the noise is unknown and without any other
observations. We propose estimators of the radius, of the center, and of the
density of the signal on the sphere that are proved consistent without further
information. The estimator of the radius is proved to have almost parametric
convergence rate for any dimension $d$. When $d=2$, the estimator of the
density is proved to achieve the same rate of convergence over Sobolev
regularity classes of densities as when the noise distribution is known.
