Sparse recovery in Wigner-D basis expansion

Arya Bangun; Arash Behboodi; Rudolf Mathar

doi:10.1109/globalsip.2016.7905849

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arXiv · 1609.01104

Sparse recovery in Wigner-D basis expansion

Arya Bangun·Arash Behboodi·Rudolf Mathar

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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.

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Arya Bangun, Arash Behboodi, Rudolf Mathar. 2016-09-05. Sparse recovery in Wigner-D basis expansion. https://doi.org/10.1109/globalsip.2016.7905849

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