# Sampling Sparse Signals on the Sphere: Algorithms and Applications

### Citation:

I. Dokmanic and Y. M. Lu, “Sampling Sparse Signals on the Sphere: Algorithms and Applications,” IEEE Transactions on Signal Processing, vol. 64, no. 1, pp. 189-202, 2016.

2015

### Abstract:

We propose a sampling scheme that can perfectly reconstruct a collection of
spikes on the sphere from samples of their lowpass-filtered observations.
Central to our algorithm is a generalization of the annihilating filter
method, a tool widely used in array signal processing and finite-rate-of-innovation
(FRI) sampling. The proposed algorithm can reconstruct $K$ spikes
from $(K+\sqrt{K})^2$ spatial samples---a sampling requirement that
improves over known sparse sampling schemes on the sphere by a factor of up
to four.

We showcase the versatility of the proposed algorithm by applying it to
three different problems: 1) sampling diffusion processes induced by
localized sources on the sphere, 2) shot-noise removal, and 3) sound source
localization (SSL) by a spherical microphone array. In particular, we show
how SSL can be reformulated as a spherical sparse sampling problem.

arXiv:1502.07577

Last updated on 05/02/2018