Sparse recovery in Wigner-D basis expansion

Authors

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 eigen- functions of Laplace-Beltrami operator and form an orthonormal system. However, since they are not uniformly bounded, the existing results on Bounded Orthonormal System (BOS) do not apply. Using previously introduced preconditioning technique, a new orthonormal and bounded system is obtained for which Restricted Isometry Property (RIP) property can be established. We show that the number of sufficient samples for sparse recovery scales with N^(1/6) s log³(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.

Index Terms

Compressed sensing, Wigner-D functions, Bounded Orthonormal Systems, Spherical Harmonics

BibT_EX Reference Entry

@inproceedings{BaBeMa16,
	author = {Arya Bangun and Arash Behboodi and Rudolf Mathar},
	title = "Sparse recovery in Wigner-D basis expansion",
	pages = "5",
	booktitle = "2016 {IEEE} Global Conference on Signal and Information Processing (GlobalSIP)",
	address = {Greater Washington D.C, USA},
	doi = 10.1109/globalsip.2016.7905849,
	month = Dec,
	year = 2016,
	hsb = RWTH-2016-11780,
	}

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