  We are concerned with the recovery of $s-$sparse Wigner-D expansions in terms
of $N$ Wigner-D functions. Considered as a generalization of spherical
harmonics, Wigner-D functions are eigenfunctions of Laplace-Beltrami operator
and form an orthonormal system. However, since they are not uniformly bounded,
the existing results on BOS do not apply. Using previously introduced
preconditioning technique, a new orthonormal and bounded system is obtained for
which RIP property can be established. We show that the number of sufficient
samples for sparse recovery scales with ${N}^{1/6} \,s\, \log^3(s) \,\log(N)$.
The phase transition diagram for this problem is also presented. We will also
discuss the application of our results in the spherical near-field antenna
measurement.
