Sparse recovery in Wigner-D basis expansion

Abstract

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.

10 pages,3 figures, Accepted to IEEE GlobalSIP 2016

Cited by in corpus (1)

• Optimizing Sensing Matrices for Spherical Near-Field Antenna Measurements